Sunday, 30 September 2012

On This Day in Math - September 30

Big whirls have little whirls,
That feed on their velocity;
And little whirls have lesser whirls,
And so on to viscosity.

~Lewis Richardson

The 274th day of the year; 274 is a tribonacci number..The tribonacci numbers are like the Fibonacci numbers, but instead of starting with two predetermined terms, the sequence starts with three predetermined terms and each term afterwards is the sum of the preceding three terms. The first few tribonacci numbers are 0, 0, 1, 1, 2, 4, 7,


1717 Colin Maclaurin (1698–1746), age 19, was appointed to the Mathematics Chair at Marischal College, Aberdeen, Scotland. This is the youngest at which anyone has been elected chair (full professor) at a university. (Guinness) In 1725 he was made Professor at Edinburgh University on the recommendation of Newton. *VFR

1810 The University of Berlin opened. *VFR It is now called The Humboldt University of Berlin and is Berlin's oldest university. It was founded as the University of Berlin (Universität zu Berlin) by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt, whose university model has strongly influenced other European and Western universities.*Wik

1890 In his desk notes Sir George Biddell Airy writes about his disappointment on finding an error in his calculations of the moon’s motion. “ I had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.” *George Biddell Airy and Wilfrid Airy (ed.), Autobiography of Sir George Biddell Airy (1896), 350.

1893 Felix Klein visits Worlds fair in Chicago, then visits many colleges. On this day the New York Mathematical society had a special meeting to honor him. *VFR

1939 an early manned rocket-powered flight was made by German auto maker Fritz von Opel. His Sander RAK 1 was a glider powered by sixteen 50 pound thrust rockets. In it, Opel made a successful flight of 75 seconds, covering almost 2 miles near Frankfurt-am-Main, Germany. This was his final foray as a rocket pioneer, having begun by making several test runs (some in secret) of rocket propelled vehicles. He reached a speed of 238 km/h (148 mph) on the Avus track in Berlin on 23 May, 1928, with the RAK 2. Subsequently, riding the RAK 3 on rails, he pushed the world speed record up to 254 km/h (158 mph). The first glider pilot to fly under rocket power, was another German, Friedrich Staner, who flew about 3/4-mile on 11 Jun 1928.*TIS

2012 A Blue moon, Second of two full moons in a single month. August had full moons on the 2nd, and 31st. September had full moons on the 1st and 30th. After this month you have to wait until July of 2015 for the next blue moon.
(The Farmer's Almanac uses a different notation for "blue moon", the third full moon in a season of four full moons.)*Wik


1550 Michael Mästin was a German astronomer who was Kepler's teacher and who publicised the Copernican system. Perhaps his greatest achievement (other than being Kepler's teacher) is that he was the first to compute the orbit of a comet, although his method was not sound. He found, however, a sun centred orbit for the comet of 1577 which he claimed supported Copernicus's heliocentric system. He did show that the comet was further away than the moon, which contradicted the accepted teachings of Aristotle. Although clearly believing in the system as proposed by Copernicus, he taught astronomy using his own textbook which was based on Ptolemy's system. However for the more advanced lectures he adopted the heliocentric approach - Kepler credited Mästlin with introducing him to Copernican ideas while he was a student at Tübingen (1589-94).*SAU

1715 Étienne Bonnot de Condillac (30 Sep 1715; 3 Aug 1780) French philosopher, psychologist, logician, economist, and the leading advocate in France of the ideas of John Locke (1632-1704). In his works La Logique (1780) and La Langue des calculs (1798), Condillac emphasized the importance of language in logical reasoning, stressing the need for a scientifically designed language and for mathematical calculation as its basis. He combined elements of Locke's theory of knowledge with the scientific methodology of Newton; all knowledge springs from the senses and association of ideas. Condillac devoted careful attention to questions surrounding the origins and nature of language, and enhanced contemporary awareness of the importance of the use of language as a scientific instrument.*TIS

1775 Robert Adrain born. Although born in Ireland he was one of the first creative mathematicians to work in America. *VFR Adrain was appointed as a master at Princeton Academy and remained there until 1800 when the family moved to York in Pennsylvania. In York Adrain became Principal of York County Academy. When the first mathematics journal, the Mathematical Correspondent, began publishing in 1804 under the editorship of George Baron, Adrain became one of its main contributors. One year later, in 1805, he moved again this time to Reading, also in Pennsylvania, where he was appointed Principal of the Academy.
After arriving in Reading, Adrain continued to publish in the Mathematical Correspondent and, in 1807, he became editor of the journal. One has to understand that publishing a mathematics journal in the United States at this time was not an easy task since there were only two mathematicians capable of work of international standing in the whole country, namely Adrain and Nathaniel Bowditch. Despite these problems, Adrain decided to try publishing his own mathematics journal after he had edited only one volume of the Mathematical Correspondent and, in 1808, he began editing his journal the Analyst or Mathematical Museum.
With so few creative mathematicians in the United States the journal had little chance of success and indeed it ceased publication after only one year. After the journal ceased publication, Adrain was appointed professor of mathematics at Queen's College (now Rutgers University) New Brunswick where he worked from 1809 to 1813. Despite Queen's College trying its best to keep him there, Adrain moved to Columbia College in New York in 1813. He tried to restart his mathematical journal the Analyst in 1814 but only one part appeared. In 1825, while he was still on the staff at Columbia College, Adrain made another attempt at publishing a mathematical journal. Realising that the Analyst had been too high powered for the mathematicians of the United States, he published the Mathematical Diary in 1825. This was a lower level publication which continued under the editorship of James Ryan when Adrain left Columbia College in 1826. *SAU

1870 Jean-Baptiste Perrin (30 Sep 1870; 17 Apr 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids, verified Albert Einstein's explanation of this phenomenon and thereby confirmed the atomic nature of matter. Using a gamboge emulsion, Perrin was able to determine by a new method, one of the most important physical constants, Avogadro's number (the number of molecules of a substance in so many grams as indicated by the molecular weight, for example, the number of molecules in two grams of hydrogen). The value obtained corresponded, within the limits of error, to that given by the kinetic theory of gases. For this achievement he was honoured with the Nobel Prize for Physics in 1926.*TIS

1882 Hans Wilhelm Geiger  (30 Sep 1882; 24 Sep 1945) was a German physicist who introduced the Geiger counter, the first successful detector of individual alpha particles and other ionizing radiations. After earning his Ph.D. at the University of Erlangen in 1906, he collaborated at the University of Manchester with Ernest Rutherford. He used the first version of his particle counter, and other detectors, in experiments that led to the identification of the alpha particle as the nucleus of the helium atom and to Rutherford's statement (1912) that the nucleus occupies a very small volume in the atom. The Geiger-Müller counter (developed with Walther Müller) had improved durability, performance and sensitivity to detect not only alpha particles but also beta particles (electrons) and ionizing electromagnetic photons. Geiger returned to Germany in 1912 and continued to investigate cosmic rays, artificial radioactivity, and nuclear fission.*TIS

1883 Ernst David Hellinger (1883 - 1950) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. *SAU

1894 Dirk Jan Struik (30 Sept 1894 , 21 Oct 2000) Dirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician and Marxian theoretician who spent most of his life in the United States.
In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time.
Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994), Mathematics, and Marxism.
It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics.
Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.
In 1950 Stuik published his Lectures on Classical Differential Geometry.
Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.
Struik died October 21, 2000, 21 days after celebrating his 106th birthday. *Wik

1905 Sir Nevill F. Mott (30 Sep 1905; 8 Aug 1996) English physicist who shared (with P.W. Anderson and J.H. Van Vleck of the U.S.) the 1977 Nobel Prize for Physics for his independent researches on the magnetic and electrical properties of amorphous semiconductors. Whereas the electric properties of crystals are described by the Band Theory - which compares the conductivity of metals, semiconductors, and insulators - a famous exception is provided by nickel oxide. According to band theory, nickel oxide ought to be a metallic conductor but in reality is an insulator. Mott refined the theory to include electron-electron interaction and explained so-called Mott transitions, by which some metals become insulators as the electron density decreases by separating the atoms from each other in some convenient way.*TIS

1913 Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish and American mathematician born in Warsaw, Russian Empire (now in Poland) and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.
He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor was Karol Borsuk. His main interest was algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (whose names the Eilenberg–Steenrod axioms bear), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.
Eilenberg was a member of Bourbaki and with Henri Cartan, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules. Eilenberg also wrote an important book on automata theory. The X-machine, a form of automaton, was introduced by Eilenberg in 1974. *Wik

1916 Richard Kenneth Guy (born September 30, 1916, Nuneaton, Warwickshire - ) is a British mathematician, and Professor Emeritus in the Department of Mathematics at the University of Calgary.
He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory, but he has also published over 100 papers and books covering combinatorial game theory, number theory and graph theory.
He is said to have developed the partially tongue-in-cheek "Strong Law of Small Numbers," which says there are not enough small integers available for the many tasks assigned to them — thus explaining many coincidences and patterns found among numerous cultures.
Additionally, around 1959, Guy discovered a unistable polyhedron having only 19 faces; no such construct with fewer faces has yet been found. Guy also discovered the glider in Conway's Game of Life.
Guy is also a notable figure in the field of chess endgame studies. He composed around 200 studies, and was co-inventor of the Guy-Blandford-Roycroft code for classifying studies. He also served as the endgame study editor for the British Chess Magazine from 1948 to 1951.
Guy wrote four papers with Paul Erdős, giving him an Erdős number of 1. He also solved one of Erdős problems.
His son, Michael Guy, is also a computer scientist and mathematician. *Wik
1918 Leslie Fox (30 September 1918 – 1 August 1992) was a British mathematician noted for his contribution to numerical analysis. *Wik


1953 Lewis Fry Richardson, FRS (11 October 1881 - 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration.*Wik

1985 Dr. Charles Francis Richter (26 Apr 1900, 30 Sep 1985) was an American seismologist and inventor of the Richter Scale that measures earthquake intensity which he developed with his colleague, Beno Gutenberg, in the early 1930's. The scale assigns numerical ratings to the energy released by earthquakes. Richter used a seismograph (an instrument generally consisting of a constantly unwinding roll of paper, anchored to a fixed place, and a pendulum or magnet suspended with a marking device above the roll) to record actual earth motion during an earthquake. The scale takes into account the instrument's distance from the epicenter. Gutenberg suggested that the scale be logarithmic so, for example, a quake of magnitude 7 would be ten times stronger than a 6.*TIS

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Saturday, 29 September 2012

On This Day in Math - September 29

Young man, if I could remember the names of these particles, I would have been a botanist.
~Enrico Fermi

The 273rd day of the year; 273oK(to the nearest integer)is the freezing point of water, or 0oC


1801 Gauss’s Disquisitiones Arithmeticae published. It is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24. In this book Gauss brings together results in number theory obtained by mathematicians such as Fermat, Euler, Lagrange and Legendre and adds important new results of his own.
The book is divided into seven sections, which are :
Section I. Congruent Numbers in General
Section II. Congruences of the First Degree
Section III. Residues of Powers
Section IV. Congruences of the Second Degree
Section V. Forms and Indeterminate Equations of the Second Degree
Section VI. Various Applications of the Preceding Discussions
Section VII. Equations Defining Sections of a Circle.
Sections I to III are essentially a review of previous results, including Fermat's little theorem, Wilson's theorem and the existence of primitive roots. Although few of the results in these first sections are original, Gauss was the first mathematician to bring this material together and treat it in a systematic way. He was also the first mathematician to realize the importance of the property of unique factorization (sometimes called the fundamental theorem of arithmetic), which he states and proves explicitly.
From Section IV onwards, much of the work is original. Section IV itself develops a proof of quadratic reciprocity; Section V, which takes up over half of the book, is a comprehensive analysis of binary quadratic forms; and Section VI includes two different primality tests. Finally, Section VII is an analysis of cyclotomic polynomials, which concludes by giving the criteria that determine which regular polygons are constructible i.e. can be constructed with a compass and unmarked straight edge alone. *Wik

In 1988, the space shuttle Discovery blasted off from Cape Canaveral, Fla., marking America's return to manned space flight following the Challenger disaster. *TIS

1994 HotJava ---- Programmers first demonstrated the HotJava prototype to executives at Sun Microsystems Inc. A browser making use of Java technology, HotJava attempted to transfer Sun's new programming platform for use on the World Wide Web. Java is based on the concept of being truly universal, allowing an application written in the language to be used on a computer with any type of operating system or on the web, televisions or telephones.*CHM


1561 Adriaan van Roomen (29 Sept 1561 , 4 May 1615) is often known by his Latin name Adrianus Romanus. After studying at the Jesuit College in Cologne, Roomen studied medicine at Louvain. He then spent some time in Italy, particularly with Clavius in Rome in 1585.
Roomen was professor of mathematics and medicine at Louvain from 1586 to 1592, he then went to Würzburg where again he was professor of medicine. He was also "Mathematician to the Chapter" in Würzburg. From 1603 to 1610 he lived frequently in both Louvain and Würzburg. He was ordained a priest in 1604. After 1610 he tutored mathematics in Poland.
One of Roomen's most impressive results was finding π to 16 decimal places. He did this in 1593 using 230 sided polygons. Roomen's interest in π was almost certainly as a result of his friendship with Ludolph van Ceulen.
Roomen proposed a problem which involved solving an equation of degree 45. The problem was solved by Viète who realised that there was an underlying trigonometric relation. After this a friendship grew up between the two men. Viète proposed the problem of drawing a circle to touch 3 given circles to Roomen (the Apollonian Problem) and Roomen solved it using hyperbolas, publishing the result in 1596.
Roomen worked on trigonometry and the calculation of chords in a circle. In 1596 Rheticus's trigonometric tables Opus palatinum de triangulis were published, many years after Rheticus died. Roomen was critical of the accuracy of the tables and wrote to Clavius at the Collegio Romano in Rome pointing out that, to calculate tangent and secant tables correctly to ten decimal places, it was necessary to work to 20 decimal places for small values of sine, see [2]. In 1600 Roomen visited Prague where he met Kepler and told him of his worries about the methods employed in Rheticus's trigonometric tables. *SAU

1803 Jacques Charles-François Sturm (29 Sep 1803; 18 Dec 1855) French mathematician whose work resulted in Sturm's theorem, an important contribution to the theory of equations. .While a tutor of the de Broglie family in Paris (1823-24), Sturm met many of the leading French scientists and mathematicians. In 1826, with Swiss engineer Daniel Colladon, he made the first accurate determination of the velocity of sound in water. A year later wrote a prizewinning essay on compressible fluids. Since the time of René Descartes, a problem had existed of finding the number of solutions of a given second-order differential equation within a given range of the variable. Sturm provided a complete solution to the problem with his theorem which first appeared in Mémoire sur la résolution des équations numériques (1829; “Treatise on Numerical Equations”). Those principles have been applied in the development of quantum mechanics, as in the solution of the Schrödinger equation and its boundary values. *TIS Sturm is also remembered for the Sturm-Liouville problem, an eigenvalue problem in second order differential equations.*SAU

1812 Gustav Adolph Göpel (29 Sept 1812, 7 June 1847) Göpel's doctoral dissertation studied periodic continued fractions of the roots of integers and derived a representation of the numbers by quadratic forms. He wrote on Steiner's synthetic geometry and an important work, Theoriae transcendentium Abelianarum primi ordinis adumbratio levis, published after his death, continued the work of Jacobi on elliptic functions. This work was published in Crelle's Journal in 1847. *SAU

1895 Harold Hotelling​, 29 September 1895 - 26 December 1973   He originally studied journalism at the University of Washington, earning a degree in it in 1919, but eventually turned to mathematics, gaining a PhD in Mathematics from Princeton in 1924 for a dissertation dealing with topology. However, he became interested in statistics that used higher-level math, leading him to go to England in 1929 to study with Fisher.
Although Hotelling first went to Stanford University in 1931, he not many years afterwards became a Professor of Economics at Columbia University, where he helped create Columbia's Stat Dept. In 1946, Hotelling was recruited by Gertrude Cox​ to form a new Stat Dept at the University of North Carolina at Chapel Hill. He became Professor and Chairman of the Dept of Mathematical Statistics, Professor of Economics, and Associate Director of the Institute of Statistics at UNC-CH. (When Hotelling and his wife first arrived in Chapel Hill they instituted the "Hotelling Tea", where they opened their home to students and faculty for tea time once a month.)
Dr. Hotelling's major contributions to statistical theory were in multivariate analysis, with probably his most important paper his famous 1931 paper "The Generalization of Student's Ratio", now known as Hotelling's T^2, which involves a generalization of
Student's t-test for multivariate data. In 1953, Hotelling published a 30-plus-page paper on the distribution of the correlation coefficient, following up on the work of Florence Nightingale David in 1938. *David Bee

1901 Enrico Fermi (29 Sep 1901; 28 Nov 1954) Italian-American physicist who was awarded the Nobel Prize for physics in 1938 as one of the chief architects of the nuclear age. He was the last of the double-threat physicists: a genius at creating both esoteric theories and elegant experiments. In 1933, he developed the theory of beta decay, postulating that the newly-discovered neutron decaying to a proton emits an electron and a particle he called a neutrino. Developing theory to explain this decay later resulted in finding the weak interaction force. He developed the mathematical statistics required to clarify a large class of subatomic phenomena, discovered neutron-induced radioactivity, and directed the first controlled chain reaction involving nuclear fission. *TIS

1925 Paul Beattie MacCready (29 Sep 1925; 28 Aug 2007) was an American engineer who invented not only the first human-powered flying machines, but also the first solar-powered aircraft to make sustained flights. On 23 Aug 1977, the pedal-powered aircraft, the Gossamer Condor successfully flew a 1.15 mile figure-8 course to demonstrate sustained, maneuverable manpowered flight, for which he won the £50,000 ($95,000) Kremer Prize. MacCready designed the Condor with Dr. Peter Lissamen. Its frame was made of thin aluminum tubes, covered with mylar plastic supported with stainless steel wire. In 1979, the Gossamer Albatross won the second Kremer Prize for making a flight across the English Channel.*TIS

1931 James Watson Cronin (29 Sep 1931, ) American particle physicist, who shared (with Val Logsdon Fitch) the 1980 Nobel Prize for Physics for "the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons." Their experiment proved that a reaction run in reverse does not follow the path of the original reaction, which implied that time has an effect on subatomic-particle interactions. Thus the experiment demonstrated a break in particle-antiparticle symmetry for certain reactions of subatomic particles.*TIS

1935 Hillel (Harry) Fürstenberg (September 29, 1935, ..)) is an American-Israeli mathematician, a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Wolf Prize in Mathematics. He is known for his application of probability theory and ergodic theory methods to other areas of mathematics, including number theory and Lie groups. He gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers. He proved unique ergodicity of horocycle flows on a compact hyperbolic Riemann surfaces in the early 1970s. In 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem. The Fürstenberg boundary and Fürstenberg compactification of a locally symmetric space are named after him. *Wik


1939 Samuel Dickstein (May 12, 1851 – September 29, 1939) was a Polish mathematician of Jewish origin. He was one of the founders of the Jewish party "Zjednoczenie" (Unification), which advocated the assimilation of Polish Jews.
He was born in Warsaw and was killed there by a German bomb at the beginning of World War II. All the members of his family were killed during the Holocaust.
Dickstein wrote many mathematical books and founded the journal Wiadomości Mathematyczne (Mathematical News), now published by the Polish Mathematical Society. He was a bridge between the times of Cauchy and Poincaré and those of the Lwów School of Mathematics. He was also thanked by Alexander Macfarlane for contributing to the Bibliography of Quaternions (1904) published by the Quaternion Society.
He was also one of the personalities, who contributed to the foundation of the Warsaw Public Library in 1907.*Wik

1941 Friedrich Engel (26 Dec 1861, 29 Sept 1941)Engel was taught by Klein who recognized that he was the right man to assist Lie. At Klein's suggestion Engel went to work with Lie in Christiania (now Oslo) from 1884 until 1885. In 1885 Engel's Habilitation thesis was accepted by Leipzig and he became a lecturer there. The year after Engel returned to Leipzig from Christiania, Lie was appointed to succeed Klein and the collaboration of Lie and Engel continued.
In 1889 Engel was promoted to assistant professor and, ten years later he was promoted to associate professor. In 1904 he accepted the chair of mathematics at Greifswald when his friend Eduard Study resigned the chair. Engel's final post was the chair of mathematics at Giessen which he accepted in 1913 and he remained there for the rest of his life. In 1931 he retired from the university but continued to work in Giessen.
The collaboration between Engel and Lie led to Theorie der Transformationsgruppen a work on three volumes published between 1888 and 1893. This work was, "... prepared by S Lie with the cooperation of F Engel... "
In many ways it was Engel who put Lie's ideas into a coherent form and made them widely accessible. From 1922 to 1937 Engel published Lie's collected works in six volumes and prepared a seventh (which in fact was not published until 1960). Engel's efforts in producing Lie's collected works are described as, "... an exceptional service to mathematics in particular, and scholarship in general. Lie's peculiar nature made it necessary for his works to be elucidated by one who knew them intimately and thus Engel's 'Annotations' completed in scope with the text itself. "
Engel also edited Hermann Grassmann's complete works and really only after this was published did Grassmann get the fame which his work deserved. Engel collaborated with Stäckel in studying the history of non-euclidean geometry. He also wrote on continuous groups and partial differential equations, translated works of Lobachevsky from Russian to German, wrote on discrete groups, Pfaffian equations and other topics. *SAU

1955 L(ouis) L(eon) Thurstone (29 May 1887, 29 Sep 1955) was an American psychologist who improved psychometrics, the measurement of mental functions, and developed statistical techniques for multiple-factor analysis of performance on psychological tests. In high school, he published a letter in Scientific American on a problem of diversion of water from Niagara Falls; and invented a method of trisecting an angle. At university, Thurstone studied engineering. He designed a patented motion picture projector, later demonstrated in the laboratory of Thomas Edison, with whom Thurstone worked briefly as an assistant. When he began teaching engineering, Thurstone became interested in the learning process and pursued a doctorate in psychology. *TIS

2003 Ovide Arino (24 April 1947 - 29 September 2003) was a mathematician working on delay differential equations. His field of application was population dynamics. He was a quite prolific writer, publishing over 150 articles in his lifetime. He also was very active in terms of student supervision, having supervised about 60 theses in total in about 20 years. Also, he organized or coorganized many scientific events. But, most of all, he was an extremely kind human being, interested in finding the good in everyone he met. *Euromedbiomath

2010 Georges Charpak (1 August 1924 – 29 September 2010) was a French physicist who was awarded the Nobel Prize in Physics in 1992 "for his invention and development of particle detectors, in particular the multiwire proportional chamber". This was the last time a single person was awarded the physics prize. *Wik

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Friday, 28 September 2012

On This Day in Math - September 28

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.

~ Julian Lowell Coolidge

The 272nd day of the year; 272 = 24·17, and is the sum of four consecutive primes (61 + 67 + 71 + 73). 272 is also a Pronic or Heteromecic number, the product of two consecutive factors, 16x17 (which makes it twice a triangular #).


490 B.C. In one of history’s great battles, the Greeks defeated the Persians at Marathon. A Greek soldier was dispatched to notify Athens of the victory, running the entire distance and providing the name and model for the modern “marathon” race. *VFR

1695 After fitting several comets data using Newton's proposal that they followed parabolic paths, Edmund Halley was "inspired" to test his own measurements of the 1682 comet against an elliptical orbit. He writes to Newton, "I am more and more confirmed that we have seen that Comet now three times since Ye Year 1531." *David A Grier, When Computer's Were Human

1791 Captain George Vancouver observed this Wednesday morning a partial solar eclipse. He went on the name the barren rocky cluster of isles, by the name of Eclipse Islands. *NSEC
1858, Donati's comet (discovered by Giovanni Donati, 1826-1873) became the first to be photographed. It was a bright comet that developed a spectacular curved dust tail with two thin gas tails, captured by an English commercial photographer, William Usherwood, using a portrait camera at a low focal ratio. At Harvard, W.C. Bond, attempted an image on a collodion plate the following night, but the comet shows only faintly and no tail can be seen. Bond was subsequently able to evaluate the image on Usherwood's plate. The earliest celestial daguerreotypes were made in 1850-51, though after the Donati comet, no further comet photography took place until 1881, when P.J.C. Janssen and J.W. Draper took the first generally recognized photographs of a comet*TIS “William Usherwood, a commercial photographer from Dorking, Surrey took the first ever photograph of a comet when he photographed Donati’s comet from Walton Common on the 27th September 1858, beating George Bond from Harvard Observatory by a night! Unfortunately, the picture taken by Usherwood has been lost.” *Exposure web site 

1917 Richard Courant wrote to Nina Runge, his future wife, that he finally got the opportunity to talk to Ferdinand Springer about “a publishing project” and that things looked promising. This meeting led to a contract and a series of books now called the "Yellow Series". *VFR

1938 Paul Erdos boards the Queen Mary bound for the USA. Alarmed by Hitler's demands to annex the Sudatenland, Euler hurriedly left Budapest and made his way through Italy and France to London. He would pass through Ellis Island on his way to a position at Princeton's Institute for Advanced Study on October 4. * Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdos

1969 Murchison meteorite , a meteorite fell over Murchison, Australia. Only 100-kg of this meteorite have been found. Classified as a carbonaceous chondrite, type II (CM2), this meteorite is suspected to be of cometary origin due to its high water content (12%). An abundance of amino acids found within this meteorite has led to intense study by researchers as to its origins. More than 92 different amino acids have been identified within the Murchison meteorite to date. Nineteen of these are found on Earth. The remaining amino acids have no apparent terrestrial source. *TIS

2009: goes online. *Peter Krautzberger, comments

2011 President Barack Obama announced that Richard Alfred Tapia was among twelve scientists to be awarded the National Medal of Science, the top award the United States offers its researchers. Tapia is currently the Maxfield and Oshman Professor of Engineering; Associate Director of Graduate Studies, Office of Research and Graduate Studies; and Director of the Center for Excellence and Equity in Education at Rice University. He is a renowned American mathematician and champion of under-represented minorities in the sciences. *Wik


551 B.C. Birthdate of the Chinese philosopher and educator Confucius. His birthday is observed as “Teacher’s Day” in memory of his great contribution to the Chinese Nation. His most famous aphorism is: “With education there is no distinction between classes or races of men.” *VFR

1605 Ismael Boulliau (28 Sept 1605 , 25 Nov 1694) was a French clergyman and amateur mathematician who proposed an inverse square law for gravitation before Newton. Boulliau was a friend of Pascal, Mersenne and Gassendi and supported Galileo and Copernicus. He claimed that if a planetary moving force existed then it should vary inversely as the square of the distance (Kepler had claimed the first power), "As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d2. *SAU

1698 Pierre-Louis Moreau de Maupertuis (28 Sep 1698; 27 Jul 1759)French mathematician, biologist, and astronomer. In 1732 he introduced Newton's theory of gravitation to France. He was a member of an expedition to Lapland in 1736 which set out to measure the length of a degree along the meridian. Maupertuis' measurements both verified Newton's predictions that the Earth would be an oblate speroid, and they corrected earlier results of Cassini. Maupertuis published on many topics including mathematics, geography, astronomy and cosmology. In 1744 he first enunciated the Principle of Least Action and he published it in Essai de cosmologie in 1850. Maupertuis hoped that the principle might unify the laws of the universe and combined it with an attempted proof of the existence of God.*TIS

1761 François Budan de Boislaurent (28 Sept 1761, 6 Oct 1840) was a Haitian born amateur mathematician best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan is considered an amateur mathematician and he is best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan's rule was in a memoir sent to the Institute in 1803 but it was not made public until 1807 in Nouvelle méthode pour la résolution des équations numerique d'un degré quelconque. In it Budan wrote, "If an equation in x has n roots between zero and some positive number p, the transformed equation in (x - p) must have at least n fewer variations in sign than the original." *SAU (Sounds like a nice followup extension to Descartes Rule of signs in Pre-calculus classes. Mention the history, how many times do your students hear about a Haitian mathematician?)

1824 George Johnston Allman (28 September 1824 – 9 May 1904) was an Irish professor, mathematician, classical scholar, and historian of ancient Greek mathematics.*Wik

1873 Birthdate of the American geometer Julian Lowell Coolidge. (28 Sep 1873; 5 Mar 1954) After an education at Harvard (B.A. 1895), Oxford (B.Sc. 1897), Turin (with Corrado Serge) and Bonn (with Eouard Study, Ph.D. 1904), he came back to Harvard to teach until he retired in 1940. He was an enthusiastic teacher with a flair for witty remarks. [DSB 3, 399] *VFR
He published numerous works on theoretical mathematics along the lines of the Study-Segre school. He taught at Groton School, Conn. (1897-9) where one of his pupils was Franklin D Roosevelt, the future U.S. president. From 1899 he taught at Harvard University. Between 1902 and 1904, he went to Turin to study under Corrado Segre and then to Bonn where he studied under Eduard Study. His Mathematics of the Great Amateurs is perhaps his best-known work. *TIS

1881 Edward Ross studied at Edinburgh and Cambridge universities. After working with Karl Pearson in London he was appointed Professor of Mathematics at the Christian College in Madras India. Ill health forced him to retire back to Scotland. *SAU

1901 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.*Wik

1925 Martin David Kruskal (September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His single most celebrated contribution was the discovery and theory of solitons.*wik

1925 Seymour R. Cray (28 Sep 1925; 5 Oct 1996) American electronics engineer who pioneered the use of transistors in computers and later developed massive supercomputers to run business and government information networks. He was the preeminent designer of the large, high-speed computers known as supercomputers. *TIS Cray began his engineering career building cryptographic machinery for the U.S. government and went on to co-found Control Data Corporation​ (CDC) in the late 1950s. For over three decades, first with CDC then with his own companies, Cray consistently built the fastest computers in the world, leading the industry with innovative architectures and packaging and allowing the solution of hundreds of difficult scientific, engineering, and military problems. Many of Cray's supercomputers are on exhibit at The Computer Museum History Center. Cray died in an automobile accident in 1996.*CHM


1694 Gabriel Mouton was a French clergyman who worked on interpolation and on astronomy.*SAU

1869 Count Guglielmo Libri Carucci dalla Sommaja (1 Jan 1803, 28 Sept 1869) Libri's early work was on mathematical physics, particularly the theory of heat. However he made many contributions to number theory and to the theory of equations. His best work during the 1830s and 1840s was undoubtedly his work on the history of mathematics. From 1838 to 1841 he published four volumes of Histoire des sciences mathématiques en Italie, depuis la rénaissanace des lettres jusqu'à la fin du dix-septième siècle. He intended to write a further two volumes, but never finished the task. It is an important work but suffers from over-praise of Italians at the expense of others. *SAU

1953 Edwin Powell Hubble (20 Nov 1889, 28 Sep 1953)American astronomer, born in Marshfield, Mo., who is considered the founder of extragalactic astronomy and who provided the first evidence of the expansion of the universe. In 1923-5 he identified Cepheid variables in "spiral nebulae" M31 and M33 and proved conclusively that they are outside the Galaxy. His investigation of these objects, which he called extragalactic nebulae and which astronomers today call galaxies, led to his now-standard classification system of elliptical, spiral, and irregular galaxies, and to proof that they are distributed uniformly out to great distances. Hubble measured distances to galaxies and their redshifts, and in 1929 he published the velocity-distance relation which is the basis of modern cosmology.*TIS

1992 John Leech is best known for the Leech lattice which is important in the theory of finite simple groups.*SAU

2004 Jacobus Hendricus ("Jack") van Lint (1 September 1932, 28 September 2004) was a Dutch mathematician, professor at the Eindhoven University of Technology, of which he was rector magnificus from 1991 till 1996. His field of research was initially number theory, but he worked mainly in combinatorics and coding theory. Van Lint was honored with a great number of awards. He became a member of Royal Netherlands Academy of Arts and Sciences in 1972, received four honorary doctorates, was an honorary member of the Royal Netherlands Mathematics Society (Koninklijk Wiskundig Genootschap), and received a Knighthood.*Wik

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA= Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Thursday, 27 September 2012

On This Day in Math - September 27

Algebra exists only for the elucidation of geometry.
~William Edge

The 271st day of the year; 271 is a prime number and is the sum of eleven consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43).


14 A.D.: A total lunar eclipse marked the death of Augustus: "The Moon in the midst of a clear sky became suddenly eclipsed; the soldiers who were ignorant of the cause took this for an omen referring to their present adventures: to their labors they compared the eclipse of the planet, and prophesied 'that if to the distressed goodness should be restored her wonted brightness and splendor, equally successful would be the issue of their struggle.' Hence they made a loud noise, by ringing upon brazen metal, and by blowing trumpets and cornets; as she appeared brighter or darker they exulted or lamented"
- Tacitus *NASA Lunar Eclipses
1830 American Statesman Charles Sumner (1811-1874) paid little attention as an undergraduate at Harvard, but a year after graduation he became convinced that mathematics was a necessary part of a complete education. To a classmate he wrote: “Just a week ago yesterday, I commenced Walker’s Geometry, and now have got nearly half through. All those problems, theorems, etc., which were such stumbling-blocks to my Freshman-year career, unfold themselves as easily as possible now. You will sooner have thought, I suppose, that fire and water would have embraced than mathematics and myself; but, strange to tell, we are close friends now. I really get geometry with some pleasure. I usually devote four hours in the forenoon to it.” Quoted from Florian Cajori’s Mathematics in Liberal Education (1928), p. 115. *VFR (Sumner was nearly beaten to death by a South Carolina Congressional Representative after a vindictive speech attacking the Kansas-Nebraska act, and it's authors. His speech included direct insults, sexual innuendo, and made fun of South Carolina Senator Andrew Butler, one of the authors, by imitating his stroke impaired speech and mannerisms. Butler's Nephew, Preston Brooks, having decided that a duel could not take place between a gentleman (himself) and a drunk-lout(Sumner) stopped by Sumner's desk to confront him and nearly beat him to death with his cane. Sumner lost the fight, but the incident put his star on the rise in the Northern states.)

In 1831, the first annual meeting of the British Association for the Advancement of Science was held in York. The British Association had been established in the same year by Sir David Brewster, R.I. Murchison and others. One of the association's main objectives was to "promote the intercourse of those who cultivate science with each other." The second annual meeting was held at Oxford (1832), and in following years at Cambridge, Edinburgh, Dublin, Bristol, Liverpool, Newcastle, Birmingham, Glasgow, Plymouth, Manchester and Cork respectively, until returning to York in 1844. It is incorporated by Royal Charter dated 21 Apr 1928.*TIS

1892 Mykhailo Pilipovich Krawtchouk (27 Sept 1892 in Chovnitsy, (now Kivertsi) Ukraine - 9 March 1942 in Kolyma, Siberia, USSR) In 1929 Krawtchouk published his most famous work, Sur une généralisation des polynômes d'Hermite. In this paper he introduced a new system of orthogonal polynomials now known as the Krawtchouk polynomials, which are polynomials associated with the binomial distribution.
However his mathematical work was very wide and, despite his early death, he was the author of around 180 articles on mathematics. He wrote papers on differential and integral equations, studying both their theory and applications. Other areas he wrote on included algebra (where among other topics he studied the theory of permutation matrices), geometry, mathematical and numerical analysis, probability theory and mathematical statistics. He was also interested in the philosophy of mathematics, the history of mathematics and mathematical education. Krawtchouk edited the first three-volume dictionary of Ukrainian mathematical terminology. *SAU
1905 E=mc2 the day that Einstein's paper outlining the significance of the equation arrived in the offices of the German journal Annalen der Physik. "Does the inertia of a body depend on its energy content?"

1919 Einstein writes to his ailing mother that "H. A. Lorenztz has just telegraphed me that the British Expeditions have definitely confirmed the deflection of light by the sun." He adds consolation on her illness and wishes her "good days", and closes with "affectionately, Albert *Einstein Archives
In 1922, scientists at the Naval Aircraft Radio Laboratory near Washington, D.C., demonstrated that if a ship passed through a radio wave being broadcast between two stations, that ship could be detected, the essentials of radar. *TIS

1996 Kevin Mitnick, 33, was indicted on charges resulting from a 2 ½-year hacking spree. Police accused the hacker, who called himself "Condor," of stealing software worth millions of dollars from major computer corporations. The maximum possible sentence for his crimes was 200 years. *CHM Mitnick served five years in prison — four and a half years pre-trial and eight months in solitary confinement — because, according to Mitnick, law enforcement officials convinced a judge that he had the ability to "start a nuclear war by whistling into a pay phone".[11] He was released on January 21, 2000. During his supervised release, which ended on January 21, 2003, he was initially forbidden to use any communications technology other than a landline telephone. Mitnick fought this decision in court, eventually winning a ruling in his favor, allowing him to access the Internet. Under the plea deal, Mitnick was also prohibited from profiting from films or books based on his criminal activity for seven years. Mitnick now runs Mitnick Security Consulting​ LLC, a computer security consultancy. *Wik

2011 President Obama today named seven eminent researchers as recipients of the National Medal of Science and five inventors as recipients of the National Medal of Technology and Innovation, the highest honors bestowed by the United States government on scientists, engineers, and inventors. The recipients will receive their awards at a White House ceremony later this year.

This year’s recipients are listed below.
National Medal of Science
Jacqueline K. Barton
California Institute of Technology
For discovery of a new property of the DNA helix, long-range electron transfer, and for showing that electron transfer depends upon stacking of the base pairs and DNA dynamics.  Her experiments reveal a strategy for how DNA repair proteins locate DNA lesions and demonstrate a biological role for DNA-mediated charge transfer.
Ralph L. Brinster
University of Pennsylvania
For his fundamental contributions to the development and use of transgenic mice.  His research has provided experimental foundations and inspiration for progress in germline genetic modification in a range of species, which has generated a revolution in biology, medicine, and agriculture.
Shu Chien
University of California, San Diego
For pioneering work in cardiovascular physiology and bioengineering, which has had tremendous impact in the fields of microcirculation, blood rheology and mechanotransduction in human health and disease.
Rudolf Jaenisch
Whitehead Institute for Biomedical Research and Massachusetts Institute of Technology
For improving our understanding of epigenetic regulation of gene expression: the biological mechanisms that affect how genetic information is variably expressed.  His work has led to major advances in our understanding of mammalian cloning and embryonic stem cells.
Peter J. Stang
University of Utah
For his creative contributions to the development of organic supramolecular chemistry and for his outstanding and unique record of public service.
Richard A. Tapia
Rice University
For his pioneering and fundamental contributions in optimization theory and numerical analysis and for his dedication and sustained efforts in fostering diversity and excellence in mathematics and science education.
Srinivasa S.R. Varadhan
New York University
For his work in probability theory, especially his work on large deviations from expected random behavior, which has revolutionized this field of study during the second half of the twentieth century and become a cornerstone of both pure and applied probability.  The mathematical insights he developed have been applied in diverse fields including quantum field theory, population dynamics, finance, econometrics, and traffic engineering.
National Medal of Technology and Innovation
Rakesh Agrawal
Purdue University
For an extraordinary record of innovations in improving the energy efficiency and reducing the cost of gas liquefaction and separation. These innovations have had significant positive impacts on electronic device manufacturing, liquefied gas production, and the supply of industrial gases for diverse industries.
B. Jayant Baliga
North Carolina State University
For development and commercialization of the Insulated Gate Bipolar Transistor and other power semiconductor devices that are extensively used in transportation, lighting, medicine, defense, and renewable energy generation systems.
C. Donald Bateman
For developing and championing critical flight-safety sensors now used by aircraft worldwide, including ground proximity warning systems and wind-shear detection systems.
Yvonne C. Brill
RCA Astro Electronics (Retired)
For innovation in rocket propulsion systems for geosynchronous and low earth orbit communication satellites, which greatly improved the effectiveness of space propulsion systems.
Michael F. Tompsett
For pioneering work in materials and electronic technologies including the design and development of the first charge-coupled device (CCD) imagers. *The White House


1677 Johann Doppelmayr was a German mathematician who wrote on astronomy, spherical trigonometry, sundials and mathematical instruments.*SAU

1719 Abraham Kästner was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. His work on the parallel postulate influenced Bolyai and Lobachevsky*SAU

1814 Daniel Kirkwood (27 Sep 1814; 11 Jun 1895) American mathematician and astronomer who noted in about 1860 that there were several zones of low density in the minor-planet population. These gaps in the distribution of asteroid distances from the Sun are now known as Kirkwood gaps. He explained the gaps as resulting from perturbations by Jupiter. An object that revolved in one of the gaps would be disturbed regularly by the planet's gravitational pull and eventually would be moved to another orbit. Thus gaps appeared in the distribution of asteroids where the orbital period of any small body present would be a simple fraction of that of Jupiter. Kirwood showed that a similar effect accounted for gaps in Saturns rings.*TIS The asteroid 1951 AT was named 1578 Kirkwood in his honor and so was the lunar impact crater Kirkwood, as well as Indiana University's Kirkwood Observatory. He is buried in the Rose Hill Cemetery in Bloomington, Indiana, where Kirkwood Avenue is named for him. *Wik

1824 Benjamin Apthorp Gould (27 Sep 1824; 26 Nov 1896) American astronomer whose star catalogs helped fix the list of constellations of the Southern Hemisphere Gould's early work was done in Germany, observating the motion of comets and asteroids. In 1861 undertook the enormous task of preparing for publication the records of astronomical observations made at the US Naval Observatory since 1850. But Gould's greatest work was his mapping of the stars of the southern skies, begun in 1870. The four-year endeavor involved the use of the recently developed photometric method, and upon the publication of its results in 1879 it was received as a signicant contribution to science. He was highly active in securing the establishment of the National Academy of Sciences.*TIS

1843 Gaston Tarry was a French combinatorialist whose best-known work is a method for solving mazes.*SAU

1855 Paul Appell (27 September 1855 – 24 October 1930), also known as Paul Émile Appel, was a French mathematician and Rector of the University of Paris. The concept of Appell polynomials is named after him, as is rue Paul Appell in the 14th arrondissement of Paris.*Wik

1876 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California. He worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.*Wik

1879 Hans Hahn was an Austrian mathematician who is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass. *SAU

1918 Sir Martin Ryle (27 Sep 1918; 14 Oct 1984) British radio astronomer who developed revolutionary radio telescope systems and used them for accurate location of weak radio sources. Ryle helped develop radar for British defense during WW II. Afterward, he was a leader in the development of radio astronomy. With his aperture synthesis technique of interferometry he and his team located radio-emitting regions on the sun and pinpointed other radio sources so that they could be studied in visible light. Ryle's 1C - 5C Cambridge catalogues of radio sources led to the discovery of numerous radio galaxies and quasars. Using this technique, eventually radio astronomers surpassed optical astronomers in angular resolution. He observed the most distant known galaxies of the universe. For his aperture synthesis technique, Ryle shared the Nobel Prize for Physics in 1974 (with Antony Hewish), the first in recognition of astronomical research. He was the 12th Astronomer Royal (1972-82).*TIS

1919 James Hardy Wilkinson (27 September 1919 – 5 October 1986) was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.
He received the Turing Award in 1970 "for his research in numerical analysis to facilitate the use of the high-speed digital computer, having received special recognition for his work in computations in linear algebra and 'backward' error analysis." In the same year, he also gave the John von Neumann Lecture at the Society for Industrial and Applied Mathematics. The J. H. Wilkinson Prize for Numerical Software is named in his honour.*Wik


1783 Étienne Bézout was a French mathematician who is best known for his theorem on the number of solutions of polynomial equations.*SAU

1997 William Edge graduated from Cambridge and lectured at Edinburgh University. He wrote many papers in Geometry. He became President of the EMS in 1944 and an honorary member in 1983. *SAU

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA= Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Wednesday, 26 September 2012

On This Day in Math - September 26

"mathematics is not yet ready for such problems"
~Paul Erdos in reference to Collatz's problem

The 270th day of the year; the harmonic mean of the factors of 270 is an integer. The first three numbers with this property are 1, 6, and 28.. what is the next one?


1874 James Clerk Maxwell in a letter to Professor Lewis Campbell describes Galton, "Francis Galton, whose mission it seems to be to ride other men's hobbies to death, has invented the felicitous expression 'structureless germs'. " *Lewis Campbell and William Garnett (eds.), The Life of James Clerk Maxwell (1884), 299.
1991 The first two year closed mission of Biosphere 2 began just outside Tucson, Arizona. *David Dickinson ‏@Astroguyz
 2011 Astronauts had this view of the aurora on September 26, 2011. Credit: NASA

We’ve had some great views of the aurora submitted by readers this week, but this one taken from the International Space Station especially highlights the red color seen by many Earth-bound skywatchers, too. Karen Fox from the Goddard Space Flight Center says the colors of the aurora depend on which atoms are being excited by the solar storm. In most cases, the light comes when a charged particle sweeps in from the solar wind and collides with an oxygen atom in Earth’s atmosphere. This produces a green photon, so most aurora appear green. However, lower-energy oxygen collisions as well as collisions with nitrogen atoms can produce red photons — so sometimes aurora also show a red band as seen here. *Universe Today


1688 Willem 'sGravesande (26 September 1688 – 28 February 1742)was a Dutch mathematician who expounded Newton's philosophy in Europe. In 1717 he became professor in physics and astronomy in Leiden, and introduced the works of his friend Newton in the Netherlands.
His main work is Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam or Mathematical Elements of Natural Philosophy, Confirm'd by Experiments (Leiden 1720), in which he laid the foundations for teaching physics. Voltaire and Albrecht von Haller were in his audience, Frederic the Great invited him in 1737 to come to Berlin.
His chief contribution to physics involved an experiment in which brass balls were dropped with varying velocity onto a soft clay surface. His results were that a ball with twice the velocity of another would leave an indentation four times as deep, that three times the velocity yielded nine times the depth, and so on. He shared these results with Émilie du Châtelet, who subsequently corrected Newton's formula E = mv to E = mv2. (Note that though we now add a factor of 1/2 to this formula to make it work with coherent systems of units, the formula as expressed is correct if you choose units to fit it.) *Wik

1754 Joseph-Louis Proust (26 Sep 1754; 5 Jul 1826) French chemist who proved (1808) that the relative quantities of any given pure chemical compound's constituent elements remain invariant, regardless of the compound's source, and thus provided crucial evidence in support of John Dalton's “law of definite proportions,” which holds that elements in any compound are present in fixed proportion to each other. *TIS

1784 Christopher Hansteen (26 Sep 1784; 15 Apr 1873) Norwegian astronomer and physicist noted for his research in geomagnetism. In 1701 Halley had already published a map of magnetic declinations, and the subject was studied by Humboldt, de Borda, and Gay-Lussac, among others. Hansteen collected available data and also mounted an expedition to Siberia, where he took many measurements for an atlas of magnetic strength and declination.*TIS

1854 Percy Alexander MacMahon (26 Sept 1854 , 25 Dec 1929) His study of symmetric functions led MacMahon to study partitions and Latin squares, and for many years he was considered the leading worker in this area. His published values of the number of unrestricted partitions of the first 200 integers which proved extremely useful to Hardy and Littlewood in their own work on partitions. He gave a Presidential Address to the London Mathematical Society on combinatorial analysis in 1894. MacMahon wrote a two volume treatise Combinatory analysis (volume one in 1915 and the second volume in the following year) which has become a classic. He wrote An introduction to combinatory analysis in 1920. In 1921 he wrote New Mathematical Pastimes, a book on mathematical recreations. *SAU

1887 Sir Barnes (Neville) Wallis (26 Sep 1887; 30 Oct 1979) was an English aeronautical designer and military engineer whose famous 9000-lb bouncing "dambuster" bombs of WW II destroyed the German Möhne and Eder dams on 16 May 1943. He designed the R100 airship, and the Vickers Wellesley and Wellington bombers. The specially-formed RAF 617 Squadron precisely delivered his innovative cylindrical bombs which were released from low altitude, rotating backwards at high speed that caused them to skip along the surface of the water, right up to the base of the dam. He later designed the 5-ton Tallboy and 10-ton Grand Slam earthquake bombs (which used on many enemy targets in the later years of the war). Postwar, he developed ideas for swing-wing aircraft. *TIS (His courtship with his wife has been written by his daughter, Mary Stopes-Roe from the actual courtship in the entertaining, but perhaps overpriced book, Mathematics With Love: The Courtship Correspondence of Barnes Wallis, Inventor of the Bouncing Bomb.)

1891 Hans Reichenbach (September 26, 1891, April 9, 1953) was a leading philosopher of science, educator and proponent of logical empiricism. Reichenbach is best known for founding the Berlin Circle, and as the author of The Rise of Scientific Philosophy.*Wik

1924 Jean Hoerni, a pioneer of the transistor, is born in Switzerland. A physicist, Hoerni in 1959 invented the planar process, which, combined with Robert Noyce's technique for placing a layer of silicon dioxide on a transistor, led to the creation of the modern integrated circuit. Hoerni's planar process allowed the placement of complex electronic circuits on a single chip. *CHM

1926 Colin Brian Haselgrove (26 September 1926 , 27 May 1964) was an English mathematician who is best known for his disproof of the Pólya conjecture in 1958. the Pólya conjecture stated that 'most' (i.e. more than 50%) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was posited by the Hungarian mathematician George Pólya in 1919.. The size of the smallest counter-example is often used to show how a conjecture can be true for many numbers, and still be false. *Wik

1927 Brian Griffiths (26 Sept 1927 , 4 June 2008) He was deeply involved in the 'School Mathematics Project', he served as chairman of the 'Joint Mathematical Council', and chaired the steering group for the 'Low Attainers Mathematics Project' from 1983 to 1986. This project became the 'Raising Achievement in Mathematics Project' in 1986 and he chaired this from its foundation to 1989. *SAU


1766 Giulio Carlo Fagnano dei Toschi died. He is important for the identity
\pi = 2i\log{1 - i \over 1 +i}
and for his rectification of the lemmiscate. *VFR An Italian mathematician who worked in both complex numbers and on the geometry of triangles.*SAU

1802 Jurij Vega (23 Mar 1754, 26 Sept 1802) wrote about artillery but he is best remembered for his tables of logarithms and trigonometric functions. Vega calculated π to 140 places, a record which stood for over 50 years. This appears in a paper which he published in 1789.
In September 1802 Jurij Vega was reported missing. A search was unsuccessful until his body was found in the Danube near Vienna. The official cause of death was an accident but many suspect that he was murdered. *SAU

1867 James Ferguson (31 Aug 1797, 26 Sep 1867) Scottish-American astronomer who discovered the first previously unknown asteroid to be detected from North America. He recorded it on 1 Sep 1854 at the U.S. Naval Observatory, where he worked 1848-67. This was the thirty-first of the series and is now known as 31 Euphrosyne, named after one of the Charites in Greek mythology. It is one of the largest of the main belt asteroids, between Mars and Jupiter. He was involved in some of the earliest work in micrometry was done at the old U.S. Naval Observatory at Foggy Bottom in the midst of the Civil War using a 9.6 inch refractor. He also contributed to double star astronomy. Earlier in his life he was a civil engineer, member of the Northwest Boundary Survey, and an assistant in the U.S. Coast Survey *TIS

1868 August Ferdinand Mobius died. He discovered his famous strip in September 1858. Johann Benedict Listing discovered the same surface two months earlier.*VFR (It is somewhat amazing that we call it after Mobius when Listing discovered it first and published, and it seems, Mobius did not. However Mobius did seem to have thought on the four color theorem before Guthrie, or anyone else to my knowledge.)

1877 Hermann Günther Grassmann (15 Apr 1809, 26 Sep 1877) German mathematician chiefly remembered for his development of a general calculus of vectors in Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844; "The Theory of Linear Extension, a New Branch of Mathematics"). *TIS

1910 Thorvald Nicolai Thiele (24 Dec 1838, 26 Sept 1910) He is remembered for having an interpolation formula named after him, the formula being used to obtain a rational function which agrees with a given function at any number of given points. He published this in 1909 in his book which made a major contribution to numerical analysis. He introduced cumulants (under the name of "half-invariants") in 1889, 1897, 1899, about 30 years before their rediscovery and exploitation by R A Fisher. *SAU

1976 Paul (Pál) Turán (18 August 1910, 26 September 1976) was a Hungarian mathematician who worked primarily in number theory. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers. *SAU

1978 Karl Manne Georg Siegbahn (3 Dec 1886, 26 Sep 1978) Swedish physicist who was awarded the Nobel Prize for Physics in 1924 for his discoveries and investigations in X-ray spectroscopy. In 1914 he began his studies in the new science of x-ray spectroscopy which had already established from x-ray spectra that there were two distinct 'shells' of electrons within atoms, each giving rise to groups of spectral lines, labeled 'K' and 'L'. In 1916, Siegbahn discovered a third, or 'M', series. (More were to be found later in heavier elements.) Refining his x-ray equipment and technique, he was able to significantly increase the accuracy of his determinations of spectral lines. This allowed him to make corrections to Bragg's equation for x-ray diffraction to allow for the finer details of crystal diffraction. *TIS

1990 Lothar Collatz​ (July 6, 1910, , September 26, 1990) was a German mathematician. In 1937 he posed the famous Collatz conjecture, which remains unsolved. The Collatz-Wielandt formula for positive matrices important in the Perron–Frobenius theorem is named after him. *Wik The Collatz conjeture is an iteration problem that deals with the following algorithm..
If a number n is odd, then f(n)= 3n+1
if n is even, then f(n) = 1/2 (n)
Each answer then becomes the new value to input into the function. The problem, or should I say problems, resolve around what happens to the sequence of outcomes when we keep putting the answer back into the function. For example if we begin with 15 we get the following sequence, also called the orbit of the number:
15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1...
One of the unproven conjectures is that for any number n, the sequence will always end in the number 1. This has been shown to be true for all numbers up to just beyond 1016. A second interesting question is how long it takes for a number to return to the value of 1. For the example above, the number 15 took 17 steps to get back to the unit value. Questions such as which three (or other n) digit number has the longest orbit. There are many vairations of the problem, but if you are interested in a good introduction, check this link from Simon Fraser University"
Collatz's Problem is often also called the Syracuse Algorithm, Hasse's problem, Thwaite's problem, and Ulam's problem after people who have worked and written on the problem. It is unclear where the problem originated, as it seems to have had a long history of being passed by word of mouth before it was ever written down. It is often attributed to Lothar Collatz from the University of Hamburg who wrote about the problem as early as 1932. The name "Syracuse Problem" was applied by after H. Hasse, an associate of Collatz, visited and discussed the problem at Syracuse University in the 1950's. During the 1960's Stan Ulam circulated the problem at Los Alamos laboratory. One famous quote about the problem is from Paul Erdos who stated, "mathematics is not yet ready for such problems". *Personal notes

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA= Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Tuesday, 25 September 2012

On This Day in Math - September 25

I am undecided wheter or not the Milky Way​ is but one of countless others all of which form an entire system. Perhaps the light from these infinitely distant galaxies is so faint that we cannot see them.

~ Johann H Lambert

This is the 269th day of the year, the date is written 26/9 in much of Europe. This is the only day of the year which presents itself in this way. (Are there any days that work using month/day?) 269 is prime and is a regular prime, an Eisenstein prime with no imaginary part, a long prime, a Chen prime, a Pillai prime, a Pythagorean prime, a twin prime, a sexy prime, a Higgs prime, a strong prime, and a highly cototient number. So many new terms to look up... Well? Look them up.


1493 Columbus set sail on his second voyage to America.
1513 Balboa discovered the Pacific.

1608 The oldest written mention of the telescope: In a letter of introduction from the Council of Zeeland to Zeeland’s Delegates to the States General (the Netherlands parliament) in Den Haag asking them to organise an audience with Prince Maurice of Nassau for a spectacle maker from Middelburg who had invented a “…certain device by means of which all things at a very great distance can be seen as if they were nearby, by looking through glasses…”; the oldest written mention of the telescope. On an unknown day between 25th and 29th September: Hans Lipperhey (1570 – 1619) the spectacle maker from Middelburg (who was actually a German from Wesel) demonstrates his new invention at the court of Prince Maurice, where a peace conference in the Dutch-Spanish War is taking place along with the first visit to Europe of the Ambassador of Siam. Lipperhey’s demonstration is described in detail in a French flyer describing the Ambassadors visit and the news of the new invention is thus spread rapidly throughout Europe. *Renaissance Mathematicus,

1654 Fermat writes to Pascaal defending his combinatorial method that Pascal had previously regarded as incorrect.*VFR

1820 Arago announces electromagnetism ... Francois Arago announced that a copper wire between the poles of a voltaic cell, could laterally attract iron filings to itself (Ann. de Chim. et de Physique., xv. p.93). His discovery came in the same year that Oersted discovered that an electric current flowing in a wire would deflect a neighbouring compass needle. Arago in the same publication described how he had successfully succeeded in causing permanent magnetism in steel needles laid at right angles to the copper wire. Arago and André-Marie Ampère, discussed and experimented with forming the copper wire into a helix to intensify the magnetizing action. However, it was not until 1825 that the electromagnet in its familiar form was invented by William Sturgeon. *TIS

1944 Denmark issued a stamp commemorating the 300th anniversary of the birth of Ole Roemer,*VFR

1989 IBM announces plans to develop a new design for transmitting information within a computer, called Micro Channel Architecture, which it said could transfer data at 160 million bytes per second or eight times faster than the fastest speed at the time. Although IBM was hoping to make its system the industry standard, manufacturers of IBM-compatible computers largely chose other methods. *CHM


1644 Olaus Roemer, Danish astronomer, born. He was the first to measure the speed of light. *VFR (25 Sep 1644;23 Sep 1710) Astronomer who demonstrated conclusively that light travels at a finite speed. He measured the speed by precisely measuring the length of time between eclipses of Jupiter by one of its moons. This observation produces different results depending on the position of the earth in its orbit around the sun. He reasoned that meant light took longer to travel the greater distance when earth was traveling in its orbit away from Jupiter.*TIS

1819 George Salmon (25 September 1819 – 22 January 1904) made many discoveries about ruled surfaces and other surfaces. *SAU His publications in algebraic geometry were widely read in the second half of the 19th century. A Treatise on Conic Sections remained in print for over fifty years, going though five updated editions in English, and was translated into German, French and Italian. *Wik

1825 Carl Harald Cramer,(25 September 1893 ,5 October 1985) was a Swedish mathematical statisticians and is one of the prominent figures in the statistical theory. He was once described by John Kingman as "one of the giants of statistical theory". 
In number theory, Cramér's conjecture,in 1936  states that
p_{n+1}-p_n=O((\log p_n)^2),\
where pn denotes the nth prime number, O is big O notation, and "log" is the natural logarithm. Intuitively, this means the gaps between consecutive primes are always small, and it quantifies asymptotically just how small they can be. This conjecture has not been proven or disproven.

1846 Wladimir (Peter) Köppen (25 Sep 1846; 22 Jun 1940) German meteorologist and climatologist best known for his delineation and mapping of the climatic regions of the world. He played a major role in the advancement of climatology and meteorology for more than 70 years. The climate classification system he developed remains popular because it uses easily obtained data (monthly mean temperatures and precipitation) and straightforward, objective criteria. He recognized five principal climate groups: (A) Humid tropical -winterless climates; (B) Dry - evaporation constantly exceed precipitation; (C) humid mid-latitude, mild winters; (D) humid mid-latitude, severe winters; and (E) Polar - summerless climates. *TIS

1888 Stefan Mazurkiewicz (25 Sept 1888 , 19 June 1945) His main work was in topology and the theory of probability. His notion of dimension of a compact set preceded that of Menger and Urysohn by seven years. Mazurkiewicz applied topological methods to the theory of functions, obtaining powerful results. His theory gave particularly strong results when applied to the Euclidean plane, giving deep knowledge of its topological structure. *SAU


1777 Johann Heinrich Lambert (26 Aug 1728, 25 Sep 1777) Swiss-German mathematician, astronomer, physicist, and philosopher who provided the first rigorous proof that pi ( the ratio of a circle's circumference to its diameter) is irrational, meaning it cannot be expressed as the quotient of two integers. He also devised a method of measuring light intensity. *TIS In 1766 Lambert wrote Theorie der Parallellinien which was a study of the parallel postulate. By assuming that the parallel postulate was false, he managed to deduce a large number of non-euclidean results. He noticed that in this new geometry the sum of the angles of a triangle increases as its area decreases. *SAU

1852 Christoph Gudermann (March 25, 1798, September 25, 1852) was born in Vienenburg. He was the son of a school teacher and became a teacher himself after studying at the University of Göttingen, where his advisor was Karl Friedrich Gauss. He began his teaching career in Kleve and then transferred to a school in Münster.
He is most known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions, 1839–1840, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.
Gudermann originated the concept of uniform convergence, in an 1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and applied uniform convergence.
His researches into spherical geometry and special functions focused on particular cases, so that he did not receive the credit given to those who published more general works. The Gudermannian function, or hyperbolic amplitude, is named after him.Gudermann died in Münster. *Wik

1877 Urbain-Jean-Joseph Le Verrier (11 May 1811, 25 Sep 1877) French astronomer who predicted the position of a previously unknown planet, Neptune, by the disturbance it caused in the orbit of Uranus. In 1856, the German astronomer Johan G. Galle discovered Neptune after only an hour of searching, within one degree of the position that had been computed by Le Verrier, who had asked him to look for it there. In this way Le Verrier gave the most striking confirmation of the theory of gravitation propounded by Newton. Le Verrier also initiated the meteorological service for France, especially the weather warnings for seaports. *TIS (He died the day after the anniversary of the sighting of his most famous prediction. Between that moment of fame in 1846 and his death, he mistakenly attributed the variability of Mercury's orbit to another small planet he named "Vulcan". It took the theory of General Relativity to explain the variations. He was buried in Montparnasse cemetery in Paris. A large globe sits atop grave. Arago described him as, "the man who discovered a planet with the point of his pen."

1933 Paul Ehrenfest (January 18, 1880, September 25, 1933) was an Austrian and Dutch physicist and mathematician, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. *Wik

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Monday, 24 September 2012

On This Day in Math - September 24

Scipio Ferro of Bologna well-nigh thirty years ago discovered this rule and handed it on to Antonio Maria Fior of Venice, whose contest with Niccolo Tartaglia of Brescia gave Niccolo occasion to discover it. He [Tartaglia] gave it to me in response to my entreaties, though withholding the demonstration. Armed with this assistance, I sought out its demonstration in [various] forms. This was very difficult.
~Girolamo Cardano

This is the 268th day of the year, 268 is the smallest number whose product of digits is 6 times the sum of its digits. (A good classroom exploration might be to find numbers in which the product of the digits is n x the sum of the digits for various values of n.. more generally, for what percentage of numbers is the sum a factor of the product at all?)


1846 Neptune First observed… “Just after midnight on September 24th of this year, Neptune will be exactly 165 earth years older. It was on that date, back in 1846, that German Astronomer Johann Galle, assisted by graduate student Heinrich Louis d’Arrest, trained the 24 centimeter (9 inch) Fraunhofer Refractor of the Berlin Observatory on a patch of sky near the Aquarius-Capricorn border (see illustration below) and observed the small, blue disk of Neptune. On July 12th of this year, Neptune completed exactly one orbit since its discovery. One hundred and sixty five years ago a series of events played out in France, England and Germany that would culminate in a watershed moment in the history science and astronomy, a discovery that would prove to be unique and unrepeatable. These events were rife with centuries-old rivalries, political conspiracy and intrigue, all mixed together with good mathematics, some good science, some bad science, some luck and much mayhem.” more of this interesting story from Tom Madigan’s website.


1501 Girolamo Cardano (24 Sep 1501; 21 Sep 1576) Famous for his Ars magna of 1545, which contained detailed and systematics algebraic solutions to cubic and quartic equations. He was one of the most colorful figures in the whole history of mathematics, as is well illustrated in his autobiography, The Book of My Life. *VFR
Italian physician, mathematician, and astrologer who was the first to give a clinical description of typhus fever. His book, Ars magna ("Great Art," 1545) was one of the great achievements in the history of algebra, in which he published the solutions to the cubic and quartic equations. His mechanical inventions included the combination lock, the compass gimbal consisting of three concentric rings, and the universal joint to transmit rotary motion at various angles (as used in present-day vehicles). He contributed to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science and introduced the Cardan grille, a cryptographic tool (1550). *TIS

1625 Jan de Witt born. This statesman for the Netherlands wrote, before 1650, one of the first systematic developments of the analytic geometry of the straight line and conics. It was printed in Van Schooten’s second Latin edition of Descartes’ geometry (1659–1661).*VFR A nice short article about his unusual death, and life are at this blog by The Renaissance Mathematicus

1844 Max Noether born (24 September 1844 – 13 December 1921) . One of the leaders of nineteenth century algebraic geometry. Although himself a very distinguished mathematician, his daughter Emmy Noether was to bring greater innovation to mathematics than did her father. *SAU

1870 Georges Claude (24 Sep 1870; 23 May 1960) The French engineer, chemist, and inventor of the neon light, Georges Claude, was born in Paris. He invented the neon light, which was the forerunner of the fluorescent light. Claude was the first to apply an electrical discharge to a sealed tube of neon gas, around 1902 and make a neon lamp ("Neon" from Greek "neos," meaning "new gas.") He first publicly displayed the neon lamp on 11 Dec 1910 in Paris. His French company Claude Neon, introduced neon signs to the U.S. with two "Packard" signs for a Packard car dealership in Los Angeles, purchased by Earle C. Anthony for $24,000. *TIS

1891 William F. Friedman (24 Sep 1891; 12 Nov 1969) one of the world's greatest cryptologists, who helped decipher enemy codes from World War I to World War II. He was born as Wolfe Kishinev, Russia. He emigrated to the U.S. in 1893. Originally trained as an agricultural geneticist, he had become interested in cryptology. During World War I, with his wife Elizebeth, he set up a cryptology school for military personnel, which led to appointment by the U.S. as head of the Signal Intelligence Service (1930). He broke the Japanese "Purple" code (1937-40), thus allowing Americans to read much of Japan's secret messages during World War II. *TIS There is a bust of him at the National Cryptologic Museum in Fort Meade Maryland on which he is identified as the "Dean of American Cryptology". There is an interesting biography here .

1896 Tadeusz Ważewski (24 September 1896 – 5 September 1972) was a Polish mathematician.
Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. He is most famous for applying the topological concept of retract, introduced by Karol Borsuk to the study of the solutions of differential equations. *Wik
Ważewski studied at the Jagiellonian University in 1914–1920. He started from physics but very quickly turned to mathematics. Ważewski was a pupil of Zaremba.
He spent three years in Paris and got a doctoral diploma from Sorbona.
Ważewski’s research started from topology. In his doctoral dissertation he obtained interesting results on dendrites (locally connected continua not containing simple closed curves). *Ciesielski & Pogoda, EMS Newsletter December 2012

1898 Charlotte Moore Sitterly (24 Sep 1898; 3 Mar 1990) astrophysicist who organized, analyzed, and published definitive books on the solar spectrum and spectral line multiplets. From 1945 to age 90, she conducted this work at the U.S. National Bureau of Standards and the Naval Research Laboratory. She detected that technetium, an unstable element (previously known only as a result of laboratory experiments with nuclear reactions) exists in nature. She made major contributions to the compilation of tables for atomic-energy levels associated with optical spectra, which are now standard reference material. As instruments carried in space rockets provided new data in the ultraviolet, she extended these tables beyond the optical range. She was awarded the Bruce Medal in 1990.*TIS

1904 Evan T Davies graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations.*SAU

1906 Pol(idore) Swings, (24 Sep 1906; 1983) Belgian astrophysicist, made spectroscopic studies to identify elements and structure of stars and comets. He discovered the first interstellar molecule, the CH radical (1937). In comet atmospheres he studied the "Swings bands" - certain carbon emission lines. In 1941, with a slit spectrograph he identified a "Swings effect" in the violet CN bands (3875 A) - a fluorescence partly due to solar radiation that shows emmission line excitation differences dependant on the Doppler shift caused by a comet's motion relative to the Sun. He co-authored an Atlas of Cometary Spectra with Leo Haser in 1956. *TIS

1923 Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-born mathematician who made fundamental contributions to topology and differential geometry*SAU

1923 René Thom (September 2, 1923 – October 25, 2002) is known for his development of catastrophe theory, a mathematical treatment of continuous action producing a discontinuous result. *SAU

1930 John Watts Young (24 Sep 1930, ) astronaut who was the commander of the first ever Space Shuttle mission (STS-1, 12 Apr 1981), walked on the Moon during the Apollo 16 mission (21 Apr 1972), made the first manned flight of the Gemini spacecraft with Virgil Grissom. *TIS


1054 Hermann of Reichenau (1013 July 18 – 1054 September 24), was a German mathematician who important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe. Hermann introduced three important instruments into central Europe, knowledge of which came from Arabic Spain. He introduced the astrolabe, a portable sundial and a quadrant with a cursor.
His works include De Mensura Astrolabii and De Utilitatibus Astrolabii (some parts of these works may not have been written by Hermann).
Hermann's contributions to mathematics include a treatise dealing with multiplication and division, although this book is written entirely with Roman numerals. He also wrote on a complicated game based on Pythagorean number theory which was derived from Boethius. *SAU

1651 Etienne Pascal died (Clermont, May 2, 1588 - Paris, September 24, 1651). The Pascal limacon is named after him, and not after his famous son who later came blazing on the scene. *VFR Étienne is famed as the discoverer of the curve the Limaçon of Pascal. The curve, so named by Roberval, can be used to trisect an angle. He discovered the curve in around 1637. (Limacon is from the Latin word for a snail the curve is a roulette formed when a circle rolls around the outside of another circle.) In a letter (see Lettre d'Étienne Pascal et Roberval à Fermat, samedi 16 août 1636) he actively argued in favour of Fermat's De maximis et minimis in opposition to Descartes who viewed the work in a very negative light. *SAU

1938 Lew Genrichowitsch Schnirelmann (2 January(15January 1905greg.) in Gomel; 24 September 1938 in Moscaw) . He was a Belarussian mathematician who made important contributions to the Goldbach conjecture. Using these ideas of compactness of a sequence of natural numbers he was able to prove a weak form of the Goldbach conjecture showing that every number is the sum of ≤ 20 primes.*SAU

1945 Hans (Wilhelm) Geiger (30 Sep 1882, 24 Sep  1945) was a German physicist who introduced the Geiger counter, the first successful detector of individual alpha particles and other ionizing radiations. After earning his Ph.D. at the University of Erlangen in 1906, he collaborated at the University of Manchester with Ernest Rutherford. He used the first version of his particle counter, and other detectors, in experiments that led to the identification of the alpha particle as the nucleus of the helium atom and to Rutherford's statement (1912) that the nucleus occupies a very small volume in the atom. Geiger returned to Germany in 1912 and continued to investigate cosmic rays, artificial radioactivity, and nuclear fission. *TIS
1999 Anneli Cahn Lax (23 Feb 1922 in Katowice, Poland - 24 Sept 1999 in New York City, New York, USA) Anneli Cahn was born in Katowice, then a German city, but now part of Poland, on February 23, 1922. Her family fled Hitler’s regime in 1935 and settled in New York. She married Peter Lax, a fellow mathematician,
in 1948. Their lives together included a shared love for mathematics. Perhaps her most important contribution to mathematics was as editor of the New Mathematics Library. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt on every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. Out of this endeavor grew the New Mathematical Library. The notion was to make accessible to interested high school students, and to a more general public, deep results in mathematics
described by research mathematicians. (This sort of work had long been going on in Eastern Europe.) Lax was asked to take over as general editor for this series, and under her guidance it grew to be the foremost mathematical expository
series in the language. Upon her death it was renamed in her honor. *Mark Saul, Obituary for the AMS VOl 47,#7

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell