**Mathematics is not a careful march**

down a well-cleared highway,

but a journey into a strange wilderness,

where the explorers often get lost.

Rigour should be a signal to the historian

that the maps have been made,

and the real explorers have gone elsewhere.

down a well-cleared highway,

but a journey into a strange wilderness,

where the explorers often get lost.

Rigour should be a signal to the historian

that the maps have been made,

and the real explorers have gone elsewhere.

~W.S. Anglin

The 164th day of the year; With the ordered digits of 164 we can form 3 2-digits numbers. Those 3 numbers ± 3 are all prime (16 + 3 = 19, 16 - 3 = 13, 14 + 3 = 17, 14 - 3 = 11, 64 + 3 = 67, 64 - 3 = 61). *Prime Curios

In base 10, 164 is the smallest number that can be expressed as a concatenation of two squares in two different ways: as 1 + 64 or 16 + 4

There are 164 ways to place 5 nonattacking queens on a 5 by 8 board. */derektionary.webs.com/april-june

**EVENTS**

**1611**a publication on the newly discovered phenomenon of sunspots was dedicated.

*Narratio de maculis in sole observatis et apparente earum cum sole conversione*. ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun"). This first publication on such observations, was the work of Johannes Fabricius, a Dutch astronomer who was among the first ever to observe sunspots through a telescope. On 9 Mar 1611, at dawn, Johannes had used his telescope to view the rising sun and had seen several dark spots on it. He called his father to investigate this new phenomenon with him. The brightness of the Sun's center was very painful, and the two quickly switched to a projection method by means of a camera obscura.

**1676**Newton sent Oldenburg the “Epistola prior” for transmission to Leibniz. Among other things it contained the ﬁrst statement of the binomial theorem for negative and fractional exponents. *VFR This may be the first use of fractional and negative exponents in the modern sense (cajori, 308 pgs 370-371)

**1699**John Wallis writes a letter to the Archbishop of Canterbury suggesting that switching from the Julian to Gregorian calendar might be a mistake and expressing his fear that, "..if we go to alter that, it will be attended with a greater mischief than the present inconvenience. "

In a postscript he comments that Lock's suggestion of omitting the Feb 29 from eleven consecutive leap years would lead to ".. a confusion for four and forty years together, wherein we should agree neither with the old nor with the new account." *Philosophical Transactions, 1699 21, 343-354

In accordance with a 1750 act of Parliament, England and its colonies changed calendars in 1752. *Wik

**1771**Lagrange presented, to the Berlin Academy, the ﬁrst proof of Wilson’s theorem (n is prime iff n divides (n − 1)! + 1). Edward Waring published the theorem in 1770, but Leibniz knew it previously . *VFR

**1865**Only three months before his death, Sir William Rowan Hamilton received a letter from the American astronomer, Benjamin Gould, informing him that the newly created U.S. National Academy of Sciences had elected him ﬁrst on its list of Foreign Associates, thereby signifying that the academy considered him the greatest living scientist. [T. L. Hawkins, Hamilton, p. xv] *VFR

**1878**Arthur Cayley addresses the London Mathematical Society brings the four color theorem to a wider audience when printed in the Society’s proceedings (Dave Richeson, Euler’s Gem, pg 132)

The conjecture was first proposed in 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. At the time, Guthrie's brother, Fredrick, was a student of Augustus De Morgan at University College. Francis inquired with Fredrick regarding it, who then took it to De Morgan (Francis Guthrie graduated later in 1852, and later became a professor of mathematics in South Africa). According to De Morgan:

"A student of mine [Guthrie] asked me to day to give him a reason for a fact which I did not know was a fact — and do not yet. He says that if a figure be any how divided and the compartments differently coloured so that figures with any portion of common boundaryOthers have suggested that Mobius presented the challenge of drawing a map requiring five colors as early as 1840.lineare differently coloured — four colours may be wanted but not more — the following is his case in which four coloursarewanted. Query cannot a necessity for five or more be invented… *Wik

**1878**Thomas Craig received his Ph.D. at The Johns Hopkins University under the direction of J. J. Sylvester for a dissertation on “The representation of one surface upon another; and on some points in the theory of the curvature of surfaces.” He was one of the four to receive his degree there (the philosopher Josiah Royce was another). These were the ﬁrst Ph.D.s oﬀered by Johns Hopkins, a university founded in 1876 to advance graduate education. *VFR

**1959**France issued a stamp picturing Jean Le Rond d’Alembert.

D'ALEMBERT (1717 1783) was abandoned by his parents on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame. Foster parents were found and he was christened with the name of the saint of the church. When he became famous, his mother attempted to reclaim him, but he rejected her.

**1983**Pioneer 10, launched 3 March 1972, leaves the solar system, being the ﬁrst man-made object to do so. It has traveled over three billion miles.

**1994**Lynchburg College Professor Thomas Nicely, discovers a flaw in the Pentium chip from Intel while trying to calculate Brun's constant,(The sum of the reciprocals of all the twin primes, 1/3+1/5+1/5+1/7+1/11+1/13.... which converges to about 1.902.)

The Pentium chip occasionally gave wrong answers to a floating-point (decimal) division calculations due to errors in five entries in a lookup table on the chip. Intel spent millions of dollars replacing the faulty chips.

Nicely first noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors until October 19, 1994. On October 24, 1994 he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro. *Wik

**BIRTHS**

**Giovanni Antonio Magini**(in Latin, Maginus) (June 13, 1555; Padua, Italy – February 11, 1617; Bologna, Italy) was an Italian astronomer, astrologer, cartographer, and mathematician.

Dedicating himself to astronomy, in 1582 he wrote Ephemerides coelestium motuum, translated into Italian the following year.

In 1588 he was chosen over Galileo Galilei to occupy the chair of mathematics at the University of Bologna after the death of Egnatio Danti. He died in .

Magini supported a geocentric system of the world, in preference to Copernicus's heliocentric system. Magini devised his own planetary theory, in preference to other existing ones. The Maginian System consisted of eleven rotating spheres, which he described in his Novæ cœlestium orbium theoricæ congruentes cum observationibus N. Copernici (Venice, 1589).

In his De Planis Triangulis (1592), he described the use of quadrants in surveying and astronomy. In 1592 Magini published Tabula tetragonica, and in 1606 devised extremely accurate trigonometric tables. He also worked on the geometry of the sphere and applications of trigonometry, for which he invented calculating devices. He also worked on the problem of mirrors and published on the theory of concave spherical mirrors.

He also published a commentary on Ptolemy’s Geographia (Cologne, 1596).

As a cartographer, his life's work was the preparation of Italia or the Atlante geografico d'Italia (Geographic Atlas of Italy), printed posthumously by Magini's son in 1620. This was intended to include maps of every Italian region with exact nomenclature and historical notes. A major project, its production (begun in 1594) proved expensive and Magini assumed various additional posts in order to fund it, including becoming tutor in mathematics to the sons of Vincenzo I of Gonzaga, Duke of Mantua, a major patron of the arts and sciences. He also served as court astrologer. The Duke of Mantua, to whom the atlas is dedicated, assisted him with this project and allowed for maps of the various states of Italy to be brought to Magini. The governments of Messina and Genoa also assisted Magini financially in this project. Magini did not do any of the mapping himself.

He was also interested in pursuits which today would be considered pseudoscientific. A strong supporter of astrology, he defended its use in medicine in his De astrologica ratione (Venice, 1607). Magini collaborated closely with Valentine Naibod, and in this book he published De annui temporis mensura in Directionibus and De Directionibus from Naibod's unfinished manuscript Claudii Ptolemaei Quadripartitae Constructionis Apotelesmata Commentarius novus et Eiusdem Conversio nova. He was also interested in metoposcopy.

He corresponded with Tycho Brahe, Clavius, Abraham Ortelius, and Johann Kepler.

*Wik

**1580 Willebrord Snellius**(Willebrord Snel van Royen) (13 June 1580; Leiden, Netherlands – 30 October 1626, Leiden) was a Dutch astronomer and mathematician, known in the English-speaking world as Snell. In the west, especially the English speaking countries, his name has been attached to the law of refraction of light for several centuries, but it is now known that this law was first discovered by Ibn Sahl in 984. The same law was also investigated by Ptolemy and in the Middle Ages by Witelo, but due to lack of adequate mathematical instruments (trigonometric functions) their results were saved as tables, not functions.

Snell also improved the classical method of calculating approximate values of π by polygons which he published in Cyclometricus (1621). Using his method 96 sided polygons gives π correct to 7 places while the classical method yields only 2 places. Van Ceulen's 35 places could be found with polygons of 230 sides rather than 262. In fact Van Ceulen's 35 places of π appear in print for the first time in this book by Snell.

*Wik *SAU

**1773 Thomas Young**(13 June 1773 – 10 May 1829) was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphs (specifically the Rosetta Stone) before Jean-François Champollion eventually expanded on his work. He was admired by, among others, Herschel and Einstein.

Young made notable scientific contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony and Egyptology.*Wik .. For someone as talented as Young, he received relatively few honours. The one which pleased him most was election as a foreign member of the Institute in Paris in 1827. When Young died two years later, Arago gave the eulogy at the Institute saying:-

The death of Young in his own country attracted but little regard. *SAU

I recently learned that Young was also the first Secretary of the Board of Longitude, and also served as Superintendent of the Nautical Almanac" thanks to * Sophie Waring @atinybitwaring

**1806 George Parker Bidder**(13 June 1806 – 20 September 1878) was an English engineer and calculating prodigy. Born in the town of Moretonhampstead, Devon, England, he displayed a natural skill at calculation from an early age. In childhood, his father, William Bidder, a stonemason, exhibited him as a "calculating boy", first in local fairs up to the age of six, and later around the country. In this way his talent was turned to profitable account, but his general education was in danger of being completely neglected.

Still many of those who saw him developed an interest in his education, a notable example being Sir John Herschel. His interest led him to arrange it so George could be sent to school in Camberwell. There he did not remain long, being removed by his father, who wished to exhibit him again, but he was saved from this misfortune and enabled to attend classes at the University of Edinburgh, largely through the kindness of Sir Henry Jardine,

On leaving college in 1824 he received a post in the ordnance survey, but gradually drifted into engineering work.

Bidder died at Dartmouth, Devon and was buried at Stoke Fleming.

His son, George Parker Bidder, Jr. (1836–1896), who inherited much of his father's calculating power, was a successful parliamentary counsel and an authority on cryptography. His grandson, also named George Parker Bidder, became a marine biologist and president of the Marine Biological Association of the United Kingdom from 1939 to 1945. *Wik

**1831 James Clerk Maxwell**(13 June 1831 – 5 November 1879) Scottish physicist and mathematician. Maxwell's researches united electricity and magnetism into the concept of the electro-magnetic field. In London, around 1862, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He proposed that the phenomenon of light is therefore an electromagnetic phenomenon. The four partial differential equations, now known as Maxwell's equations, first appeared in fully developed form in Electricity and Magnetism (1873). He died relatively young; some of the theories he advanced in physics were only conclusively proved long after his death. Maxwell's ideas also paved the way for Einstein's special theory of relativity and the quantum theory. *TIS My favorite anecdote about Maxwell: It is said that on his arrival at Cambridge University he was informed that there would be a compulsory 6 a.m. church service. After a moment of thought he replie, "Aye, I suppose I could stay up that late. "

**1871 Ernst Steinitz**(13 June 1871 – 29 September 1928) In 1910 he gave a general abstract deﬁnition of a ﬁeld. He is responsible for introducing a number of concepts into the Theory of Fields, including prime subﬁelds, separable elements, and perfect ﬁelds. *VFR

**1868 Wallace Clement Ware Sabine**(June 13, 1868, Richwood, Ohio, U.S.—died Jan 10, 1919, Cambridge, Mass.) was a U.S. physicist who founded the science of architectural acoustics. After experimenting in the Fogg lecture room at Harvard, to investigate the effect of absorption on the reverberation time, on 29 of October 1898 he discovered the type of relation between these quantities. The duration T of the residual sound to decay below the audible intensity, starting from a 1,000,000 times higher initial intensity is given by: T = 0.161 V/A (V=room volume in m

^{3}, A=total absorption in m

^{2}). The first auditorium Sabine designed applying his new insight in acoustics, was the new Boston Music Hall, formally opened on 15 Oct 1900. Now known as the Symphony Hall, and still considered one of the world's three finest concert halls.*TIS

1872 Jessie Chrystal MacMillan (13 June 1872 in Edinburgh, Scotland - 21 September 1937 in Edinburgh, Scotland) was the first female science graduate at Edinburgh University and the first female honours graduate in Mathematics. She went on to study at Berlin. She was the first woman to plead a case before the House of Lords. She became active in the Women's Suffrage Movement and went on to become a lawyer.

A Millennial plaque is at Kings Buildings (West Mains Road), in Edinburgh. It reads:

In honour of*SAU

JESSIE CHRYSTAL MACMILLAN

1872-1937

Suffragist, founder of Women's International League for Peace and Freedom,

first woman science graduate of the University (1896).

**1876 William S. Gosset**(June 13, 1876–October 16, 1937) This brew-master/statistician published under the name “student.”. He developed the "small sample" or t-test for statistical testing. Among many things of interest is a remark in Section 1 in the Comment by Persi Diaconis and Erich Lehmann indicating that Laplace was on the verge of first finding the t pdf but 'fell for the easy normal approximation' (quotation and discussion from the 1998 book A History of Mathematical Statistics From 1750 to 1930 by Anders Hald)

**1876 William Sealy Gosset**(13 June 1876; Canterbury, England- 16 October 1937 in Beaconsfield, England)

Gosset was the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset who came from Watlington in Oxfordshire. William was educated at Winchester, where his favourite hobby was shooting, then entered New College Oxford where he studied chemistry and mathematics. While there he studied under Airy. He obtained a First Class degree in both subjects, being awarded his mathematics degree in 1897 and his chemistry degree two years later.

Gosset obtained a post as a chemist with Arthur Guinness Son and Company in 1899. Working in the Guinness brewery in Dublin he did important work on statistics. In 1905 he contacted Karl Pearson and arranged to go to London to study at Pearson's laboratory, the Galton Eugenics Laboratory, at University College in session 1906-07. At this time he worked on the Poisson limit to the binomial and the sampling distribution of the mean, standard deviation, and correlation coefficient. He later published three important papers on the work he had undertaken during this year working in Pearson's laboratory.

Many people are familiar with the name "Student" but not with the name Gosset. In fact Gosset wrote under the name "Student" which explains why his name may be less well known than his important results in statistics. He invented the t-test to handle small samples for quality control in brewing. Gosset discovered the form of the t distribution by a combination of mathematical and empirical work with random numbers, an early application of the Monte-Carlo method.

McMullen says:-

To many in the statistical world "Student" was regarded as a statistical advisor to Guinness's brewery, to others he appeared to be a brewer devoting his spare time to statistics. ... though there is some truth in both these ideas they miss the central point, which was the intimate connection between his statistical research and the practical problems on which he was engaged. ... "Student" did a very large quantity of ordinary routine as well as his statistical work in the brewery, and all that in addition to consultative statistical work and to preparing his various published papers.

From 1922 he acquired a statistical assistant at the brewery, and he slowly built up a small statistics department which he ran until 1934.

Gosset certainly did not work in isolation. He corresponded with a large number of statisticians and he often visited his father in Watlington in England and on these occasions he would visit University College, London, and the Rothamsted Agricultural Experiment Station. He would discuss statistical problems with Fisher, Neyman and Pearson. *SAU

**1911 Luis Walter Alvarez**(June 13, 1911 – September 1, 1988) was an American experimental physicist, inventor, and professor who was awarded the Nobel Prize in Physics in 1968. The American Journal of Physics commented, "Luis Alvarez was one of the most brilliant and productive experimental physicists of the twentieth century.

In 1940 Alvarez joined the MIT Radiation Laboratory, where he contributed to a number of World War II radar projects, from early improvements to Identification Friend or Foe (IFF) radar beacons, now called transponders, to a system known as VIXEN for preventing enemy submarines from realizing that they had been found by the new airborne microwave radars. The radar system for which Alvarez is best known and which has played a major role in aviation, most particularly in the post war Berlin airlift, was Ground Controlled Approach (GCA). Alvarez spent a few months at the University of Chicago working on nuclear reactors for Enrico Fermi before coming to Los Alamos to work for Robert Oppenheimer on the Manhattan project. Alvarez worked on the design of explosive lenses, and the development of exploding-bridgewire detonators. As a member of Project Alberta, he observed the Trinity nuclear test from a B-29 Superfortress, and later the bombing of Hiroshima from the B-29 The Great Artiste.

After the war Alvarez was involved in the design of a liquid hydrogen bubble chamber that allowed his team to take millions of photographs of particle interactions, develop complex computer systems to measure and analyze these interactions, and discover entire families of new particles and resonance states. This work resulted in his being awarded the Nobel Prize in 1968. He was involved in a project to x-ray the Egyptian pyramids to search for unknown chambers. With his son, geologist Walter Alvarez, he developed the Alvarez hypothesis which proposes that the extinction event that wiped out the dinosaurs was the result of an asteroid impact. *Wik

**1906**

**Bruno de Finetti**(13 June 1906 - 20 July 1985) De Finetti was born in Innsbruck, Austria, and was a big contributor to subjective/personal probability and Bayesian inference along with L.J. ("Jimmie") Savage (1917-1971), both of whom are discussed briefly in Chapter 13 ("The Bayesian Heresy") of David Salsburg's book The Lady Tasting Tea and in Salsburg's concluding Chapter 29.*David Bee

**1928 John Forbes Nash**, Jr ( June 13, 1928-May 23, 2015) is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Serving as a Senior Research Mathematician at Princeton University during the later part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.

Nash is the subject of the Hollywood movie

*A Beautiful Mind*. The film, loosely based on the biography of the same name, focuses on Nash's mathematical genius and struggle with paranoid schizophrenia*Wik

**1966 Grigori Yakovlevich Perelman**(13 June 1966, - ) is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.

In 1994, Perelman proved the soul conjecture. In 2003, he proved Thurston's geometrization conjecture. This consequently solved in the affirmative the Poincaré conjecture, posed in 1904, which before its solution was viewed as one of the most important and difficult open problems in topology.

In August 2006, Perelman was awarded the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow." Perelman declined to accept the award or to appear at the congress, stating: "I'm not interested in money or fame, I don't want to be on display like an animal in a zoo." On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics.

On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. *Wik

**DEATHS**

**1916 Silvanus P. Thomson**(19 June 1851 – 12 June 1916) In 1910 he published Calculus Made Easy, which was published anonymously until after his death in 1916. It is still in print. *VFR He was a noted physicist and engineer, and a celebrated teacher and writer on electricity and magnetism. He also wrote popular biographies of Faraday and Lord Kelvin. At his death he was professor at City and Guilds Technical College at Finsbury (London)

**1939 Hermann Wiener**(15 May 1857 in Karlsruhe, Germany-13 June 1939 in Darmstadt, Germany)

was a German mathematician who worked on the foundations of geometry*SAU

**1994 John Leslie Britton**(November 18, 1927 – June 13, 1994) was an English mathematician from Yorkshire who worked in combinatorial group theory and was an expert on the word problem for groups. Britton was a member of the London Mathematical Society and was Secretary of Meetings and Membership with that organization from 1973-1976. Britton died in a climbing accident on the Isle of Skye. *Wik

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*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