**Geometry is the science of**

**correct reasoning on incorrect figures.**

~George Polya

The 152nd day of the year; the eighth prime number is 19, and 8 x 19 = 152.... 152 is also the largest known even number that can be expressed as the sum of two primes in exactly four ways. (Students should find all four ways.)

**EVENTS**

**1503**Copernicus received a doctoral degree in canon law from the University of Ferrara. *VFR

**1676**Antonie van Leeuwenhoek describes the little animals he sees through a microscope. "The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite." *The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 75.

**1753**A View of the Relation between the Celebrated. Dr. Halley's Tables, and the Notions of Mr. De Buffon, for Establishing a Rule for the Probable Duration of the Life of Man; By Mr. William Kersseboom, of the Hague. Translated from the French, by James Parsons, M. D. and F. R. S. read by the Royal Society on May 31.

**1764**“I went this far with him: ‘Sir, allow me to ask you one question. If the Church should say to you, ‘two and three make ten,’ what would you do? ‘Sir,’ said he, ‘I should believe it, and I should count like this: one, two, three, four, ten.’ I was now fully satisﬁed.” From Boswell’s Journal as quoted by J. Gallian, Contemporary Abstract Algebra, p. 43. *VFR (

*Now you know, It was Boswell who invented Base Five...*)

**1790**US Copyright law passed. *VFR

**1796**Gauss records in his diary a prime number theorem conjecture. Clifford Pickover, in “The Math Book”, points out that 1796 was “an auspicious year for Gauss, when his ideas gushed like a fountain from a fire hose.” In addition to the construction of the 17-gon in March, and the prime number theorem conjecture, he proved that every positive number could be expressed as the sum of (at most) three triangular numbers in July, and another about solutions of polynomials in October.

On May 31 he conjectured that π(n), the number of primes less than n is approximated (for large n) by the area under the logarithmic integral (from 2 to n I assume).

Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in the same year that π(x) is approximated by the function x/(ln(x)-1.08),. Gauss considered the same question and he came up with his own approximating function, the logarithmic integral li(x), although he did not publish his results. Both Legendre's and Gauss' formulas imply the same conjectured asymptotic equivalence of π(x) = x / ln(x), although Gauss' approximation is closer in terms of the differences instead of quotients.

Most teachers tell the story of Gauss as a nine-year old summing the digits from 1 to 100 in his head. Here is another nice Gauss anecdote about his ability to do mental calculations: Once, when asked how he had been able to predict the trajectory of Ceres with such accuracy he replied, "I used logarithms." The questioner then wanted to know how he had been able to look up so many numbers from the tables so quickly. "Look them up?" Gauss responded. "Who needs to look them up? I just calculate them in my head!"

**1813**Louis Poinsot elected to the mathematics section of of the French Acad´emie des Sciences, replacing Lagrange. [DSB 11, 61] *VFR Although little known today, he was a French mathematician and physicist. Poinsot was the inventor of geometrical mechanics, showing how a system of forces acting on a rigid body could be resolved into a single force and a couple. When Gustave Eiffel built the famous tower, he included the names of 72 prominent French scientists on plaques around the first stage, Poinsot included.*Wik

**1823**In a letter to a cousin, William Rowan Hamilton disclosed that he had made a “very curious discovery.” It is believed that he was referring to the characteristic function. [Thanks to Howard Eves] *VFR

1868 During the eclipse of 18 August 1868 from the Red Sea through India to Malaysia and New

Guinea, prominences are first studied with spectroscopes and shown to be composed primarily of hydrogen by James Francis Tennant, John Herschel, George Rayet, Norman Pogson

and others. *NSEC

**1975**“I had today my virginal experience with the HP [Hewlett-Packard 65 calculator] as a celestial triangle-breaker ... it worked! But I’ll keep plotting the sun to make sure.” William F. Buckley Jr. discussing celestial navigation in his delightful book, Airborn, a Sentimental Journey, about sailing. His caution was justified, for later he learned that the prepackaged program contained errors. *VFR

**1985**Marion Tinsley retains the world checker championship by defeating Asa Long 6–1. The one game Long won was the ﬁrst time in nearly 25 years that anyone has beaten Tinsley in a checkers game. But then perhaps Tinsley had an unfair advantage—a Ph.D. in mathematics from Ohio State with a dissertation in combinatorics directed by Herbert Ryser. [Clipping of June 2, 1985] *VFR

He is considered the greatest checkers player who ever lived. He was world champion from 1955–1958 and 1975–1991. Tinsley never lost a World Championship match, and lost only seven games (two of them to the Chinook computer program) in his entire 45 year career.[1] He withdrew from championship play during the years 1958–1975, relinquishing the title during that time. (anyone know why?) Tinsley retired from championship play in 1991. In August 1992, he defeated the Chinook computer program 4–2 (with 33 draws) in a match. Chinook had placed second at the U.S. Nationals in 1990, which usually qualifies one to compete for a national title. However, the American Checkers Federation and the English Draughts Association refused to allow a computer to play for the title. Unable to appeal their decision, Tinsley resigned his title as World Champion and immediately indicated his desire to play against Chinook. The unofficial yet highly publicized match was quickly organized, and was won by Tinsley.

In one game, Chinook, playing with white pieces, made a mistake on the tenth move. Tinsley remarked, "You're going to regret that." Chinook resigned after move 36, fully 26 moves later.[2] The ACF and the EDA were placed in the awkward position of naming a new world champion, a title which would be worthless as long as Tinsley was alive. They granted Tinsley the title of World Champion Emeritus as a solution.

In August 1994, a second match with Chinook was organized, but Tinsley withdrew after only six games (all draws) for health reasons. Don Lafferty, rated the number two player in the world at the time, replaced Tinsley and fought Chinook to a draw. Tinsley was diagnosed with pancreatic cancer a week later. Seven months later, he died. *Wik

**BIRTHS**

1912 Martin Schwarzschild (31 May 1912; 10 Apr 1997 at age 84) German-born American astronomer who in 1957 introduced the use of high-altitude hot-air balloons to carry scientific instruments and photographic equipment into the stratosphere for solar research.*TIS

**1926 John Kemeney**(May 31, 1926 – December 26, 1992) born in Budapest, Hungary. He worked on logic with Alonzo Church at Princeton, was Einstein’s assistant at the IAS, developed the computer language BASIC, and served as President of Dartmouth College. To learn more about him, see the interview in Mathematical People. Proﬁles and Interviews (1985), edited by Donald J. Albers and G. L. Alexanderson. *VFR

In his 66-year life, Kemeny had a significant impact on the history of computers, particularly during his years at Dartmouth College, where he worked with Thomas Kurtz to create BASIC, an easy-to-use programming language for his computer students. Kemeny earlier had worked with John von Neumann in Los Alamos, N.M., during the Manhattan Project years of World War II. *CHM

1930 Ronald Valentine Toomer (31 May 1930; 26 Sep 2011 at age 81) was an American engineer who was a legendary creator of steel roller coasters. His early career, was in the aerospace industry, where he helped design the heat shield for Apollo spacecraft and was also involved with NASA's first satellite launches. In 1965, he joined the Arrow Development Company to apply tubular steel technology to the design the Runaway Mine Ride, the world's first all-steel roller coaster. It opened the following year at Six Flags over Texas. By 1975, he designed the Roaring 20's Corkscrew for Knott's Berry Farm, introducing first 360° looping rolls, in fact two of them. Later, his design included seven inversions in the Shockwave roller coaster for Six Flags Great America. He produced over 80 roller coasters before retiring.in 1998. *TIS

1931 John Robert Schrieffer (31 May 1931; Oak Park, Illinois,USA- )John Robert Schrieffer is an American physicist who shared (with John Bardeen and Leon N. Cooper) the 1972 Nobel Prize for Physics for developing the BCS theory (for their initials), the first successful microscopic theory of superconductivity. Although first described by Kamerlingh Onnes (1911), no theoretical explanation had been accepted. It explains how certain metals and alloys lose all resistance to electrical current at extremely low temperatures. The insight of the BCS theory is that at very low temperatures, under certain conditions, electrons can form bound pairs (Cooper pairs). This pair of electrons acts as a single particle in superconductivity. Schrieffer continued to focus his research on particle physics, metal impurities, spin fluctuations, and chemisorption. *TIS

**DEATHS**

**1832 Evariste Galois**(25 October 1811 – 31 May 1832) died of peritonitis from a gunshot wound of the previous day. He died in the Cochin Hospital – this is now at 27 Rue du Faubourg St. Jacques,in the 14th district of Paris. He was buried in a common grave at Montparnasse Cemetery, but no trace of the grave remains.

**1841 George Green**(14 July 1793 – 31 May 1841) British mathematical physicist who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Green, 1828).[1] The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions. George Green was the first person to create a mathematical theory of electricity and magnetism and his theory formed the foundation for the work of other scientists such as James Clerk Maxwell, William Thomson, and others. His work ran parallel to that of the great mathematician Gauss (potential theory).

Green's life story is remarkable in that he was almost entirely self-taught. He was born and lived for most of his life in the English town of Sneinton, Nottinghamshire, nowadays part of the city of Nottingham. His father (also named George) was a baker who had built and owned a brick windmill used to grind grain. The younger Green only had about one year of formal schooling as a child, between the ages of 8 and 9.

Self taught at a reading library while working full time as the manager of the family mill, He wrote a pivotal paper in applied calculus. George Green is buried in the family grave in the north east corner of St Stephens churchyard, just across the road from Green's Mill and car park. After his death the plaque below was placed in Westminster Abbey near the memorial to Newton. There are also memorials to Faraday, and Lord Kelvin. The Green Family mill has been completely restored and is now a Science center.

1931 Eugène Maurice Pierre Cosserat (4 March 1866 in Amiens, France - 31 May 1931 in Toulouse, France) Cosserat studied the deformation of surfaces which led him to a theory of elasticity. *SAU

1986 (Leo) James Rainwater (9 Dec 1917, 31 May 1986 at age 68)was an American physicist who won a share of the Nobel Prize for Physics in 1975 for his part in determining the asymmetrical shapes of certain atomic nuclei. During WW II, Rainwater worked on the Manhattan Project to develop the atomic bomb. In 1949 he began formulating a theory that not all atomic nuclei are spherical, as was then generally believed. The theory was tested experimentally and confirmed by Danish physicists Aage N. Bohr(4th son of Niels Bohr) and Ben R. Mottelson. For their work the three scientists were awarded jointly the 1975 Nobel Prize for Physics. He also conducted valuable research on X rays and took part in Atomic Energy Commission and naval research projects. *TIS

Credits

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*SAU=St Andrews Univ. Math History

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics. Grinstein & Campbell