**Geometry is the science of**

**correct reasoning on incorrect figures.**

**The 151st Day of the Year**

151 is the larger of a pair of twin primes

The 151st day of the year; The smallest prime that begins a 3-run of sums of 5 consecutive primes: 151 + 157 + 163 + 167 + 173 = 811; and 811 + 821 + 823 + 827 + 829 = 4111; and 4111 + 4127 + 4129 + 4133 + 4139 = 20639. *Prime Curios... Can you find the smallest 4-run example?

151 is the 36th prime number, and a Palindromic Prime. Did I ever mention that palindrome is drawn almost directly from an Ancient Greek word that literally means "running back again." First used in English in 1636 in "Camdon's Remains Epitaths".

151 is also the mean (and median) of the first five three digit palindromic primes, 101, 131, 151, 181, 191

Thanks to Derek Orr, who also pointed out that any day in May (in non-leap year) 5/d is such that 5! + d = year day, so today, 5/31, is 5!+31=151.

151 is an undulating palindrome in base 3 (12121)

Thanks to Derek Orr, who also pointed out that any day in May (in non-leap year) 5/d is such that 5! + d = year day

In 1927 Babe Ruth hit 60 Home Runs, a long lasting record. He hit them in 151 games.

And from base to torch, Lady Liberty is 151 ft tall.

$151 is the largest prime amount you can make with three distinct US bank notes.

**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.

Halley made two forays into financial economics, demography, and actuarial science. The second work (1705,1717) was on compound interest. He derived formulae for approximating the annual percentage rate of interest implicit in financial transactions and annuities. His first contribution (1693) was seminal, Halley developed the first life table based on sound demographic data; and he discussed several applications of his life table, including calculations of life contingencies. Halley obtained demographic data for Breslau, a city in Silesia which is now the Polish city Wroclaw. Breslau kept detailed records of births, deaths, and the ages of people when they died. In comparison, when John Graunt (1620-1674) published his famous demographic work (1662), ages of deceased people were not recorded in London and would not be recorded until the 18th century.

**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... *)

**1780 Laplace’s **“Memoir on Probability” read to the Academy of Sciences on this date. This and his “Memoir on the Probability of events” are among the most important and the most difficult works in the early history of mathematical probability, and together they are the are the most influential 18th Century on the use of probability in inference. The History of Statistics, S. M. Stigler (A treasure of a book.)

**1790**US Copyright law passed. *VFR the first copyright law is enacted under the new United States Constitution. Modeled off Britain's Statute of Anne, the new law is relatively limited in scope, protecting books, maps, and charts for only fourteen years with a renewal period of another fourteen years.

**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 was 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

**1859**

clockworks for Elizabeth Tower Clock |

The name Big Ben is often used to describe the tower, the clock and the bell but the name was first given to the Great Bell. *parliament.uk

**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 Also known as "The King of Siam's eclipse".

**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. 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. 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

**2008**Buzz Lightyear lifts off the Earth for real. A Buzz Lightyear toy was launched aboard the space shuttle Discovery with mission STS-124 and returned on Discovery 15 months later with STS-128, the 12-inch action figure is the longest-serving toy in space. Disney Parks partnered with NASA to send Buzz Lightyear to the International Space Station and create interactive games, educational worksheets and special messages encouraging students to pursue careers in science, technology, engineering and mathematics (STEM). The action figure will go on display in the museum’s "Moving Beyond Earth" gallery in the summer. in 2012 the Toy Story character became part of the National Air and Space Museum’s popular culture collection. *http://airandspace.si.edu [I still have a Buzz Lightyear toy on my book case given to me by some students because I used to use his trademark quote in (

*my very questionable*) Latin, "ad infinitum, et ultra." ]

**2013**At a Harvard seminar on May 13, 2013, the first crack was produced in solving the twin primes conjecture. A lecturer from the University of New Hampshire, Yitang Zhang, had proved that there are infinitely many pairs of primes that differ by no ,ore than 70,000,000. It was a long way from differing by two, but it was an even greater distance from infinity. He had submitted his paper to the Annals of Mathematics in April, and they had rushed to get reviews, which turned out to be enthusiastically positive. By May 21, 2013, the paper was accepted for publication on the 1st of May 2014.

This work led to a 2013 Ostrowski Prize, a 2014 Cole Prize, a 2014 Rolf Schock Prize, and a 2014 MacArthur Fellowship. Zhang became a professor of mathematics at the University of California, Santa Barbara in fall 2015.

**BIRTHS**

**1683 Jean-Pierre Christin**(May 31, 1683 – January 19, 1755) was a French physicist, mathematician, astronomer and musician. His proposal to reverse the Celsius thermometer scale (from water boiling at 0 degrees and ice melting at 100 degrees, to water boiling at 100 degrees and ice melting at 0 degrees) was widely accepted and is still in use today.

Christin was born in Lyon. He was a founding member of the Académie des sciences, belles-lettres et arts de Lyon and served as its Permanent Secretary from 1713 until 1755. His thermometer was known in France before the Revolution as the thermometer of Lyon. *Wik

**1847 Egor Ivanovich Zolotarev** (March 31, 1847, Saint Petersburg – July 19, 1878, Saint Petersburg) produced fundamental work on analysis and number theory. *SAU

In 1857 he began to study at the fifth St Petersburg gymnasium, a school which centered on mathematics and natural science. He finished it with the silver medal in 1863. In the same year he was allowed to be an auditor at the physico-mathematical faculty of St Petersburg university.

He had not been able to become a student before 1864 because he was too young. Among his academic teachers were Somov, Chebyshev and Aleksandr Korkin, with whom he would have a tight scientific friendship. In November 1867 he defended his Kandidat thesis “About the Integration of Gyroscope Equations”, after 10 months there followed his thesis pro venia legendi About one question on Minima. With this work he was given the right to teach as a private lecturer at St Petersburg university.

Zolotarev's steep career ended abruptly with his early death. He was on his way to his dacha when he was run over by a train in the Tsarskoe Selo station. On 19 July 1878 he died from blood poisoning.

Yegor Ivanovich is not to be confused with the probabilist Vladimir Mikhaelovich Zolotarev, Kolmogorov's disciple, who worked on stable distributions with well known results on their parametrization.

**1861 William Peddie FRSE LLD**(31 May 1861 – 2 June 1946) was a Scottish physicist and applied mathematician, known for his research on colour vision and molecular magnetism.

**1872 Charles Greeley Abbot**(31 May 1872; 17 Dec 1973 at age 101) was an American astrophysicist who is thought to have been the first scientist to suspect that the radiation of the Sun might vary over time. In 1906, Abbot became director of the Smithsonian Astrophysical Observatory and, in 1928, fifth Secretary of the Smithsonian. To study the Sun, SAO established a network of solar radiation observatories around the world-- usually at remote and desolate spots chosen primarily for their high percentage of sunny days. Beginning in May 1905 and continuing over decades, his studies of solar radiation led him to discover, in 1953, a connection between solar variations and weather on Earth, allowing general weather patterns to be predicted up to 50 years ahead. *TIS

**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

**1912**Chien-Shiung Wu (simplified Chinese: 吴健雄; traditional Chinese: 吳健雄; pinyin: Wú Jiànxióng, May 31, 1912 – February 16, 1997) was a Chinese American experimental physicist who made significant contributions in the field of nuclear physics. Wu worked on the Manhattan Project, where she helped develop the process for separating uranium metal into uranium-235 and uranium-238 isotopes by gaseous diffusion. She is best known for conducting the Wu experiment, which contradicted the hypothetical law of conservation of parity. This discovery resulted in her colleagues Tsung-Dao Lee and Chen-Ning Yang winning the 1957 Nobel Prize in physics, and also earned Wu the inaugural Wolf Prize in Physics in 1978. Her expertise in experimental physics evoked comparisons to Marie Curie. Her nicknames include "the First Lady of Physics", "the Chinese Madame Curie", and the "Queen of Nuclear Research".*Wik

**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**(May 31, 1931 – July 27, 2019 )

**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). 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

**1998 Michio Suzuki**(October 2, 1926 – May 31, 1998) was a Japanese mathematician who studied group theory.

A Professor at the University of Illinois at Urbana-Champaign from 1953 until his death. Suzuki received his Ph.D in 1952 from the University of Tokyo, despite having moved to the United States the previous year. He was the first to attack the Burnside conjecture, that every finite non-abelian simple group has even order.

A notable achievement was his discovery in 1960 of the Suzuki groups, an infinite family of the only non-abelian simple groups whose order is not divisible by 3. The smallest, of order 29120, was the first simple group of order less than 1 million to be discovered since Dickson's list of 1900.

There is also a sporadic simple group called the Suzuki group, which he announced in 1968. The Tits ovoid is also referred to as the Suzuki ovoid. *Wik

**2000 Erich Kähler**(16 January 1906, Leipzig – 31 May 2000, Wedel) was a German

Kähler was born in Leipzig, and studied there.

As a mathematician he is known for a number of contributions: the Cartan–Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Élie Cartan.

His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted. *Wik

**2019 Margaret Eva Rayner CBE**(21 August 1929 – 31 May 2019) was a British mathematician who became vice principal of St Hilda's College, Oxford and president of the Mathematical Association. She was known for her research on isoperimetric inequalities, her work in mathematics education, and her publications on the history of mathematics and of St Hilda's College.

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

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