there is no permanent place in the world for ugly mathematics.
~Godfrey Harold Hardy
The 335th day of the year; 2335 is the smallest power of two which equals the sum of four consecutive primes *Prime Curios This seems astounding to me, that such a huge number would be the first.
There are 67 primes smaller than 335, and so 335 is divisible by the number of primes less than itself.. How common is that for integers.
Lagrange's theorem tells us that each positive integer can be written as a sum of four squares (perhaps including zero), but many can be written as the sum of only one or two non-zero squares. 335 is one of the numbers that can not be written with less than four non-zero squares. The smallest examples are 7, 15, and 23. If you take any number in this sequence, and raise it to an odd positive power, you get another number in the sequence (Why teachers?), so now you know that 73 = 343 is also not expressible as the sum of less than four non-zero squares.
1729 Euler/Goldbach correspondence begins: Goldbach was also a kind of mentor to Leonhard Euler. For over 25 years they exchanged letters, 196 of which survive. These letters give us a window into Euler’s scientific and personal life. In Goldbach’s very first letter to Euler, dated December 1, 1729, Goldbach got Euler interested in number theory. Goldbach added note at the end of the letter: “P. S. Have you noticed the observation of Fermat that all numbers of the form 22x+1, that is 3, 5, 17, etc., are prime numbers, but he did not dare to claim he could demonstrate it, nor, as far as I know, has anyone else been able to prove it.” Three years later, in a five-page paper that now bears the index number E26, Euler shows that the F(5) = 4,294,967,297 = 641× 6,700,417 . That is, Fermat was wrong. *Ed Sandifer, How Euler Did It (Like Fermat before him, Euler found most mathematicians less than excited about problems in Number Theory, but for most of his life, Goldbach would be his mentor, and his student in this area.)
1764 Alexander Small writes Benjamin Franklin from England, "My Namesake the Virginian Professor (William Small) is here; and desires to be most particularly remembered to you."
Small is known for being Thomas Jefferson's professor of Natural Philosophy at William and Mary, and for having an influence on the young Jefferson. (I could not determine if Alexander and William Small are related) *Natl. Archives
Small left for England in 1764 to acquire scientific instruments for the college but never returned. While in England, he received a medical degree and became an adviser to Matthew Boulton and James Watt. Boulton, Small, and Erasmus Darwin helped establish the Birmingham Lunar Society, a learned society whose participants included Watt, Joseph Priestley, Josiah Wedgwood, William Withering (after Small's death), and others. Small died in Birmingham of what was called putrid or jail fever. It has been assumed that the fatal disease was malaria since Small had been in Virginia; indeed, it may have been malaria, but he was diagnosed by Erasmus Darwin, Alexander Small, and William Heberden. Jefferson's last letter to Small was dated May 7, 1775.
1783 J. A. C. Charles was the first man to see the sun set twice in one day. He did it by making a flight (to 9000 feet) in a hydrogen balloon. *VFR (Charles is often considered the inventor of the hydrogen balloon.) The first manned voyage of a hydrogen balloon left Paris carrying Professor Jacques Alexander Cesar Charles and Marie-Noel Robert to about 600 m and landed 43 km away after 2 hours in the air. Robert then left the balloon, and Charles continued the flight briefly to 2700 m altitude, measured by a barometer. This hydrogen-filled balloon was generally spherical and used a net, load ring, valve, open appendix and sand ballast, all of which were to be universally adopted later. His hydrogen generator mixed huge quantities of sulfuric acid with iron filings. On 27 Aug 1783, Charles had launched an unmanned hydrogen balloon, just before the Montgolfiers' flight. *TIS (One of these altitudes is obviously wrong. )
1851 On December the first, Louis-Napoleon Bonaparte, who had been instrumental in supporting Foucault in the demonstration of his pendulum, ordered that the pendulum demonstration cease and the Pantheon return to being used as a church (Louis Philippe had secularized the Pantheon in 1830 and stopped burials in the crypt). Why did he stop the popular demonstrations? We do not know, but on the next day citizens of France awoke to find notices posted on the major buildings, “The National Assembly is dissolved… “ Louis-Napoleon had taken his first step to becoming Emperor of France. *Amir D Aczel, Pendulum, pg 174
1890, after regular competition, Peano was named extraordinary
professor of infinitesimal calculus at the University of Turin. *Hubert Kennedy
Eight Mathematical Biographies Pg 23
1896 Frank Broaker of New York City received certificate No. 1 from the New York State Board of Certified Public Account Examiners thus becoming the first CPA in the US. *JN Kane, Famous First Facts,
1671 John Keill (1 Dec 1671; 31 Aug 1721) Scottish mathematician and natural philosopher, who was a major proponent of Newton’s theories. He began his university education at Edinburgh under David Gregory, whom he followed to Oxford, where Keill lectured on Newton's work, and eventually became professor of astronomy. In his book, An Examination of Dr. Burnett's Theory of the Earth (1698), Keill applied Newtonian principles challenging Burnett's unsupportable speculations on Earth's formation. In 1701, Keill published Introductio ad Veram Physicam, which was the first series of experimental lectures and provided a clear and influential introduction to Isaac Newton’s Principia. He supported Newton against priority claims by Leibnitz for the invention of calculus. *TIS
1792 Nikolay Ivanovich Lobachevsky (1 Dec 1792; 24 Feb 1856) Russian mathematician who, with János Bolyai of Hungary, is considered the founder of non-Euclidean geometry. Lobachevsky constructed and studied a type of geometry in which Euclid's parallel postulate is false (the postulate states that through a point not on a certain line only one line can be drawn not meeting the first line). This was not well received at first, but his greatest vindication came with the advent of Einstein's theory of relativity when it was demonstrated experimentally that the geometry of space is not described by Euclid's geometry. Apart from geometry, Lobachevsky also did important work in the theory of infinite series, algebraic equations, integral calculus, and probability. *TIS William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. Lobachevsky is the subject of songwriter/mathematician Tom Lehrer's humorous song "Lobachevsky" from his Songs by Tom Lehrer album. In the song, Lehrer portrays a Russian mathematician who sings about how Lobachevsky influenced him: "And who made me a big success / and brought me wealth and fame? / Nikolai Ivanovich Lobachevsky is his name." Lobachevsky's secret to mathematical success is given as "Plagiarize!", as long as one is always careful to call it "research". According to Lehrer, the song is "not intended as a slur on [Lobachevsky's] character" and the name was chosen "solely for prosodic reasons".*Wik (The lyrics are here)
1847 Christine Ladd-Franklin (1 Dec 1847; 5 Mar 1930) American scientist and logician known for contributions to the theory of colour vision accounting for the development of man's color sense which countered the established views of Helmholtz, Young, and Hering. Her position was that color-sense developed in stages. Ladd- Franklin's conclusions were particularly useful in accounting for color-blindness in some individuals. In logic, she published an original method for reducing all syllogisms to a single formula *TIS Ladd-Franklin was the first woman to have a published paper in the Analyst (at this time, 1877, it was more of a recreational mathematics publication still edited by the self-educated Ohio farmboy, Joel E Hendricks. The article was simply titled "Quaternions." ). She was also the first woman to receive a Ph.D. in mathematics and logic. The majority of her publications were based on visual processes and logic. Her views on logic influenced Charles S. Peirce’s logic and she was highly praised by Prior. *Wik
1892 Krishnaswami Ayyangar (1 Dec 1892 in Attipattu, Chingleput district, Tamil Nadu, India - June 1953 in Mysore, India) was an Indian mathematician who worked in Mysore. He produced important work on the history of Hindu mathematics. *SAU
1913 Colossus' Team Member Chandler is Born W.W. Chandler was born in Bridport, England. He obtained his B.Sc. from London University in 1938 by private study while working as a telephone engineer at the British Post Office Research Department. During the war he was responsible for the installation and maintenance of the Colossus at Bletchley Park. The Colossus represented the first electronic computer, however it was programmed by a mechanical switchboard. Its was used to crack the German Fish codes which guarded the highest levels of German communication. Winston Churchill characterized the Bletchley Park team as the geese who laid the golden eggs but never cackled.
After the war Chandler participated in development and installation of the MOSAIC computer and worked on optical character recognition. He died on September 11, 1989. *CHM
1941 Stephen A. Benton (1 Dec 1941; 9 Nov 2003.) American physicist who was a pioneer in medical imaging and fine-arts holography. His fascination with optical phenomena began with the 3-D glasses he used as an 11-year-old to watch the 1953 movie "House of Wax." In 1968, he invented the "rainbow holograms" as seen on credit cards while working for Polaroid Corporation. He turned to academia as an assistant professor at Harvard (1968) and later a professor at Massachusetts Institute of Technology from 1985 where he helped set up the Spatial Imaging Group and headed the M.I.T. media art and sciences program. Benton was a pioneer in natural light holography as a artistic medium, and was a curator at the Museum of Holography in Manhattan until it closed in 1992.*TIS
1750 Johann Doppelmayr (27 Sept 1677 in Nuremberg, Germany - 1 Dec 1750 in Nuremberg, Germany)was a German mathematician who wrote on astronomy, spherical trigonometry, sundials and mathematical instruments. Doppelmayr also wrote a book of tremendous value giving biographical details of 360 mathematicians and instrument makers of Nuremberg from the 15th to the 18th century. This had the lengthy title Historische Nachricht von den Nürnbergischen Mathematicis und Künstlern, welche fast von dreyen Seculis her durch ihre Schriften und Kunst-Bemühungen die Mathematic und mehrere Künste in Nürnberg vor andern trefflich befördert und sich um solche sehr wohl verdient gemacht zu einem guten Exempel, und zur weitern rühmlichen Nachahmung and was published in 1730. *SAU
1866 Sir George Everest (1790, 1 Dec 1866) British military engineer and geodesist, born in Gwernvale, Powys, Wales, UK. He worked on the trigonometrical survey of India (1818-43), providing the accurate mapping of the subcontinent. For more than twenty-five years and despite numerous hardships, he surveyed the longest arc of the meridian ever accomplished at the time. Everest was relentless in his pursuit of accuracy. He made countless adaptations to the surveying equipment, methods, and mathematics in order to minimize problems specific to the Great Survey: immense size and scope, the terrain, weather conditions, and the desired accuracy. Mount Everest, formerly called Peak XV, was renamed in his honour in 1865. *TIS (Mary Boole, self-taught mathematician and wife of George Boole was his niece)
1935 Bernhard Voldemar Schmidt (30 Mar 1879, 1 Dec 1935) Astronomer and optical instrument maker who invented the telescope named for him. In 1929, he devised a new mirror system for reflecting telescopes which overcame previous problems of aberration of the image. He used a vacuum to suck the glass into a mold, polishing it flat, then allowing in to spring back into shape. The Schmidt telescope is now widely used in astronomy to photograph large sections of the sky because of its large field of view and its fine image definition. He lost his arm as a child while experimenting with explosives. Schmidt spent the last year of his life in a mental hospital.*TIS
1947 Godfrey Harold Hardy (1877, 1 Dec 1947)English mathematician known for his work in number theory and mathematical analysis. Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes. Although Hardy considered himself a pure mathematician, early in his career, he nevertheless worked in applied mathematics when he formulated a law that describes how proportions of dominant and recessive genetic traits will propagate in a large population (1908). Hardy considered it unimportant but it has proved of major importance in blood group distribution. As it was also independently discovered by Weinberg, it is known as the Hardy-Weinberg principle. *TIS G. H. Hardy died—on the same day that the Copley Medal was to be presented to him by the Royal Society of London. [Collected Papers of G. H. Hardy, vol. 1, p. 8].
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| *Wik |
1964 J.B.S.(John Burdon Sanderson) Haldane (5 Nov 1892, 1 Dec 1964) was a British geneticist and biometrician who opened new paths of research in population genetics and evolution. He began studying science at the age of eight, as assistant to his father (the noted physiologist John Scott Haldane). J.B.S. Haldane also worked in biochemistry, and on the effects of diving on human physiology. A Marxist from the 1930s, Haldane was well known for his outspoken Marxist views.He resigned from the Communist Party c. 1950 on the issue of Lysenko's claims to have manipulated the genetic structure of plants and "Stalin's interference with science". He became known to a large public as a witty popularizer of science with such works as Daedalus (1924), and Possible Worlds (1927).*TIS
Haldane's article on abiogenesis in 1929 introduced the "primordial soup theory", which became the foundation for the concept of the chemical origin of life. He established human gene maps for haemophilia and colour blindness on the X chromosome, and codified Haldane's rule on sterility in the heterogametic sex of hybrids in species. He correctly proposed that sickle-cell disease confers some immunity to malaria. He was the first to suggest the central idea of in vitro fertilisation, as well as concepts such as hydrogen economy, cis and trans-acting regulation, coupling reaction, molecular repulsion, the darwin (as a unit of evolution), and organismal cloning.*Wik
1977 Kenneth O. May (July 8, 1915, Portland, Or. – December 1,1977) was an American mathematician and historian of mathematics, who developed May's theorem. The Kenneth O. May Prize is awarded for outstanding contributions to the history of mathematics. Ken May established Historia Mathematica, and preserved it by separating it from its creator, "The distinguished predecessors of HM were associated with their founders and died with them. If HM is to avoid this fate, we must prepare and carry through a prompt transfer of editorial responsibility to younger hands." His list of publications numbers above 300. *Henry S. Tropp, E'loge, Isis 70, Sept 1979, Pgs 419-422
May’s Theorem
• Theorem: assume a two candidate election with an odd
number of voters. Majority rule adheres to these four
conditions. Furthermore, these four conditions imply
majority rule.
1. Decisiveness
– The voting rule must specify a unique decision (even if the decision is indifference)
for any set of individual preferences.
2. Anonymity
– A voting rule must treat all voters alike, in the sense that if any two voters traded
ballots, the outcome of the election would remain the same.
– Ex: if Abdullah Abdullah won with Asa voting for him and Ara voting against, then
Abdullah Abdullah should win if Ara voted for him and Asa voted against him.
3. Neutrality
– A voting rule must treat all candidates alike, rather than favor one over the other.
– Ex: if the names Abdullah and Karzai are switched on the ballot but the votes
remain the same, then the result should be the same (but favor of the other
candidate).
4. Positive Responsiveness (monotonicity)
– if the group decision is indifference or favorable to x, and if individual preferences
remain the same except that a single individual changes his/her vote in favor of x,
then the group decision should be x (rather than y or remain indifferent).
– Ex: If Abdullah wins or ties, then he should win if he gains votes without losing
votes.
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1983 Leon Mirsky (19 Dec 1918 in Russia - 1 Dec 1983 in Sheffield, England)worked in Number Theory, Linear Algebra and Combinatorics.*SAU
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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