## Thursday 7 September 2023

### On This Day in Math - September 7

If there is a problem you can't solve,
then there is an easier problem you can solve: find it.

~George Polya, How to Solve It

The 250th day of the year; 250 is the smallest number expressible as the
sum of two positive cubes, which is also expressible as the sum of two (unique)
positive squares in more than one way. ( on Feb. 16, 1745 Euler wrote to Goldbach and shows that numbers represented in two different ways as a sum of two squares must be composite; hence 250 is composite. )
53+ 5 3 = 250
152+ 5 2 = 250 ; 13 2 + 92 = 250

and 250 = (3!)3 + (2!)^5 + (1!)7+ (0!)9 *Derek Orr

250 is the smallest multidigit prime where the sum of the squares of its prime factors is the same as the sum of the squares of its digits. *Prime Curios

250 = 1^2 + 2^2 + 7^2 + 14^2, the sum of the squares of its divisors.

250 is the 49th prime - 1. Its square is also one less than a prime

Strange that I would learn this from a Brit, but "Length of a baseball pitch, pitcher to batter (18.44 m) is 250 x Diameter of regulation baseball (73.7 mm)  *http://www.isthatabignumber.com
He used the term for the "pitch" (pitching or bowling area) in cricket, and btw, the cricket pitch is 1 chain, or 22 yards long, and that's 20.12 meters (but the batting (popping) crease is almost 1 1/4 meters in front of the stumps, so the pitching distances are very similar.

EVENTS

1460 Founding of the University of Basel. Both Bernoulli brothers later taught there. *VFR Johann Bernoulli took over as professor of mathematics, replacing his deceased older brother Jacob.

1715 "Steal This Math Book" , William Johnson, of the Parish of St. Clement Danes, was indicted for feloniously stealing one Whiston's Astronomy, value 5 s. the Goods of Joseph Brown. Brown swore the Prisoner came into his Shop inquiring for some Mathematical Books, and took an Opportunity to steal the Book mention'd in the Indictment, which he afterwards sold to one Chapman in Chancery-lane , where the Book was found; and the Prisoner coming again to offer another Book to sell, he was secur'd. The Prisoner said he bought it of one Mohun , a Scholar of his; but could not prove it. The Jury found him Guilty to the value of 10 d. *Proceedings of the Old Bailey

1844 In a letter to George Boole, Arthur Cayley indicated that he is “much interested” in a paper on quaternions by Sir William Rowan Hamilton: “the remarkable part of which is evidently that the factors of the product are not convertible [commutative], but as he observes, why should they be? ” Hamilton’s discovery of quaternions was an important step in the development of abstract algebra. *Desmond MacHale, George Boole, His Life and Work, Boole Press, Dublin,micrometer caliper (calibre à vis et à vernier circulaire). (1985), p. 57.  (The term "commutative" was created by Francois-Joseph Servois in a paper in Annales de Gergonne on October 1, 1814). *PB notes

He almost discovered Quaternions well before Hamilton.    Carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published until 1900.  The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized.

The term then appeared in English in 1838. in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.*Wik

Notice the non commutative nature can be seen in this Irish stamp commemorating the discovery of quaternions.  the product of i*j is k, but the reversal j*i =-k.

1848 Jean-Laurent Palmer, French instrument maker and inventor of the micrometer received his patent, no. 7518, for the micrometer caliper (calibre à vis et à vernier circulaire), which he exhibited at the Paris Exposition of 1867 as 'Systeme Palmer'.

The idea for a micrometer – an instrument that measures distance or thickness by counting the turns of a screw – was 180 years old, and calipers were far older, but no one had ever combined the two into a single hand-held tool. Palmer's micrometer had two numerical scales--one to count the screw turns, and another to measure fractions of a turn. Since the threads were 1 mm apart, and since the fractional scale was divided into 20 parts, that means Palmers' instrument could measure thickness to an accuracy of .05 mm, and with a Vernier scale that could be reduced to .01 mm – one hundred-thousandth of a meter.  Impressive for such a simple instrument.

 *Linda Hall org

1858 "Neither at Olmos nor Piura, did any enceinte woman leave her room during the eclipse, whilst some from curiosity, but more through fear, were in the streets, yet not daring to look upon the sun, lest malady befall them. The somber green light gave them the appearance of corpses, and they apprehended that a plague might be visited upon them. Afterwards, the muleteers told us that their animals stopped eating, and huddled together in evident alarm." Lieut. J M Gillis An Account of the Total Eclipse of the Sun on September 7,*NSEC

1909 The ﬁrst junior high school in the United States, Indianola School, was opened in Columbus, Ohio. *Ohio and Its Resources, Ohio Chamber of Commerce, p. 7
Its school building still exists and is owned by the Columbus City Schools, though it is now occupied by Graham Expeditionary Middle School, a charter operated by the Graham Family of Schools. *Wik

1923 The AMS adopted a resolution “sanctioning the establishment of a lectureship to be known as the Josiah Willard Gibbs Lectureship, the lecture to deal in semi-popular form with some aspect of mathematics or its applications.” *VFR

1927 The ﬁrst Polish Mathematical Congress opened in Lwow. Presenters included Alfred Tarski, Waclaw Sierpinski, Bronislaw Knaster, Stanislaw Mazur, J.von Neumann *Kuratowski, A Half-Century of Polish Mathematics, p. 53 *John F Ptak Science books

We present electronic version of archival document. Memorial Book of the First Congress of Mathematics,

Lviv, 7-10.IX.1927

1930 Kurt Godel, in a discussion on the foundations of mathematics organized by the Vienna Circle, announced his famous theorem on the incompleteness of arithmetic: There are true but unprovable statements. *VFR

BIRTHS

1707 Georges-Louis Leclerc, (7 September 1707 – 16 April 1788) Compte de Buffon born. Buffon’s needle experiment uses probability to estimate π. He introduced calculus into probability theory. *VFR A French naturalist, who formulated a crude theory of evolution and was the first to suggest that the earth might be older than suggested by the Bible. In 1739 he was appointed keeper of the Jardin du Roi, a post he occupied until his death. There he worked on a comprehensive work on natural history, for which he is remembered, Histoire naturelle, générale et particulière. He began this work in 1749, and it dominated the rest of his life. It would eventually run to 44 volumes, including quadrupeds, birds, reptiles and minerals. He proposed (1778) that the Earth was hot at its creation and, from the rate of cooling, calculated its age to be 75,000 years, with life emerging some 40,000 years ago*TIS

Thomas Jefferson in his notes Notes on the State of Virginia (1785), in which, among other topics, he famously defended his country against those Europeans who said that the Americas (North, South and Central) were unhealthy places populated by lesser animals and plants, compared with those of the Old World, and inhabited by peoples who were similarly weak and degenerate.  Leclerc was the most direct target of these rebuttals. The Histoire naturelle, générale et particulière, written in 44 quarto volumes between 1749 and 1809 by Georges-Louis Leclerc, Comte de Buffon, and his associates. Buffon had never been to the New World, but that did not prevent him from damning it.

In 1781, in the midst of the American Revolutionary War, the British army rousted Thomas Jefferson from his home in Monticello. Politically unpopular, he retired from the governorship of Virginia and threw himself into writing. The result was his only book, Notes on the State of Virginia (1785), in which, among other topics, he famously defended his country against those Europeans who said that the Americas (North, South and Central) were unhealthy places populated by lesser animals and plants, compared with those of the Old World, and inhabited by peoples who were similarly weak and degenerate.

The immediate source of these libels was Histoire naturelle, générale et particulière, written in 44 quarto volumes between 1749 and 1809 by Georges-Louis Leclerc, Comte de Buffon, and his associates. A product of the age of French encyclopedists, Histoire naturelle pulled together a vast array of facts about natural history around the world. It was also the vehicle for Buffon's many ideas about the history of the Earth and the organisms that inhabit it. Buffon had never been to the New World, but that did not prevent him from damning it. His critique carried an importance far greater than its questionable scientific value. Anything that lessened the public opinion of America—awash in foreign debt, at war with a global superpower, supplicant to the thrones of France and Spain—had political significance. Buffon had to be answered.

The Secretary to the French delegation in Philadelphia was Francois, Marquis de Barbé-Marbois. (Later, as minister of the treasury for Napoleon I, he negotiated the Louisiana Purchase.) The French government had instructed Barbé-Marbois to assemble data on the 13 colonies, and he responded by preparing a 22-point questionnaire. A copy of this survey was given to Joseph Jones, a delegate from Virginia to the Continental Congress in Philadelphia, in late 1780. Jones realized that Jefferson would be the best person to respond. Whereas other states sent in replies of a few pages, Jefferson's response became a book in which he distilled all his knowledge of Virginia's political and constitutional history, geography and ethnography, and of the whole country's natural history. He also rebutted specific points from Histoire naturelle (although the pagination in Jefferson's octavo edition differed from the original). Using all his rhetorical skills, Jefferson destroyed Buffon's case for American inferiority.

Buffon was not the first to assert American degeneracy, and this idea was not based on natural history alone: Politics also played a part. Buffon's immediate source was a book by a Spanish naval officer, Don Antonio d'Ulloa (Relación histórica del viaje hecho de orden de su Majestad a la América Meridional, 1748). d'Ulloa's thesis was that the human condition in the Americas was degenerate as a result of a long history of colonialism, slavery, exploitation of natural resources and subjugation of the native peoples. To d'Ulloa, it was natural that America lacked the large mammals of the Old World and was rife with noxious insects and poisonous reptiles.

Buffon, focusing on North America, developed d'Ulloa's observations into a complex theory in which climate played a central role. In his ninth volume, published in 1761, Buffon compared mammalian species and noted examples in which the same species lived on both sides of the Atlantic Ocean. He claimed the New-World versions were always smaller and weaker. European livestock exported to America were always stunted. Species indigenous to the New World were always smaller than comparable species in the Old World (the largest American mammal was the tapir, nowhere near the size of an elephant). Of American Indians, he wrote, "the organs of generation (of the savage) are small and feeble. He has no hair, no beard, no ardour for the female. Though nimbler than the European, his strength is not so great. His sensations are less acute; and yet he is more timid and cowardly." And so on.

Jefferson refuted Buffon's claims, citing for example the American (black) bear at 412 pounds and the European bear at 153, the American beaver at 45 pounds and the European at 18. Jefferson's data do not bear close scrutiny (he listed the cow in America at 2,500 pounds and at 763 in Europe),

Buffon would later correct some of his previous criticisms of the New World.  *notes from New Scientist article

 *Linda Hall org

1819 Jean Claude Bouquet (7 Sept 1819 , 9 Sept 1885) was a French mathematician who worked on differential geometry and on series expansions of functions and elliptic functions. *Wik

1884 Georges Jean Marie Valiron (7 September 1884, March 1955) was a French mathematician, notable for his contributions to analysis, in particular, the asymptotic behavior of entire functions of finite order and Tauberian theorems*Wik

1903 Dudley Ernest Littlewood (7 September 1903, 6 October 1979) was a British mathematician known for his work in group representation theory.*SAU

1912 David Packard (7 Sep 1912; 26 Mar 1996) U.S. entrepreneur and electrical engineer who cofounded the Hewlett-Packard Co., a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with William R. Hewlett, a friend and Stanford classmate. HP's first product was a resistance-capacitance audio oscillator based on a design developed by Hewlett when he was in graduate school. The company's first "plant" was a small garage in Palo Alto, and the initial capital amounted to \$538 *TIS

1914 James Alfred Van Allen (7 Sep 1914; 9 Aug 2006)American physicist who discovered the Earth's magnetosphere, two toroidal zones of radiation due to trapped charged particles encircling the Earth (also known as the Van Allen radiation belts). During WWII he gained experience miniaturizing electronics, such as in the proximity fuse of a missile. After the war, he studied cosmic radiation, taking advantage of the unused German stock of V2 rockets launched into the outer regions of the atmosphere, carrying research devices using radio to relay back the data gathered. He was also involved in the early U.S. space program, and he had radiation measuring instruments on the first U.S. satellite, Explorer 1, launched 31 Jan 1958 with follow-up carried out by satellites Explorer 3 and 4 later the same year*TIS

1936 Peter George Oliver Freund (7 September 1936 - ) is a professor emeritus of theoretical physics at the University of Chicago. He has made important contributions to particle physics and string theory. He is also active as a writer. *Wik

1948 Cheryl Elisabeth Praeger, AM (born 7 September 1948, ) is an Australian mathematician. She is currently a professor of mathematics at the University of Western Australia. She is best known for her works in group theory, algebraic graph theory and combinatorial designs.*Wik

1955 Efim Isaakovich Zelmanov (7 Sep 1955, --)Russian mathematician who was awarded the 1994 Fields Medal for his work on combinatorial problems in nonassociative algebra and group theory and particularly his solution of the Restricted Burnside problem. His Ph.D. (1980) Ph.D. thesis was on nonassociative algebra, wherein his treatment extending results from the classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras. In 1887, he showed that the Engel identity for Lie algebras implies nilpotence, in the previously unsolved case of infinite dimensions. The Restricted Burnside problem that he solved was a narrower condition arising out of Burnside's 1902 question whether a finitely generated group in which every element has finite order, is finite.*TIS

DEATHS

1682 Juan Caramuel y Lobkowitz (23 May 1606, 7 Sept 1682) was a Spanish Cistercian who expounded the general principle of numbers to base n pointing out the benefits of some other bases than 10. *SAU

1767 John Pond FRS (1767 – 7 September 1836) was a renowned English astronomer who became the sixth Astronomer Royal, serving from 1811 to 1835. Pond was born in London and, although the year of his birth is known, the records indicating the day and month have been lost to posterity. Pond's father made a fortune as a London merchant, enabling young John to enter Trinity College, Cambridge in 1784 at the age of sixteen. He took no degree, however, as his course was being interrupted by severe pulmonary attacks which compelled a long residence abroad. He was admitted to the Inner Temple in 1794, but his poor health prompted him to withdraw.
In 1811 Pond succeeded Nevil Maskelyne as Astronomer Royal. During an administration of nearly twenty-five years, he effected a reform of practical astronomy in England comparable to that brought about by Friedrich Bessel in Germany. In 1821 he began to employ the method of observation by reflection and in 1825 devised means of combining two mural circles in the determination of the place of a single object, the one serving for direct and the other for reflected vision. Under his auspices the instrumental equipment at Greenwich was completely changed and the number of assistants increased from one to six. The superior accuracy of his determinations was attested by Seth Carlo Chandler's 1894 discussion of them in the course of his researches into the variation of latitude. Between 1810 and 1824 he persistently controverted the reality of Ireland's Astronomer Royal John Brinkley's imaginary star-parallaxes. During the 1829-31 period, he briefly served as Superintendent of the Nautical Almanac. Delicacy of health obliged his retirement in the autumn of 1835.
died in Blackheath, London in the year of his 69th birthday and was buried beside and near fellow Astronomers Royal Edmond Halley and Nathaniel Bliss, respectively, in the churchyard of St Margaret's in nearby Lee. *Wik

1918 Peter Ludvig Mejdell Sylow died (12 December 1832 – 7 September 1918) . Sylow was a high school teacher who proved, in 1872, what is perhaps the most profound result in the theory of finite groups. The Sylow theorems are a collection of theorems that give detailed information about the number of subgroups of fixed Order of a group that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups. *Wik

1936 Marcel Grossmann (April 9, 1878 – September 7, 1936) mathematician and a friend and classmate of Albert Einstein. He became a Professor of Mathematics at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, specializing in descriptive geometry.
It was Grossmann who emphasized the importance of a non-Euclidean geometry called elliptic geometry to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossman mentored Einstein in tensor theory as well.
The community of relativists celebrates Grossmann's contributions to physics by organizing Marcel Grossman meetings every three years.*Wik

1947 Michele Cipolla (28 October 1880; 7 September 1947) was an Italian mathematician, mainly specializing in number theory. He developed (among other things) a theory for sequences of sets and Cipolla's algorithm for finding square roots modulo a prime number. He also solved the problem of binomial congruence. *Wik

1951 Harry Schmidt was a German mathematician who wrote on the application of mathematics to physics. *SAU

1970 Percy Le Baron Spencer (9 Jul 1894, 7 Sep 1970) was the American engineer who invented the microwave oven. In 1940, Sir John Randall and Dr. H. A. Boot invented the magnetron tube to produce radar microwaves. After the war, Dr. Percy Spencer at the Raytheon Company was investigating the magnetron tube. During one experiment, he discovered that a chocolate bar in his pocket had totally melted, though the heating effect of microwaves was known earlier. Dr. Spencer deduced the magnetron radiation had melted the chocolate, not his body heat. This led Spencer to researched cooking food. The first commercial microwave ovens were made for restaurants.*TIS

1985 George P´olya, (December 13, 1888 – September 7, 1985) Professor Emeritus at Stanford died at the age of 97. In 1963, P´olya received the MAA award for Distinguished Service to Mathematics. The George P´olya Award for noteworthy expository articles in the College Mathematics Journal is named in his honor. *VFR Pólya worked in probability, analysis, number theory, geometry, combinatorics and mathematical physics. *Wik (Most of us remember him as an influential educator and his book "How to Solve it")

A classic quote of Polya, "There are many questions which fools can ask that wise men cannot answer."

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