Friday 16 September 2022

On This Day in Math - September 16

...[T]o many it is not knowledge but the quest for knowledge that gives greater interest to thought—to travel hopefully is better than to arrive

~Sir James Jeans

The 259th day of the year;259 expressed in base six is a repunit, 1111 (63+62+ 61+60= 216+36+6+1=259)

Probably 259 is the largest number that can be written in two ways as \(2^x + 3y\). Here \(259 = 2^8 + 3^1 = 2^4 + 3^5\).

259 can be expressed as the sum of four cubes in two different ways, 259 = 13 + 23 + 53 + 53= 23 + 23 + 33 + 63

and for my ex-students from Japan, 259  is The number of Pokémon originally available in Pokémon Gold and Silver


1566 Tycho Brahe departs Wittenberg to avoid the plague. Early In 1566 he left Denmark and arrived at Wittenberg on the 15th of April. The University of Wittenberg had been founded in 1502, and had then for nearly fifty years been one of the most renowned in Europe. He Studied under Caspar Peucer, distinguished as a mathematician, a physician, and a historian. Tycho, however, did not profit very much from Peucer's instruction, as the plague broke out at Wittenberg, so that he was induced to leave it on the 16th September, after a stay of only five months. *TYCHO BRAHE, A PICTURE OF SCIENTIFIC LIFE AND WORK IN THE SIXTEENTH CENTURY BY J. L. E. DREYER

1636 In a letter to Roberval, Fermat writes, If a and b are rational, and if \( a^2+b^2 = 2(a+b)x= x^2 \), then x and x2 are irrational. *Lemmemeyer, EULER, GOLDBACH, AND “FERMAT’S THEOREM”

In 1662, the first recorded astronomical observation by the (to become) first Astronomer Royal was John Flamsteed's observation of a solar eclipse from his home in Derby at the age of sixteen, about which he corresponded with other astronomers. Flamsteed's interest in astronomy was stirred by the solar eclipse, and besides reading all he could find on the subject he attempted to make his own measuring instruments. *TIS

1693 In a letter to John Locke, Newton apologized for ill thoughts that he had harbored against Locke. *VFR Locke was strongly denounced by several writers and even called an atheist, notably by John Edwards, but such charges were commonplace against every departure from Orthodoxy. During his period of insanity (following 1693) Isaac Newton made similar charges against Locke; at least he wrote Locke a strange letter apologizing for considering him a Hobbist and having charged him with attacking the root of morality,*Contra Mundum, No. 1 Fall 1991, "At the Origins of English Rationalism", by T.E. Wilder (Locke and Newton were usually friends)

1787 Jefferson writes his ex law professor, George Wythe in regard to the construction of geometric models in the classroom.  Wythe is considered one of the finest jurists of the period, and had Jefferson, Monroe, and John Marshall as students.

"I have reflected on your idea of wooden or ivory diagrams for the geometrical demonstrations. I should think wood as good as ivory; & that in this case it might add to the improvement of the young gentlemen; that they should make the figures themselves. Being furnished by a workman with a piece of veneer, no other tool than a penknife & a wooden rule would be necessary. Perhaps pasteboards, or common cards might be still more convenient. The difficulty is, how to reconcile figures which must have a very sensible breadth, to our ideas of a mathematical line, which, having neither breadth nor thickness, will revolt more at these than at simple lines drawn on paper or slate. If after reflecting on this proposition you would prefer having them made here, lay your commands on me and they shall be executed."

This is a full 100 years before Kline brought his models to America and influenced their use in American education.  The earliest record of model building dates back to 1873 and deals with a plaster model of Steiner's Roman surface built by German mathematician Ernst Kummer.  The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic nonorientable surface.  The Roman surface is one of the three possible surfaces obtained by sewing a Möbius strip to the edge of a disk.  


1804 J L Gay-Lussac sets height record of 22,000+ feet during balloon lift to make measurements of magnetism and electricity.  Earlier on August 24, 1804, Joseph Louis Gay-Lussac and Jean-Baptiste Biot ascended in a hot air balloon to a height of 4,000 meters altitude in order to conduct scientific experiments on gases. These experiments measuring the expansion of gasses led to him publishing the law he dubbed Charles Law, perhaps giving JAC Charles more credit than was due.

*Science History Inst

In 1835, British naturalist Charles Darwin, aboard the ship HMS Beagle, arrived at the Galapagos archipelago, a cluster of islands on the equator 600 miles west of South America. During his five weeks studying the fauna in the Galapagos, Darwin found the giant tortoises there greatly differed from one another according to which island they came from. Moreover, many islands developed their own races of iguanas. These observations contributed to his theory of “natural selection,” that species evolved over thousands of millions of years. *TIS 

1848 Weierstrass came to the Catholic Gymnasium in Braunsberg, his third such position. That year he taught mathematics 19 hours per week, took over the geography class after Easter, and received a special note of thanks for helping out in gym! [From the annual report of the Gymnasium in the University of Louisville’s Bullitt Collection of Mathematics. *VFR

1895 Pierson writes to Yule, "I had a most kindly and encouraging letter from Francis Galton about my Heredity paper. He really is a fine old fellow to take my modification of his views so well." *The History of Statistics: The Measurement of Uncertainty Before 1900
By Stephen M. Stigler

1986 “Four out of three jocks can’t count,” read a headline in The Harvard Lampoon’s parody of USA Today. *VFR


1494 Francisco Maurolico(September 16, 1494-July 21 or July 22, 1575) was an Italian Benedictine who wrote important books on Greek mathematics. He also worked on geometry, the theory of numbers, optics, conics and mechanics.*SAU (His Arithmeticorum libri duo (1575) includes the first known proof by mathematical induction. (First in western mathematics; The 10th Century Persian mathematician Muhammad Al-Karaji was one of the first to use the method of proof by mathematical induction to prove his results, by proving that the first statement in an infinite sequence of statements is true, and then proving that, if any one statement in the sequence is true, then so is the next one. Among other things, Al-Karaji used mathematical induction to prove the binomial theorem.) He proved that the sum of the first n odd numbers is equal to n2 .) Maurolico's astronomical observations include a sighting of the supernova that appeared in Cassiopeia in 1572. Tycho Brahe published details of his observations in 1574; the supernova is now known as Tycho's Supernova.*Wik

1736 Johannes Nikolaus Tetens (16 Sep 1736; 17 Aug 1807) German natural philosopher whose empirical approach strongly influenced the work of Immanuel Kant, and later in his life, Tetens became interested in mathematics, especially in actuarial applications. From 1760, as a teacher of natural philosophy he wrote on diverse topics but later began the development of the field of developmental psychology in Germany. He wrote Philosophische Versuche über die menschliche Natur und ihre Entwickelung (1777) on the origin and structure of knowledge. He changed career after 1789 to the civil service during which time he pursued mathematics. As a statistician he produced an Introduction to the Calculation of Life Annuities (1785) and On the Tetens Mortality Curve (1785)*TIS

1804 Squire Whipple (16 Sep 1804; 15 Mar 1888) U.S. civil engineer, inventor, and theoretician who provided the first scientifically based rules for bridge construction, was considered one of the top engineers of the 19th Century, and was known as the "father of iron bridges." He began his career as a bridge-builder in 1840 by designing and patenting an iron-bridge truss. During the next ten years he built several bridges on the Erie canal and the New York and Erie railroad. His design of the Whipple truss bridge was the model for hundreds of bridges that crossed the Erie Canal in the late 19-th century. Before developing his design, Whipple worked for several years on surveys, estimates, and reports for the enlargement of the Erie Canal, and in 1840 he patented a scale for weighing canal boats. He later built the first weighing lock scale constructed on the Erie Canal. The invention of the steam engine required bridges which could support heavy live loads and this motivated Squire to turn his attention to bridges. In 1853, he completed a 146-ft span iron railroad bridge near West Troy (now Watervliet), N.Y. His book on the design of bridges using scientific methods (1847) was the first of its kind. The formulas and his methods are still useful. He obtained a patent for his lift draw-bridge in 1872.*TIS

Ennackal Chandy George Sudarshan (also known as E. C. G. Sudarshan) (16 September 1931 - ) is a prominent Indian-American physicist, author and professor at the University of Texas at Austin. Sudarshan has made significant contributions to several areas of physics. He was the originator (with Robert Marshak) of the V-A theory of the weak force (also done later by Richard Feynman and Murray Gell-Mann), which eventually paved the way for the electroweak theory. Feynman said in 1963: "The V-A theory that was discovered by Sudarshan and Marshak, publicized by Feynman and Gell-Mann".
He also developed a quantum representation of coherent light (for which Glauber was awarded the 2005 Nobel). *Wik


1736 Gabriel Daniel Fahrenheit (24 May 1686, 16 Sep 1736) was a German-Dutch physicist and instrument maker (meteorological). He lived in Holland for most of his life. He invented the alcohol thermometer (1709) and mercury thermometer (1714) and developed the Fahrenheit temperature scale. For the zero of his scale he used the temperature of an equal ice-salt mixture; 30° for the freezing point of water; and 90° for normal body temperature. Later, he adjusted to 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 parts. He also invented a hygrometer to measure relative humidity and experimented with other liquids discovering that each liquid had a different boiling point that would change with atmospheric pressure.*TIS

1925 Alexander Alexandrovich Friedmann (16 Jun 1888, 16 Sep 1925) Russian mathematician who was the first to work out a mathematical analysis of an expanding universe consistent with general relativity, yet without Einstein's cosmological constant. In 1922, he developed solutions to the field equations, one of which clearly described a universe that began from a point singularity, and expanded thereafter. In his article On the Curvature of Space received by the journal Zeitschrift für Physik on 29 Jun 1922, he showed that the radius of curvature of the universe can be either an increasing or a periodic function of time. In Jul 1925, he made a record-breaking 7400-m balloon ascent to make meteorological and medical observations. A few weeks later he fell ill and died of typhus. *TIS

1931 Niels Nielsen (2 Dec 1865 , 16 Sept 1931) was a Danish mathematician who worked on special functions and number theory. *SAU (He also wrote two mathematical histories, one for France, and one for Denmark)

1932 Sir Ronald Ross (born 13 May 1857, 16 Sep 1932) English physician, bacteriologist and mathematician whose discovery of the malarial parasite in the gastrointestinal tract of the Anopheles mosquito led to the realization that malaria was transmitted by Anopheles. For this work, he was awarded the 1902 Nobel Prize for Physiology or Medicine, becoming the first British Nobelist. He began studying malaria in 1892. In 1894 he made an experimental investigation in India of the hypothesis of Alphonse Laveran and Patrick Manson that mosquitoes are connected with the propagation of the disease. After two and a half years' failure, Ross succeeded in demonstrating the life-cycle of the parasites of malaria in mosquitoes, thus establishing the hypothesis of Laveran and Manson. Later, in West Africa he found the species of mosquitoes which convey the deadly African fever.*TIS (He is most remembered for his work on malaria, but his greatest influence may have come from his development and publishing of a mathematical theory of epidemiology.)

1946 Sir James Hopwood Jeans (11 Sep 1877, 16 Sep 1946)was an English physicist, astronomer, and mathematician who was the first to propose that matter is continuously created throughout the universe. He made other innovations in astronomical theory but is perhaps best known as a writer of popular books about astronomy. *TIS

1979 Marion Gray (26 March 1902, 16 Sept 1979) graduated from Edinburgh University and then went to Bryn Mawr College in the USA. She completed her doctorate there and returned to posts at Edinburgh and Imperial College London. She returned to the USA and worked for AT&T for the rest of her career. The Gray graph is named after her.*SAU The Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive *Wik

1989 Allen Shields (May 7, 1927 - September 16, 1989) worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory.
An interesting story from George Piranian, of how Shields was appointed to the University of Michigan.

In 1955, on the first day of the American Mathematical Society Summer Meeting in Ann Arbor, George [Piranian] asked Chairman T H Hildebrandt for leave of absence for the Winter Term of 1956. Immediately Hildebrandt declared that he could not grant the request unless George found a replacement. On his way from Hildebrandt's office to one of the lecture sessions, George ran into Allen Shields, whom a year earlier he had met at the Summer Meeting at Laramie. Allen was cooperative, and George dashed back to report that he had found a substitute and that, after fifteen more minutes the substitute would present a ten-minute paper. ... Young as he was, Allen had already mastered the art of beginning his blackboard work in the upper left-hand corner and ending neatly at the lower right, with one minute to spare. Hildebrandt was so impressed that on the spot he offered Allen a one-term appointment. Later, the department persuaded both Shields and Hildebrandt to extend the arrangement.

Soon after George Piranian returned from his leave, he began working with Shields and they published the joint paper The sets of Luzin points of analytic functions (1957). 

2005 Gordon Gould (17 Jul 1920, 16 Sep 2005) American physicist who coined the word "laser" from the initial letters of "Light Amplification by Stimulated Emission of Radiation." Gould was inspired from his youth to be an inventor, wishing to emulate Marconi, Bell, and Edison. He contributed to the WWII Manhattan Project, working on the separation of uranium isotopes. On 9 Nov 1957, during a sleepless Saturday night, he had the inventor's inspiration and began to write down the principles of what he called a laser in his notebook. Although Charles Townes and Arthur Schawlow, also successfully developed the laser, eventually Gould gained his long-denied patent rights. *TIS

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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