Pat'sBlog

Monday, 24 September 2018

On This Day in Math - September 24

Scipio Ferro of Bologna well-nigh thirty years ago discovered this rule and handed it on to Antonio Maria Fior of Venice, whose contest with Niccolo Tartaglia of Brescia gave Niccolo occasion to discover it. He [Tartaglia] gave it to me in response to my entreaties, though withholding the demonstration. Armed with this assistance, I sought out its demonstration in [various] forms. This was very difficult.
~Girolamo Cardano

This is the 267th day of the year; 267 is the smallest number n such that n+ a googol is prime. (anyone want to find the next one? A quick mental problem for students, How do you know that 269+Googol will not be prime?))

267 can be written as the sum of five cubes in two ways, $ 267 = 1^3 + 2^3 + 2^3 + 5^3 + 5^3 = 2^3 + 2^3 + 2^3 + 3^3 + 6^3 $

EVENTS
1846 Neptune First observed… “It was on that date, back in 1846, that German Astronomer Johann Galle, assisted by graduate student Heinrich Louis d’Arrest, trained the 24 centimeter (9 inch) Fraunhofer Refractor of the Berlin Observatory on a patch of sky near the Aquarius-Capricorn border (see illustration below) and observed the small, blue disk of Neptune. On July 12th, 2011 Neptune completed exactly one orbit since its discovery. One hundred and sixty five years ago a series of events played out in France, England and Germany that would culminate in a watershed moment in the history science and astronomy, a discovery that would prove to be unique and unrepeatable. These events were rife with centuries-old rivalries, political conspiracy and intrigue, all mixed together with good mathematics, some good science, some bad science, some luck and much mayhem.” more of this interesting story from Tom Madigan’s website.

1852 The steam powered airship was made by Baptiste Jules Henri Jacques Giffard His airship, powered with a steam engine, and weighing over 180 kg (400 lb), it was the world's first passenger-carrying airship (then known as a dirigible, which was French ). Both practical and steerable, the hydrogen-filled airship was equipped with a 3 hp steam engine that drove a propeller. The engine was fitted with a downward-pointing funnel. The exhaust steam was mixed in with the combustion gases and it was hoped by these means to stop sparks rising up to the gas bag; he also installed a vertical rudder.
On 24 September 1852 Giffard made the first powered and controlled flight traveling 27 km from Paris to Élancourt. The wind was too strong to allow him to make way against it, so he was unable to return to the start. However, he was able to make turns and circles,[citation needed] proving that a powered airship could be steered and controlled. *Wik

1940 Westinghouse patent application for the Nimatron, a machine to play the game of Nim, is approved. Created by Eduard Condon, Edgewood Tawney, Gerald Tawney, and Willard Dorr, the machine would be featured in the Westinghouse exhibit at the 1940 World's Fair. The machine played 100,000 games at the fair, winning about 90,000. Most of its defeats were apparently administered by attendants to demonstrate that possibility. When the machine did lose it would "present its opponent with a token coin stamped with the words 'Nim Champ'" *historyofinformation.com

BIRTHS
1501 Girolamo Cardano (24 Sep 1501; 21 Sep 1576) Famous for his Ars magna of 1545, which contained detailed and systematics algebraic solutions to cubic and quartic equations. He was one of the most colorful ﬁgures in the whole history of mathematics, as is well illustrated in his autobiography, The Book of My Life. *VFR
Italian physician, mathematician, and astrologer who was the first to give a clinical description of typhus fever. His book, Ars magna ("Great Art," 1545) was one of the great achievements in the history of algebra, in which he published the solutions to the cubic and quartic equations. His mechanical inventions included the combination lock, the compass gimbal consisting of three concentric rings, and the universal joint to transmit rotary motion at various angles (as used in present-day vehicles). He contributed to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science and introduced the Cardan grille, a cryptographic tool (1550). *TIS
His gambling led him to formulate elementary rules in probability, making him one of the founders of the field.
One story says that it was by his own hand so as to fulﬁll his earlier astrological prediction of of his death on this date. *H. Eves, Introduction to the History of Mathematics, Pg 221...

1625 Jan de Witt born. This statesman for the Netherlands wrote, before 1650, one of the ﬁrst systematic developments of the analytic geometry of the straight line and conics. It was printed in Van Schooten’s second Latin edition of Descartes’ geometry (1659–1661).*VFR A nice short article about his unusual death, and life are at this blog by The Renaissance Mathematicus

1844 Max Noether born (24 September 1844 – 13 December 1921) . One of the leaders of nineteenth century algebraic geometry. Although himself a very distinguished mathematician, his daughter Emmy Noether was to bring greater innovation to mathematics than did her father. *SAU

1870 Georges Claude (24 Sep 1870; 23 May 1960) The French engineer, chemist, and inventor of the neon light, Georges Claude, was born in Paris. He invented the neon light, which was the forerunner of the fluorescent light. Claude was the first to apply an electrical discharge to a sealed tube of neon gas, around 1902 and make a neon lamp ("Neon" from Greek "neos," meaning "new gas.") He first publicly displayed the neon lamp on 11 Dec 1910 in Paris. His French company Claude Neon, introduced neon signs to the U.S. with two "Packard" signs for a Packard car dealership in Los Angeles, purchased by Earle C. Anthony for $24,000. *TIS

1891 William F. Friedman (24 Sep 1891; 12 Nov 1969) one of the world's greatest cryptologists, who helped decipher enemy codes from World War I to World War II. He was born as Wolfe Friedman.in Kishinev, Russia. He emigrated to the U.S. in 1893. Originally trained as an agricultural geneticist, he had become interested in cryptology. During World War I, with his wife Elizebeth, he set up a cryptology school for military personnel, which led to appointment by the U.S. as head of the Signal Intelligence Service (1930). He broke the Japanese "Purple" code (1937-40), thus allowing Americans to read much of Japan's secret messages during World War II. *TIS There is a bust of him at the National Cryptologic Museum in Fort Meade Maryland on which he is identified as the "Dean of American Cryptology". There is an interesting biography here .

1896 Tadeusz Ważewski (24 September 1896 – 5 September 1972) was a Polish mathematician.
Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. He is most famous for applying the topological concept of retract, introduced by Karol Borsuk to the study of the solutions of differential equations. *Wik
Ważewski studied at the Jagiellonian University in 1914–1920. He started from physics but very quickly turned to mathematics. Ważewski was a pupil of Zaremba.
He spent three years in Paris and got a doctoral diploma from Sorbona.
Ważewski’s research started from topology. In his doctoral dissertation he obtained interesting results on dendrites (locally connected continua not containing simple closed curves). *Ciesielski & Pogoda, EMS Newsletter December 2012

1898 Charlotte Moore Sitterly (24 Sep 1898; 3 Mar 1990) astrophysicist who organized, analyzed, and published definitive books on the solar spectrum and spectral line multiplets. From 1945 to age 90, she conducted this work at the U.S. National Bureau of Standards and the Naval Research Laboratory. She detected that technetium, an unstable element (previously known only as a result of laboratory experiments with nuclear reactions) exists in nature. She made major contributions to the compilation of tables for atomic-energy levels associated with optical spectra, which are now standard reference material. As instruments carried in space rockets provided new data in the ultraviolet, she extended these tables beyond the optical range. She was awarded the Bruce Medal in 1990.*TIS

1904 Evan T Davies graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations.*SAU

1906 Pol(idore) Swings, (24 Sep 1906; 1983) Belgian astrophysicist, made spectroscopic studies to identify elements and structure of stars and comets. He discovered the first interstellar molecule, the CH radical (1937). In comet atmospheres he studied the "Swings bands" - certain carbon emission lines. In 1941, with a slit spectrograph he identified a "Swings effect" in the violet CN bands (3875 A) - a fluorescence partly due to solar radiation that shows emmission line excitation differences dependant on the Doppler shift caused by a comet's motion relative to the Sun. He co-authored an Atlas of Cometary Spectra with Leo Haser in 1956. *TIS

1923 Raoul Bott,(September 24, 1923 – December 20, 2005)[1] was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. *Wik

1930 John Watts Young (24 Sep 1930, ) astronaut who was the commander of the first ever Space Shuttle mission (STS-1, 12 Apr 1981), walked on the Moon during the Apollo 16 mission (21 Apr 1972), made the first manned flight of the Gemini spacecraft with Virgil Grissom. *TIS

1945 Ian Nicholas Stewart FRS (24 September, 1945 - ) is an Emeritus Professor of Mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer.
While in the sixth form at school, Stewart came to the attention of the mathematics teacher. The teacher had Stewart sit mock A-level examinations without any preparation along with the upper-sixth students; Stewart placed first in the examination. This teacher arranged for Stewart to be admitted to Cambridge on a scholarship to Churchill College, where he obtained a BA in mathematics. Stewart then went to the University of Warwick for his doctorate, on completion of which in 1969 he was offered an academic position at Warwick, where he presently professes mathematics. He is well known for his popular expositions of mathematics and his contributions to catastrophe theory.
While at Warwick he edited the mathematical magazine Manifold. He also wrote a column called "Mathematical Recreations" for Scientific American magazine for several years.
Stewart has held visiting academic positions in Germany (1974), New Zealand (1976), and the U.S. (University of Connecticut 1977–78, University of Houston 1983–84). *Wik

DEATHS
1054 Hermann of Reichenau (1013 July 18 – 1054 September 24), was a German mathematician who important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe. Hermann introduced three important instruments into central Europe, knowledge of which came from Arabic Spain. He introduced the astrolabe, a portable sundial and a quadrant with a cursor.
His works include De Mensura Astrolabii and De Utilitatibus Astrolabii (some parts of these works may not have been written by Hermann).
Hermann's contributions to mathematics include a treatise dealing with multiplication and division, although this book is written entirely with Roman numerals. He also wrote on a complicated game based on Pythagorean number theory which was derived from Boethius. *SAU

1651 Etienne Pascal died (Clermont, May 2, 1588 - Paris, September 24, 1651). The Pascal limacon is named after him, and not after his famous son who later came blazing on the scene. *VFR Étienne is famed as the discoverer of the curve the Limaçon of Pascal. The curve, so named by Roberval, can be used to trisect an angle. He discovered the curve in around 1637. (Limacon is from the Latin word for a snail the curve is a roulette formed when a circle rolls around the outside of another circle.) In a letter (see Lettre d'Étienne Pascal et Roberval à Fermat, samedi 16 août 1636) he actively argued in favour of Fermat's De maximis et minimis in opposition to Descartes who viewed the work in a very negative light. *SAU

1938 Lew Genrichowitsch Schnirelmann (2 January(15January 1905greg.) in Gomel; 24 September 1938 in Moscaw) . He was a Belarussian mathematician who made important contributions to the Goldbach conjecture. Using these ideas of compactness of a sequence of natural numbers he was able to prove a weak form of the Goldbach conjecture showing that every number is the sum of ≤ 20 primes.*SAU

1945 Hans (Wilhelm) Geiger (30 Sep 1882, 24 Sep 1945) was a German physicist who introduced the Geiger counter, the first successful detector of individual alpha particles and other ionizing radiations. After earning his Ph.D. at the University of Erlangen in 1906, he collaborated at the University of Manchester with Ernest Rutherford. He used the first version of his particle counter, and other detectors, in experiments that led to the identification of the alpha particle as the nucleus of the helium atom and to Rutherford's statement (1912) that the nucleus occupies a very small volume in the atom. Geiger returned to Germany in 1912 and continued to investigate cosmic rays, artificial radioactivity, and nuclear fission. *TIS

1999 Anneli Cahn Lax (23 Feb 1922 in Katowice, Poland - 24 Sept 1999 in New York City, New York, USA) Anneli Cahn was born in Katowice, then a German city, but now part of Poland, on February 23, 1922. Her family fled Hitler’s regime in 1935 and settled in New York. She married Peter Lax, a fellow mathematician,
in 1948. Their lives together included a shared love for mathematics. Perhaps her most important contribution to mathematics was as editor of the New Mathematics Library. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt on every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. Out of this endeavor grew the New Mathematical Library. The notion was to make accessible to interested high school students, and to a more general public, deep results in mathematics
described by research mathematicians. (This sort of work had long been going on in Eastern Europe.) Lax was asked to take over as general editor for this series, and under her guidance it grew to be the foremost mathematical expository
series in the language. Upon her death it was renamed in her honor. *Mark Saul, Obituary for the AMS VOl 47,#7

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

Sunday, 23 September 2018

On This Day in Math - September 23

We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work.
~Feynman, Richard Philips Nobel Lecture, 1966.

The 266th day of the year; 266 can be expressed as 222 in base 11.

266 is the sum of four cubes, $266 = 2^3 + 2^3 + 5^3 + 5^3 $ It is also the index of the largest proper subgroups of the sporadic group known as the Janko group J₁

EVENTS 1574 Tycho Brahe's rising fame while he lived in Copenhagen brings unwanted lecturing demands. In the capital his rising fame had attracted considerable attention, and some young nobles who were studying at the University requested him to deliver a course of lectures on some mathematical subject on which there were no lectures being given at that time. His friends Dancey and Pratensis urged him to consent to this proposal, but Tycho was not inclined to do so, until the King had also requested him to gratify the wishes of the students. He then yielded, and the lectures were commenced on the 23rd of September 1574, with an oration on the antiquity and importance of the mathematical sciences. *TYCHO BRAHE, A PICTURE OF SCIENTIFIC LIFE AND WORK IN THE SIXTEENTH CENTURY BY J. L. E. DREYER

1647 Descartes, on a visit on September 23-24 to France from Holland, met with Pascal. On this occasion Descartes may have recommended the experiment of noting the variation in the height of the barometer with altitude. [J. F. Scott, The Scientiﬁc Work of Ren´e Descartes, p. 6] *VFR
His visit only lasted two days and the two argued about the vacuum which Descartes did not believe in. Pascal had done a series of experiments on atmospheric pressure and proved to his satisfaction that a vacuum existed.Descartes wrote, rather cruelly, in a letter to Huygens after this visit that Pascal, " ...has too much vacuum in his head. " *SAU

Also present were Professor Roberval, of the College de France, a voluble anti-Cartesian, and Pascal's younger sister Jacqueline. Pascal brought out a calculating machine, his recent invention, and demonstrated its ability to add and subtract. Descartes was impressed. The talk turned to the vacuum. Pascal described his experiment; Descartes expressed doubt - a polite skirmish that might have ended there. But Roberval injected his opinion, and a heated argument ensued. Descartes took his leave.

The next morning, however, he returned - not Descartes the philosopher this time, but Descartes the physician. He sat for three hours by his patient's side, listened to his complaints, examined him, prescribed soups and rest. When Pascal was sick of staying in bed, Descartes said, he would be nearly well. Their views would remain opposed, but it was the supreme rationalist in his role as kindly doctor whom Pascal would later remember, and who may have been in his mind when he observed, "The heart has its reasons which reason knows nothing of"

*The Independent UK, Saturday 15 June 1996

1673 Hooke in his diary, "bought Pappus in Cornhill for 11sh. at ye crown." *Robert Hooke ‏@HookesLondon
Suspect but an not sure that this was Commandino's translation of Pappus's Mathematicae Collectiones

1763 The Princess Louise sailed for Barbados on 23 September. During the voyage Maskelyne and Charles Green took many lunar-distance observations (with Maskelyne later claiming that his final observation was within half of degree of the truth) and struggled a couple of times with the marine chair. Maskelyne’s conclusion was that the Jupiter’s satellites method of finding longitude would simply never work at sea because the telescope magnification required was far too high for use in a moving ship.
On 29 December 1763 he wrote his brother Edmund, reporting his safe arrival on 7 November after “an agreeable passage of 6 weeks”. He noted that he had been “very sufficiently employed in making the observations recommended to me by the Commissioners of Longitude” and that it was at times “rather too fatiguing”. *Board of Longitude project, Greenwich

1740 In a letter to Euler dated August 29th, 1740, Philippe Naudé (the Younger) asked Euler in how many ways a number n can be written as a sum of positive integers. In his answer written on September 12th (23rd), Euler explained that if we denote
this “partition number” by p(n), then

*Correspondence of Leonhard Euler with Christian Goldbach, Springer

1793 The new decimalized calendar was presented to the Jacobin-controlled National Convention on 23 September 1793, which adopted it on 24 October 1793 and also extended it proleptically to its epoch of 22 September 1792. The French Republican Calendar was a calendar created and implemented during the French Revolution, and used by the French government for about 12 years from late 1793 to 1805, and for 18 days by the Paris Commune in 1871. There were twelve months, each divided into three ten-day weeks called décades. The tenth day, décadi, replaced Sunday as the day of rest and festivity. The five or six extra days needed to approximate the solar or tropical year were placed after the months at the end of each year. The new system was designed in part to remove all religious and royalist influences from the calendar, and was part of a larger attempt at decimalisation in France. *Wik

1815 The Great September Gale of 1815 came ashore in New England on this date. This was the first hurricane, although the word had not been created yet, to hit New England in 180 yrs. In the aftermath of the Great Gale, the concept of a hurricane as a "moving vortex" was presented by John Farrar, Hollis Professor of Mathematics and Natural Philosophy at Harvard University. In an 1819 paper he concluded that the storm "appears to have been a moving vortex and not the rushing forward of a great body of the atmosphere". The word "hurricane" comes from Spanish huracán, from the Taino hurakán, “god of the storm.” While the Taino have been essentially wiped out by disease brought by the Spanish, there are still several words from the language remaining in English. Two of my favorites, Barbecue and Hammock. *Assorted sources (The Merriem Webster gives the first use of Hurricane in 1555, the same year as another Taino word, Yuca, was first used in English.)

1831 Faraday writes to Richard Phillips, “ I am busy just now again on Electro-Magnetism and think I have got hold of a good thing but can't say; it may be a weed instead of a fish that after all my labour I may at last pull up.” (It was a fish Michael!) * Michael Faraday, Bence Jones (ed.), The Life and Letters of Faraday (1870), Vol. 2, 3

1846 Neptune first seen. Le Verrier's most famous achievement is his prediction of the existence of the then unknown planet Neptune, using only mathematics and astronomical observations of the known planet Uranus. Encouraged by physicist Arago, Director of the Paris Observatory, Le Verrier was intensely engaged for months in complex calculations to explain small but systematic discrepancies between Uranus's observed orbit and the one predicted from the laws of gravity of Newton. At the same time, but unknown to Le Verrier, similar calculations were made by John Couch Adams in England. Le Verrier announced his final predicted position for Uranus's unseen perturbing planet publicly to the French Academy on 31 August 1846, two days before Adams's final solution, which turned out to be 12° off the mark, was privately mailed to the Royal Greenwich Observatory. Le Verrier transmitted his own prediction by 18 September letter to Johann Galle of the Berlin Observatory. The letter arrived five days later, and the planet was found with the Berlin Fraunhofer refractor that same evening, 23 September 1846, by Galle and Heinrich d'Arrest within 1° of the predicted location near the boundary between Capricorn and Aquarius. Le Verrier will be known by the phrase attributed to Arago: "the man who discovered a planet with the point of his pen." [Le Verrier also noted that the perihelion of Mercury was advancing more rapidly than Newtonian physics could account for, but he proposed in 1845 that this was due to a planet between Mercury and the sun which he called Vulcan…..oops] *Wik (It is a strange twist of fate that he died on the date on which his most famous prediction was verified, See below under deaths)

1884 Patent ﬁled for Hollerith tabulating machine. It was used in the 1890 census and became the model for computer cards. *VFR

1983 The Los Angeles Times reported that David Slowinski of Cray research has found the 29th Mersenne prime, 2^132,049-1. It turned out that this was actually the 30th, as the 29th would turn out to be 2^110,503 -1 found by Walter Colquitt ; Luke Welsh almost five years later on Jan 28, 1988 *VFR & Wik

BIRTHS
1768 William Wallace (23 September 1768, Dysart in Fife – 28 April 1843, Edinburgh) was a Scottish mathematician and astronomer who invented the eidograph. (A form of pantograph for reproducing images on a different scale) He mainly worked in the field of geometry and in 1799 became the first to publish the concept of the Simson line, which erroneously was attributed to Robert Simson by Poncelet. In 1807 he proved a result about polygons with an equal area, that later became known as the Bolyai–Gerwien theorem. His most important contribution to British mathematics however was, that he was one of the first mathematicians introducing and promoting the advancement of the continental European version of calculus in Britain.

Wallace's grave in Greyfriars Kirkyard, Edinburgh, 2012

He was assisted in his studies by John Robison (1739–1805) and John Playfair, to whom his abilities had become known. After various changes of situation, dictated mainly by a desire to gain time for study, he became assistant teacher of mathematics in the academy of Perth in 1794, and this post he exchanged in 1803 for a mathematical mastership in the Royal Military College at Great Marlow (afterwards at Sandhurst with a recommendation by Playfair). In 1819 he was chosen to succeed John Leslie (or John Playfair?) in the chair of mathematics at Edinburgh.
He developed a reputation for being an excellent teacher. Among his students was Mary Somerville. In 1838 he retired from the university due to ill health. He died in Edinburgh and is buried in Greyfriars Churchyard. *Wik

1785 Georg Scheutz (1785-1873), who with his son built a commercially available calculator based on Charles Babbage's Difference Engine, is born in Stockholm. After reading about the Difference Engine in 1833, Scheutz and son Edvard worked on a version that could process 15-digit numbers and calculate using fourth-order differences. The result won the gold medal at the Paris Exhibition in 1855 and was used by the Dudley Observatory in New York to calculate a few tables. A second copy was used by the British Registrar General to calculate tables for the developing life insurance industry. *CHM

1791 Johann Franz Encke (23 Sep 1791; 26 Aug 1865) German astronomer who in 1819 established the period of the comet now known by as Encke's Comet. At at 3.3 years it has the shortest period of any known. *TIS It was first recorded by Pierre Méchain in 1786, but it was not recognized as a periodic comet until 1819 when its orbit was computed by Encke. Comet Encke is believed to be the originator of several related meteor showers known as the Taurids (which are encountered as the Northern and Southern Taurids across November, and the Beta Taurids in late June and early July). Near-Earth object 2004 TG10 may be a fragment of Encke. Some also think it may have already had a part of it break off and hit the earth. "In 1908 Comet Encke was making a close pass near the Earth. It is believed that a 100 meter (m) diameter chunk of ice from Encke broke off and plowed into the atmosphere over the Stony Tunguska River in Siberia. The result was an air-burst explosion liberating the equivalent of 600 Hiroshima-size nuclear bombs, so much energy that sensitive instruments around the world recorded the resulting shock waves. Trees in the Siberian forests were leveled for dozens of miles around, and horses 400 miles away were knocked from their feet. There was no known loss of human life, but this is only because the impact site was so isolated. If the same ice chunk had, by chance, struck over a major population center, Tokyo, or New York, or Bombay, mega-deaths would have resulted. " *greatdreams.com

1819 Armand-Hippolyte-Louis Fizeau (23 Sep 1819; 18 Sep 1896) French physicist who was the first to measure the speed of light successfully without using astronomical calculations (1849). Fizeau sent a narrow beam of light between gear teeth on the edge of a rotating wheel. The beam then traveled to a mirror 8 km/5 mi away and returned to the wheel where, if the spin were fast enough, a tooth would block the light. Knowing this time from the rotational speed of the wheel, and the mirror's distance, Fizeau directly measured the speed of light. He also found that light travels faster in air than in water, which confirmed the wave theory of light, and that the motion of a star affects the position of the lines in its spectrum. With Jean Foucault, he proved the wave nature of the Sun's heat rays by showing their interference (1847).*TIS

1851 Ellen Amanda Hayes (September 23, 1851 – October 27, 1930) was an American mathematician and astronomer. Born in Granville, Ohio (pop 1,127 in the 1880 census) she graduated from Oberlin College in 1878 and began teaching at Adrian College. From 1879 to her 1916 retirement, she taught at Wellesley College, where she became head of the mathematics department in 1888 and head of the new department in applied mathematics in 1897.Hayes was also active in astronomy, determining the orbit of newly discovered 267 Tirza while studying at the Leander McCormick Observatory at the University of Virginia.
She wrote a number of mathematics textbooks. She also wrote Wild Turkeys and Tallow Candles (1920), an account of life in Granville, and The Sycamore Trail (1929), a historical novel.
Hayes was a controversial figure not just for being a rare female mathematics professor in 19th century America, but for her embrace of radical causes like questioning the Bible and gender clothing conventions, suffrage, temperance, socialism, the 1912 Lawrence Textile Strike, and Sacco and Vanzetti. She was the Socialist Party candidate for Massachusetts Secretary of State in 1912, the first woman in state history to run for statewide office. She did not win the race, but did receive more votes than any Socialist candidate on the ballot, including 2500 more than their gubernatorial candidate.
Hayes was concerned about under-representation of women in mathematics and science and argued that this was due to social pressure and the emphasis on female appearance, the lack of employment opportunities in those fields for women, and schools which allowed female students to opt out of math and science courses.
Her will left her brain to the Wilder Brain Collection at Cornell University. Her ashes were buried in Granville, Ohio. *Wik

1869 Typhoid Mary Mallon (23 Sep 1869; 11 Nov 1938) famous typhoid carrier in the New York City area in the early 20th century. Fifty-one original cases of typhoid and three deaths were directly attributed to her (countless more were indirectly attributed), although she herself was immune to the typhoid bacillus (Salmonella typhi). The outbreak of Typhus in Oyster Bay, Long Island, in 1904 puzzled the scientists of the time because they thought they had wiped out the deadly disease. Mallon's case showed that a person could be a carrier without showing any outward signs of being sick, and it led to most of the Health Code laws on the books today. She died not from typhoid but from the effects of a paralytic stroke dating back to 25 Dec 1932.*TIS

1921 Albert Messiah (23 September 1921, Nice -) is a French physicist.
He spent the Second World War in the French Resistance: he embarked June 22, 1940 in Saint-Jean-de-Luz to England and participated in the Battle of Dakar with Charles de Gaulle in September 1940. He joined the Free French Forces in Chad, and the 2nd Armored Division in September 1944, and participated in the assault of Hitler's Eagle's nest at Berchtesgaden in 1945.
After the war, he went to Princeton to attend the seminar of Niels Bohr on quantum mechanics. He returned to France and introduced the first general courses of quantum mechanics in France, at the University of Orsay. His textbook on quantum mechanics (Dunod 1959) has trained generations of French physicists.
He was the director of the Physics Division at the CEA and professor at the Pierre and Marie Curie University. *Wik

1968 Wendelin Werner (September 23, 1968 - ) is a German-born French mathematician working in the area of self-avoiding random walks, Schramm-Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal. He is currently professor at ETH Zürich. *Wik

DEATHS
1657 Joachim Jungius was a German mathematician who was one of the first to use exponents to represent powers and who used mathematics as a model for the natural sciences. *SAU

1877 Urbain-Jean-Joseph Le Verrier (11 Mar 1811; 23 Sep 1877 at age 66) French astronomer who predicted by mathematical means the existence of the planet Neptune. He switched from his first subject of chemistry to to teach astronomy at the Ecole Polytechnique in 1837 and worked at the Paris Observatory for most of his life. His main activity was in celestial mechanics. Independently of Adams, Le Verrier calculated the position of Neptune from irregularities in Uranus's orbit. As one of his colleagues said, " ... he discovered a star with the tip of his pen, without any instruments other than the strength of his calculations alone. In 1856, the German astronomer Johan G. Galle discovered Neptune after only an hour of searching, within one degree of the position that had been computed by Le Verrier, who had asked him to look for it there. In this way Le Verrier gave the most striking confirmation of the theory of gravitation propounded by Newton. Le Verrier also initiated the meteorological service for France, especially the weather warnings for seaports. Incorrectly, he predicted a planet, Vulcan, or asteroid belt, within the orbit of Mercury to account for an observed discrepancy (1855) in the motion in the perihelion of Mercury. *TIS

1822 Joseph-Louis-François Bertrand (11 Mar 1822; 5 Apr 1900 at age 78) was a French mathematician and educator and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. In 1845 Bertrand conjectured that there is at least one prime between n and (2n-2) for every n>3, as proved five years later by Chebyshev. In 1855 he translated Gauss's work on the theory of errors and the method of least squares into French. He wrote a number of notes on the reduction of data from observations. *TIS At age 11 he started to attend classes at the Ecole Polytechnique, where his Uncle Duhamel was a well-known professor of mathematics. At 17 he received his doctor of science degree. *VFR

1897 “Bourbaki is a pen name of a group of younger French mathematicians who set out to publish an encyclopedic work covering most of modern mathematics.” So wrote Samuel Eilenberg in Mathematical Reviews, 3(1942), 55–56. He was the ﬁrst to reveal in print that Bourbaki was a pseudonym—but the name was appropiated from a real general, Charles Denis Sauter Bourbaki, who died on this date at the age of 81. See Joong Fang, Bourbaki, Paideia Press, 1970, pp. 24, *VFR

1919 Heinrich Bruns was interested in astronomy, mathematics and geodesy and worked on the three body problem.*SAU

1971 James Waddell Alexander (19 Sept 1888, 23 Sept 1971) In a collaboration with Veblen, he showed that the topology of manifolds could be extended to polyhedra. Before 1920 he had shown that the homology of a simplicial complex is a topological invariant. Alexander's work around this time went a long way to put the intuitive ideas of Poincaré on a more rigorous foundation. Also before 1920 Alexander had made fundamental contributions to the theory of algebraic surfaces and to the study of Cremona transformations.
Soon after arriving in Princeton, Alexander generalised the Jordan curve theorem and continued his work, now exclusively on topology, with an important paper on the Jordan-Brouwer separation theorem. This latter paper contains the Alexander Duality Theorem and Alexander's lemma on the n-sphere. In 1924 he introduced the now famous Alexander horned sphere.
In 1928 he discovered the Alexander polynomial which is much used in knot theory. In the same year the American Mathematical Society awarded Alexander the Bôcher Prize for his memoir, Combinatorial analysis situs published in the Transactions of the American Mathematical Society two years earlier. Knot theory and the combinatorial theory of complexes were the main topics on which he worked over the following few years.
The theory which is now called the Alexander-Spanier cohomology theory, was introduced in 1935 by Alexander but was generalised by Spanier in 1948 to the form seen today. Also around 1935 Alexander discovered cohomology theory, at essentially the same time as Kolmogorov, and the theory was announced in the 1936 Moscow Conference. *SAU

2004 Bryce Seligman DeWitt (January 8, 1923 – September 23, 2004) was a theoretical physicist who studied gravity and field theories.
He approached the quantization of general relativity, in particular, developed canonical quantum gravity and manifestly covariant methods that use the heat kernel. B. DeWitt formulated the Wheeler–DeWitt equation for the wavefunction of the Universe with John Archibald Wheeler and advanced the formulation of the Hugh Everett's many-worlds interpretation of quantum mechanics. With his student Larry Smarr he originated the field of numerical relativity.
He received his bachelor's, master's and doctoral degrees from Harvard University. His Ph.D. (1950) supervisor was Julian S. Schwinger. Afterwards he worked at the Institute for Advanced Study, the University of North Carolina at Chapel Hill and the University of Texas at Austin. He was awarded the Dirac Prize in 1987, the American Physical Society's Einstein Prize in 2005, and was a member of the National Academy of Sciences and the American Academy of Arts and Letters.
He was born Carl Bryce Seligman but he and his three brothers added "DeWitt" from their mother's side of the family, at the urging of their father, in 1950. This is similar to Spanish naming customs, where a person bears two surnames, one being from their father and the other from their mother. Twenty years later this change of name so angered Felix Bloch that he blocked DeWitt's appointment to Stanford University and DeWitt instead moved to Austin, Texas. He served in World War II as a naval aviator. He was married to mathematical physicist Cécile DeWitt-Morette. He died September 23, 2004 from pancreatic cancer at the age of 81. He is buried in France, and was survived by his wife and four daughters. *Wik

Saturday, 22 September 2018

On This Day in Math - September 22

Nothing is too wonderful to be true if it be consistent with the laws of nature.

~Michael Faraday in his Laboratory Notebook

The 265th day of the year; 265 is !6 (sub-factorial 6), the number of ways that six ordered objects can be mis-ordered so that each is in the wrong spot. See Subfactorial

The term "subfactorial "was introduced by Whitworth (1867 or 1878; Cajori 1993, p. 77). Euler (1809) calculated the first ten terms. For example, the only derangements of {1,2,3} are {2,3,1} and {3,1,2}, so !3=2 (Pssst, students... You can find !n by dividing n! by e, and rounding to nearest integer)

265 is the sum of two squares in two different ways, including one that is the sum of consecutive squares. $265 = 3^2 + 16^2 = 11^2 + 12^2 $

265² is also the sum of two squares in two different ways, making 265 the hypotenuse of two Pythagorean Triangles.

EVENTS
1602 In a public address at T¨ubingen University, Michael Mastlin, Kepler’s teacher, on the basis of chronological research put Jesus’ birth more than four years before the conventional date of A.D. 1. This date is now generally accepted. *VFR

1636 From a letter by Fermat to Roberval, it is clear that Fermat conceived the idea of analytic geometry as early as 1629, yet he published nothing on the subject. [Struik, Source Book, p. 397] *VFR

1792 This date is considered the beginning of the Republican Calendar of France, for on this date the Republic was proclaimed and this was also the date of the autumnal equinox in that year. The new calendar was not oﬃcially approved until 5 October 1793. *Cecil B. Read, “A book printed in the year VII,” The Mathematics Teacher, 59(1966), 138–140.

1822 “Jean-Francoise Champollion the younger wrote his famous Lettre `a Monsieur Dacier, secr´etaire perp´etuel de l’Acad´`ero¬emie royale des inscriptions et belles-lettres, relative a l’alphabet des hi´glyphes phon´etiques. On that day he opened the great book of Ancient Egypt, sealed for some two thousand years and now at last decipherable.” Quoted from p. 15 of Tutankhamen (1963) by Christiane Desroches-Noblecourt. *VFR

1986 In a decisive victory for the makers of a computer's insides, a federal judge ruled that code used to run computers and other electronic devices could be copyrighted like printed material.*CHM

2006 Britney Crystal Gallivan of Pomona, California was a keynote speaker at the September 22, 2006 National Council of Teachers of Mathematics convention. As a Junior in high school in 2002 she had disproved a commonly held mathematical myth that a piece of paper could not be folded more than eight times. Gallivan demonstrated that a single piece of toilet paper 4000 ft in length can be folded in half twelve times. Not only did she provide the empirical proof, but she also derived an equation that yielded the width of paper or length of paper necessary to fold a piece of paper of thickness t any n number of times. Wik

BIRTHS
1711 Thomas Wright (22 September 1711 – 25 February 1786) was an English astronomer, mathematician, instrument maker, architect and garden designer. He was the first to describe the shape of the Milky Way and speculate that faint nebulae were distant galaxies.
Wright is best known for his publication An original theory or new hypothesis of the Universe (1750), in which he explains the appearance of the Milky Way as "an optical effect due to our immersion in what locally approximates to a flat layer of stars."
Another of Thomas Wright's ideas, which is often attributed to Kant, was that many faint nebulae are actually incredibly distant galaxies.*Wik

1765 Paolo Ruffini born. He anticipated Abel by providing an almost correct proof of the insolubility of the quintic. *VFR Italian mathematician and physician who made studies of equations that anticipated the algebraic theory of groups. In 1799 Ruffini published a book on the theory of equations with his claim that quintics could not be solved by radicals, General theory of equations in which it is shown that the algebraic solution of the general equation of degree greater than four is impossible. Ruffini used group theory in his work but he had to invent the subject for himself. He also wrote on probability and the application of probability to evidence in court cases.*TIS (He also published the method now often called Horner's method ,,, see Horner below)

1769 Louis Puissant (22 Sept 1769, 10 Jan 1843) He is best remembered for his invention of a new map projection for a new map of France, and he was involved in the production of the map. The map was produced with considerable detail, the projection used spherical trigonometry, truncated power series and differential geometry. Puissant wrote on geodesy, the shape of the earth and spherical trigonometry. *SAU

1791 Michael Faraday born. (22 Sep 1791; 25 Aug 1867) English physicist and chemist whose many experiments contributed greatly to the understanding of electromagnetism. Although one of the greatest experimentalists, he was largely self-educated. Appointed by Sir Humphry Davy as his assistant at the Royal Institution, Faraday initially concentrated on analytical chemistry, and discovered benzene in 1825. His most important work was in electromagnetism, in which field he demonstrated electromagnetic rotation and discovered electromagnetic induction (the key to the development of the electric dynamo and motor). He also discovered diamagnetism and the laws of electrolysis. He published pioneering papers that led to the practical use of electricity, and he advocated the use of electric light in lighthouses. *TIS

DEATHS
1703 Vincento Viviani died. His problem of cutting four congruent windows in a hemispherical cupolo so that the remainder was quadrable led to Euler’s development of the double integral. *VFR The leading geometer of his time, who founded the Accademia del Cimento. As one of the first important scientific societies, this organization came before England's Royal Society. In 1639, at age 17, he became the student, secretary and assistant of Galileo (now blind) in Arcetri, until Galileo died in 1642. During his long career, Viviani published a number of books on mathematical and scientific subjects. He edited the first edition of Galileo's collected works (1655-1656), and worked tirelessly to have his master's memory rehabilitated. In 1660, together with Borelli, he measured the velocity of sound by timing the difference between the flash and the sound of a cannon. They obtained the value of 350 metres per second. *TIS

1837 William George Horner (1786 – 22 September 1837) was a British mathematician and schoolmaster. The invention of the zoetrope, in 1834 and under a different name (Daedaleum), has been attributed to him. *Wik
Horner is largely remembered only for the method, Horner's method, of solving algebraic equations ascribed to him by Augustus De Morgan and others. He published on the subject in the Philosophical Transactions of the Royal Society of London in 1819, submitting his article on 1 July. But Fuller has pointed out that, contrary to De Morgan's assertion, this article does not contain the method, although one published by Horner in 1830 does. Fuller has found that Theophilus Holdred, a London watchmaker, did publish the method in 1820 and comments"At first sight, Horner's plagiarism seems like direct theft. However, he was apparently of an eccentric and obsessive nature ... Such a man could easily first persuade himself that a rival method was not greatly different from his own, and then, by degrees, come to believe that he himself had invented it. "
This discussion is somewhat moot because the method was anticipated in 19th century Europe by Paolo Ruffini (What a strange coincidence that he dies on Ruffini's birthdate) , but had, in any case, been considered by Zhu Shijie in China in the thirteenth century. In the 19th and early 20th centuries, Horner's method had a prominent place in English and American textbooks on algebra. It is not unreasonable to ask why that should be. The answer lies simply with De Morgan who gave Horner's name and method wide coverage in many articles which he wrote.
Horner made other mathematical contributions, however, publishing a series of papers on transforming and solving algebraic equations, and he also applied similar techniques to functional equations. It is also worth noting that he gave a solution to what has come to be known as the "butterfly problem" which appeared in The Gentleman's Diary for 1815. The problem is the following:-
Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn. Suppose AD cuts PQ at X and BC cuts PQ at Y. Prove that M is also the midpoint of XY.

The butterfly problem, whose name becomes clear on looking at the figure, has led to a wide range of interesting solutions. Finally we mention that Horner published Natural magic, a familiar exposition of a forgotten fact in optics (1832). *SAU

1922 Chen Ning Yang (22 Sep 1922, )Chinese-American theoretical physicist who shared the 1957 Nobel Prize for Physics (with Tsung-Dao Lee) for a ground-breaking theory that the weak force between elementary particles did not conserve parity, thus violating a previously accepted law of physics. (Parity holds that the laws of physics are the same in a right-handed system of coordinates as in a left-handed system.) The theory was subsequently confirmed experimentally by Chien-Shiung Wu in observations of beta decay. Yang is also known for his collaboration with Robert L. Mills. They developed the Yang-Mills fields theory - a mathematical idea for describing interactions among elementary particles and fields*TIS

1956 Frederick Soddy (2 Sep 1877, 22 Sep 1956). English chemist and physicist who received the Nobel Prize for Chemistry in 1921 for investigating radioactive substances. He suggested that different elements produced in different radioactive transformations were capable of occupying the same place on the Periodic Table, and on 18 Feb 1913 he named such species "isotopes" from Greek words meaning "same place." He is credited, along with others, with the discovery of the element protactinium in 1917 *TIS
Soddy is also the author of a mathematical poem about the solution to Descarte's four tangent circles theorem from the letter to Princess Elisabeth of Bohemia. The poem is called The Kiss Precise, and begins:

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

The complete poem and more about the history of the problem can be found here.

1970 Vojtěch Jarník (22 Dec 1897 , 22 Sept 1970) a Czech mathematician. His main area of work was in number theory and mathematical analysis; he proved a number of results on lattice point problems. He also developed the graph theory algorithm known as Prim's algorithm. The Vojtěch Jarník International Mathematical Competition, held each year in Ostrava, is named in his honor.*Wik

1979 Charles Ehresmann (19 April 1905, 22 Sept 1979) He was one of the creators of differential topology. Beginning in 1941, Ehresmann made major contributions toward establishing the current view of fibre spaces, manifolds, foliations and jets. His work in the creation and development of fibre spaces followed on from the study of a special case made earlier by Seifert and Whitney.
After 1957 Ehresmann became a leader in category theory and he worked in this area for 20 years. His principal achievements in this area concern local categories and structures defined by atlases, and germs of categories. The article [3] contains a list of 139 articles written by Ehresmann during his productive career as well as listing several volumes which he edited. *SAU

Friday, 21 September 2018

On This Day in Math - September 21

To throw in a fair game at Hazards only three-spots, when something great is at stake, or some business is the hazard, is a natural occurrence and deserves to be so deemed; and even when they come up the same way for a second time if the throw be repeated. If the third and fourth plays are the same, surely there is occasion for suspicion on the part of a prudent man.
~Girolamo Cardano

The 264th day of the year; 264 = 2³x3x11 is a harshad number (a number divisible by the sum of its digits). The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The numbers were defined and named by the famous Indian Mathematician D. R. Kaprekar.

Jim Wilder @wilderlab pointed out that the sum of all 2-digit numbers you can make from 264 totals 264... 24 + 42 + 26 + 62 + 46 + 64.

264² = 69696, a palindrome; and 264 is the sum of ten consecutive primes.

Events
1781 Writing to his friend and mentor d’Alembert, Lagrange expressed concern that mathematics was reaching its creative end. “It seems,” he wrote, “that the mine is almost too deep already, and unless new seams are discovered, it will be necessary to abandon it sooner or later. Physics and chemistry now offer riches that are more brilliant and easier to exploit.” *Amir R. Alexander , Tragic Mathematics, Isis, Vol. 97, No. 4, December 2006

1784 The nation's first daily newspaper, the Pennsylvania Packet and Daily Advertiser, began publication on September 21, 1784. Many independent newspapers ran before that on a weekly or monthly basis. America's first independent newspaper, the New England Courant, was published by Benjamin Franklin's older brother in 1721. By the start of the Revolutionary War in 1775, there were 37 independent newspapers to keep the colonists informed. *Libray of Congress

1925 Edith Clarke patent for the Clark Calculator is approved. The calculator was a simple graphical device that solved equations involving electric current, voltage and impedance in power transmission lines. The device could solve line equations involving hyperbolic functions ten times faster than previous methods. She filed a patent for the calculator in 1921 and it was granted in 1925. Ms. Clarke is generally thought of as the first female electrical engineer in the U. S.

1984 Science reported (pp. 1379-1380) that Narendra Karmarkar of AT & T Bell Labs found a practical polynomial-time algorithm that is far faster than the simplex algorithm for linear programming problems. [Mathematics Magazine 58 (1985), p. 53]. *VFR

2012 Clear skies allowed a clear view of the fire balls which were witnessed right across the UK, Ireland and even parts of north west Europe.Bright 'meteor-like' tails could be seen in the sky for approximately two minutes at 10.55pm on Friday night.
The fireball was also seen in the US, "Portsmouth, RI, USA 2245 EST 4 to 5 seconds South to North Initially white, turned orange, then turned greenish-blue as it got low on horizon Like a flare but definately not a flare. Yes, from the "ball" itself. The tail was approximately 5 times longer than the ball itself. The tail remained a bright white even though the ball changed color. Was definitely not the typical "shooting star"."
According to the modeling done by Finnish mathematician Esko Lyytinen, the big UK fireball of the 21st of September was captured by Earth`s gravity.
After one circle around the Earth one of the remnants seems to have re-entered the skies over North America.
"It looks now that the fireball witnessed 155 minutes later in US and Canada, may have been one fragment of the British fireball, most probably the biggest one. This was its second entry into the Earth`s atmosphere", Lyytinen says. "If so, this is historical scientific observation, but it needs to be confirmed." * LunarMeteorite*Hunter and other sources

BIRTHS
1623 Stefano degli Angeli (21 Sept 1623 , 11 Oct 1697) His many mathematical works were on infinitesimals and he used them to study spirals, parabolas and hyperbolas. While in Venice he published De infinitorum parabolis (1654), De infinitorum spiralium spatiorum mensura (1660) which contains a generalisation of Archimedes' spiral, and De infinitorum cochlearum mensuris ac centris gravitatis (1661) which carries out Torricelli's intention of finding the centre of gravity of a solid body called a cochlea. The approach followed by Angeli in all these works is that of his teacher Cavalieri and of Torricelli, so when Guldin and Tacquet attacked these methods and defended the approach of the ancient Greeks, Angeli disputed with them over indivisibles. One has to see both sides in this argument for although Angeli's methods were much more powerful, they were less rigorous than the method of exhaustion adopted by Archimedes. Angeli examined fluid statics based on Archimedes' principle and Torricelli's experiments. He published Della gravita dell aria e fluidi in 1671 while holding the chair at Padua. He also considered the motion bodies falling towards a rotating Earth. Of course Angeli held the chair at Padua which had been held earlier by Galileo and his work shows strong influences from his predecessor. For example Angeli often refers to Galileo in his writings on physics, showing clearly how he has been influenced, particularly in terms of ways of approaching problems via the experimental method. Also clearly influenced by Galileo is Angeli's writings on the two systems of Ptolemy and Copernicus which he writes in Galileo's dialogue style.*SAU

1853 Heike Kamerlingh Onnes (21 Sep 1853; 21 Feb 1926) Dutch winner of the Nobel Prize for Physics in 1913 for his work on low-temperature physics and his production of liquid helium. He discovered superconductivity, the almost total lack of electrical resistance in certain materials when cooled to a temperature near absolute zero.*TIS

1884 Denes König (21 Sept 1884, 19 Oct 1944) His book, Theorie der endlichen und unendlichen Graphen, was published in 1936, and was a major factor in the growth of interest in graph theory worldwide. It was eventually translated into English under the title Theory of finite and infinite graphs (translated by R McCoart), Birkhauser, 1990; this also contains a biographical sketch by Tibor Gallai.
König's work on the factorisation of bipartite graphs relates closely to the marriage problem of Philip Hall. König's use of graphs to give a simpler proof of a determinant result of Frobenius seems to have led to some hostility between the two men.
After the Nazi occupation of Hungary, König worked to help persecuted mathematicians. This led to his death a few days after the Hungarian National Socialist Party took over the country. *SAU

1895 Joseph Leonard Walsh (21 Sept 1895, 6 Dec 1973) Walsh had a remarkable publication record. An obituary by Morris Marden (a student of Walsh) lists 279 articles, 7 books and 31 PhD students. He studied the relative location of the zeros of pairs of rational functions, zeros and topology of extremal polynomials, the critical points and level lines of Green's functions and other harmonic functions, conformal mappings, Padé approximation, and the interpolation and approximation of continuous, analytic or harmonic functions. Sewell writes "Polynomial approximation was neither discovered nor invented by J L Walsh (which may come as a surprise to some mathematicians). He is the one individual, however, who took a few scattered results on the subject and extended them, added mightily to them, and knit the whole together into a comprehensive, coherent theory." *SAU

1899 Juliusz Paweł Schauder (September 21, 1899, Lwów, Austria-Hungary – September 1943, Lwów, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equations and mathematical physics.
He had to fight in World War I right after his graduation from school. He was captured and imprisoned in Italy. He entered the university in Lwów in 1919 and received his doctorate in 1923. He got no appointment at the university and continued his research while working as teacher at a secondary school. Due to his outstanding results, he obtained a scholarship in 1932 that allowed him to spend several years in Leipzig and, especially, Paris. In Paris he started a very successful collaboration with Jean Leray. Around 1935 Schauder obtained the position of a senior assistant in the University of Lwów.
Schauder was Jewish, and after the invasion of German troops in Lwów it was impossible for him to continue his work. In his letters to Swiss mathematicians, he wrote that he had important new results, but no paper to write them down. He was executed by the Gestapo, probably in October 1943.
Most of his mathematical work belongs to the field of functional analysis, being part of a large Polish group of mathematicians, i.e. Lwów School of Mathematics. They were pioneers in this area with wide applications in all parts of modern analysis. Schauder is best known for the Schauder fixed point theorem which is a major tool to prove the existence of solutions in various problems, the Schauder bases (a generalization of an orthonormal basis from Hilbert spaces to Banach spaces), and the Leray−Schauder principle, a way to establish solutions of partial differential equations from a priori estimates. *Wik

1907 Sir Edward Crisp Bullard (21 Sep 1907; 3 Apr 1980) English marine geophysicist noted for his work in geomagnetism who made the first satisfactory measurements of geothermal heat-flow through the oceanic crust. In early work, he measured minute gravitational variations by timing the swings of an invariant pendulum, which he used to study the East African Rift Valley. Bullard helped to develop the theory of continental drift. He made a computer analysis of the precise fit of the rifted continental borders along the two sides of the Atlantic Ocean, and presented his results to the Royal Society of London. He developed a "dynamo" theory of geomagnetism, which explained the Earth's magnetic field results from the convection of molten material within the Earth's core. He was knighted in 1953.*TIS

1926 Donald A. Glaser (21 Sep 1926, 28 Feb 2013)American physicist, who was awarded the Nobel Prize for Physics in 1960 for his invention of the bubble chamber in which the behavior of subatomic particles can be observed by the tracks they leave. A flash photograph records the particle's path. Glaser's chamber contains a superheated liquid maintained in a superheated, unstable state without boiling. A piston causing a rapid decrease in pressure creates a tendency to boil at the slightest disturbance in the liquid. Then any atomic particle passing through the chamber leaves a track of small gas bubbles caused by an instantaneous boiling along its path where the ions it creates act as bubble-development centers.*TIS With the freedom that accompanies a Nobel Prize, he soon began to explore the new field of molecular biology, and in 1971 joined two friends, Ronald E. Cape and Peter Farley, to found the first biotechnology company, Cetus Corp., to exploit new discoveries for the benefit of medicine and agriculture. The company developed interleukin and interferon as cancer therapies, but was best known for producing a powerful genetic tool, the polymerase chain reaction, to amplify DNA. In 1991, Cetus was sold to Chiron Corp., now part of Novartis. Glaser died in his sleep Thursday morning, Feb. 28, at his home in Berkeley. He was 86. *Philosophy of Science Portal

DEATHS

1576 Girolamo Cardano (24 September 1501 – 21 September 1576) He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music.His gambling led him to formulate elementary rules in probability, making him one of the founders of the field.
One story says that it was by his own hand so as to fulﬁll his earlier astrological prediction of of his death on this date. *H. Eves, Introduction to the History of Mathematics, Pg 221...
He was the first to give a clinical description of typhus fever. His book, Ars magna ("Great Art," 1545) was one of the great achievements in the history of algebra, in which he published the solutions to the cubic and quartic equations.(Ars Magna was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learned from Tartaglia.*SAU) His mechanical inventions included the combination lock, the compass gimbal consisting of three concentric rings, and the universal joint to transmit rotary motion at various angles (as used in present-day vehicles). He contributed to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science and introduced the Cardan grille, a cryptographic tool (1550).*TIS

1842 Sir James Ivory (17 February 1765 – 21 September 1842) was a Scottish mathematician born in Dundee. He was essentially a self-trained mathematician, and was not only deeply versed in ancient and modern geometry, but also had a full knowledge of the analytical methods and discoveries of the continental mathematicians.
His earliest memoir, dealing with an analytical expression for the rectification of the ellipse, is published in the Transactions of the Royal Society of Edinburgh (1796); and this and his later papers on Cubic Equations (1799) and Kepler's Problem (1802) evince great facility in the handling of algebraic formulae. In 1804 after the dissolution of the flax-spinning company of which he was manager, he obtained one of the mathematical chairs in the Royal Military College at Marlow (afterwards removed to Sandhurst); and until the year 1816, when failing health obliged him to resign, he discharged his professional duties with remarkable success.*Wik

1859 Isidore Auguste Marie François Xavier Comte (28 January 1794 – 21 September 1859), better known as Auguste Comte (French: [oɡyst kɔ̃t]), was a French philosopher. He was a founder of the discipline of sociology and of the doctrine of positivism. He is sometimes regarded as the first philosopher of science in the modern sense of the term.
Strongly influenced by the utopian socialist Henri Saint-Simon, Comte developed the positive philosophy in an attempt to remedy the social malaise of the French Revolution, calling for a new social doctrine based on the sciences. Comte was a major influence on 19th-century thought, influencing the work of social thinkers such as Karl Marx, John Stuart Mill, and George Eliot.[3] His concept of sociologie and social evolutionism, though now outdated, set the tone for early social theorists and anthropologists such as Harriet Martineau and Herbert Spencer, evolving into modern academic sociology presented by Émile Durkheim as practical and objective social research.
Comte's social theories culminated in the "Religion of Humanity", which influenced the development of religious humanist and secular humanist organizations in the 19th century. Comte likewise coined the word altruisme (altruism)*Wik

1936 Frank Hornby (15 May 1863, 21 Sep 1936) English inventor and toy manufacturer who patented the Meccano construction set in 1901. This toy used perforated metal strips, wheels, roods, brackets, clips and assembly nuts and bolts to build unlimited numbers of models. His original sets, marketed as "Mechanics Made Easy" produced in a rented room, were initially sold at only one Liverpool toy shop. By 1908, he had formed his company, Meccano Ltd., and within five more years had established manufacturing in France, Germany, Spain and the U.S. He introduced Hornby model trains in 1920, originally clockwork and eventually electrically powered with tracks and scale replicas of associated buildings. The "Dinky" range of miniature cars and other motor vehicles was added in 1933. *TIS

1937 Chrystal Macmillan was the first female science graduate at Edinburgh University and the first female honours graduate in Mathematics. She went on to study at Berlin. She was the first woman to plead a case before the House of Lords. She became active in the Women's Suffrage Movement and went on to become a lawyer.*SAU

1950 Edward Arthur Milne (14 Feb 1896, 21 Sep 1950) English astrophysicist and cosmologist best known for his development of kinematic relativity. Poor eyesight prevented him from active service in WWI, he did important war service in research in ballistics and sound ranging, and problems related to the atmosphere of the earth.. From 1920-29, he studied problems of radiative equilibrium and the theory of stellar atmospheres. He extended work done earlier by Schuster and by Schwarzschild, which he combined in a mathematical interesting integral equation now known as Milne's integral equation. Later, he turned to the theory of stellar structure and cosmology. After 1932, he concentrated on a new form of relativity called kinematic relativity, an alternative to Einstein's general theory.*TIS (In Eurekas and Euphorias Walter Gratzer tells an interesting story about Milne's rejected offer to provide his services to the war effort in WWII. Milne had given important service (above) in WWI and wrote to offer his services for this war as well, but received a rather dismissive letter to which he took offense. He used his extensive connections to have his anger made known to the higher-ups at the War Office. Eventually he received a request from a Brigadier General to come to his office. Milne arrived and amidst his tirade advised the General that the War Office should know that this war would be a scientific one, and the way he was treated was not the way to make the best use of eminent scientists. The General waited out Milne's outburst, and then asked a single question, "Did you win the Adams Prize in your year?" When Milne said he had not, but asked what that had to do with anything, the General replied, "I did!"
I'm not sure what, if any, were Milne's contributions to the war effort in WWII.)

1981 Henry George Forder (27 Sept 1889, 21 Sept 1981) Forder spent much of his career in the Chair of Mathematics at Auckland. In fact he only once left New Zealand after settling there, this being in 1947 when he spent part of his leave in England. He spent 21 years building up the Mathematics Department at Auckland from a Department of a professor with one assistant when he arrived to one of six staff by the time he retired in 1955.
It is the books that Forder wrote which have given him a high reputation in the mathematical world. These are: The Foundations of Euclidean Geometry (1927), A School Geometry (1930), Higher Course Geometry (1931), The Calculus of Extension (1941), Geometry (1950), and Coordinates in Geometry (1953). In the Preface to the first of these, Forder writes, "Although the Euclidean geometry is the oldest of the sciences and has been studied critically for over two thousand years, it seems there is no textbook which gives a connected and rigorous account of that doctrine in the light of modern investigations. It is hoped that this book will fill the gap."
Geometry (1950) was reviewed by Donald Coxeter who was clearly fascinated by Forder's use of language, "The two-cusped epicycloid is described as the bright curve seen "when the sun shines on a cup of tea." ... The chapter on logical structure stresses the abstract nature of the order relation (ABC) by comparing it with the human relation "A prefers C to B." The possibility of coordinatising any descriptive geometry of three or more dimensions is epitomized in the statement that "we can create magnitudes from a mere muchness," and Archimedes' axiom in the statement that "you will always reach home, if you walk long enough." *SAU