**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. It is also the index of the largest proper subgroups of the sporadic group known as the Janko group

*J*

_{1 }

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**EVENTS**

**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

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

**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**born. He worked on geometry and discovered the (so-called) Simson line of a triangle. *SAU

**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 Americanmathematician 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

**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

Credits

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum