## Wednesday 27 September 2023

### On This Day in Math - September 27

Algebra exists only for the elucidation of geometry.

~William Edge

The 270th day of the year; the harmonic mean of the factors of 270 is an integer. The first three numbers with this property are 1, 6, and 28 (which are all perfect #s).. what is the next one? Often called harmoni numbers, they are sometimes called Ore numbers for Øystein Ore, who studied them, and showed that all perfect #s are harmonic. . Many of them also have the arithmetic mean of their divisors is an integer, but not all.

270 is the sum of eight consecutive primes, 270 = 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 ; and the sum of three cubes $270={3}^{3}+{3}^{3}+{6}^{3}$.

10! = 3628800 has 270 factors. (A good high school student might be able to confirm this quickly.)

EVENTS

14 A.D.: A total lunar eclipse marked the death of Augustus: "The Moon in the midst of a clear sky became suddenly eclipsed; the soldiers who were ignorant of the cause took this for an omen referring to their present adventures: to their labors they compared the eclipse of the planet, and prophesied 'that if to the distressed goodness should be restored her wonted brightness and splendor, equally successful would be the issue of their struggle.' Hence they made a loud noise, by ringing upon brazen metal, and by blowing trumpets and cornets; as she appeared brighter or darker they exulted or lamented"
- Tacitus *NASA Lunar Eclipses

1830 American Statesman Charles Sumner (1811-1874) paid little attention as an undergraduate at Harvard, but a year after graduation he became convinced that mathematics was a necessary part of a complete education. To a classmate he wrote: “Just a week ago yesterday, I commenced Walker’s Geometry, and now have got nearly half through. All those problems, theorems, etc., which were such stumbling-blocks to my Freshman-year career, unfold themselves as easily as possible now. You will sooner have thought, I suppose, that ﬁre and water would have embraced than mathematics and myself; but, strange to tell, we are close friends now. I really get geometry with some pleasure. I usually devote four hours in the forenoon to it.” Quoted from Florian Cajori’s Mathematics in Liberal Education (1928), p. 115. *VFR  (Sumner was nearly beaten to death by a South Carolina Congressional Representative after a vindictive speech attacking the Kansas-Nebraska act, and it's authors.  His speech included direct insults, sexual innuendo, and made fun of South Carolina Senator Andrew Butler, one of the authors, by imitating his stroke impaired speech and mannerisms.  Butler's Nephew,  Preston Brooks, having decided that a duel could not take place between a gentleman (himself) and a drunk-lout(Sumner) stopped by Sumner's desk to confront him and nearly beat him to death with his cane.  Sumner lost the fight, but the incident put his star on the rise in the Northern states.)

In 1831, the first annual meeting of the British Association for the Advancement of Science was held in York. The British Association had been established in the same year by Sir David Brewster, R.I. Murchison and others. One of the association's main objectives was to "promote the intercourse of those who cultivate science with each other." The second annual meeting was held at Oxford (1832), and in following years at Cambridge, Edinburgh, Dublin, Bristol, Liverpool, Newcastle, Birmingham, Glasgow, Plymouth, Manchester and Cork respectively, until returning to York in 1844. It is incorporated by Royal Charter dated 21 Apr 1928.*TIS

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1858
Donati's Comet was successfully photographed  by W. Usherwood, a portrait photographer at Walton-on-the-Hill, Surrey, using a 7-second exposure with an f/2.4 portrait lens, the first time a comet had been photographed.  The second brightest comet of the century, and described by many as the most beautiful ever, it was first witnessed on June 2.  No record of the photograph is known to exist, although the Comet itself is still extant.

1905 E=mc2 the day that Einstein's paper outlining the significance of the equation arrived in the offices of the German journal Annalen der Physik.  "Does the inertia of a body depend on its energy content?"

1915 Giacomo Ciamician published his prediction of the use of solar energy in Science. He predicted that humans would one day be able to directly convert sunlight into energy, stored in a ‘fuel’ as an alternative to fossil fuels. Today, photovoltaic solar panels can produce electricity, but scientists are also working towards other methods of harnessing the sun’s power, such as solar fuels that mimic photosynthesis. *rsc.org

1919 Einstein writes to his ailing mother that "H. A. Lorentz has just telegraphed me that the British Expeditions have definitely confirmed the deflection of light by the sun." He adds consolation on her illness and wishes her "good days", and closes with "affectionately, Albert *Einstein Archives

In 1922, scientists at the Naval Aircraft Radio Laboratory near Washington, D.C., demonstrated that if a ship passed through a radio wave being broadcast between two stations, that ship could be detected, the essentials of radar. *TIS

1996 Kevin Mitnick, 33, was indicted on charges resulting from a 2 ½-year hacking spree. Police accused the hacker, who called himself "Condor," of stealing software worth millions of dollars from major computer corporations. The maximum possible sentence for his crimes was 200 years. *CHM    Mitnick served five years in prison — four and a half years pre-trial and eight months in solitary confinement — because, according to Mitnick, law enforcement officials convinced a judge that he had the ability to "start a nuclear war by whistling into a pay phone". He was released on January 21, 2000. During his supervised release, which ended on January 21, 2003, he was initially forbidden to use any communications technology other than a landline telephone. Mitnick fought this decision in court, eventually winning a ruling in his favor, allowing him to access the Internet. Under the plea deal, Mitnick was also prohibited from profiting from films or books based on his criminal activity for seven years. Mitnick now runs Mitnick Security Consulting​ LLC, a computer security consultancy. *Wik

BIRTHS

1677 Johann Doppelmayr was a German mathematician who wrote on astronomy, spherical trigonometry, sundials and mathematical instruments.*SAU   One of his most prominent  publications, the Historische Nachricht (1730), a history of mathematicians and artists of Nuremberg, Doppelmayr's home city.  This is a different kind of Nuremberg Chronicle, with short biographical accounts of a variety of scholars and painters, along with medallion portraits of many of them.

1719 Abraham Kästner was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. His work on the parallel postulate influenced Bolyai and Lobachevsky*SAU

1814  Daniel Kirkwood (27 Sep 1814; 11 Jun 1895) American mathematician and astronomer who noted in about 1860 that there were several zones of low density in the minor-planet population. These gaps in the distribution of asteroid distances from the Sun are now known as Kirkwood gaps. He explained the gaps as resulting from perturbations by Jupiter. An object that revolved in one of the gaps would be disturbed regularly by the planet's gravitational pull and eventually would be moved to another orbit. Thus gaps appeared in the distribution of asteroids where the orbital period of any small body present would be a simple fraction of that of Jupiter. Kirwood showed that a similar effect accounted for gaps in Saturns rings.*TIS  The asteroid 1951 AT was named 1578 Kirkwood in his honor and so was the lunar impact crater Kirkwood, as well as Indiana University's Kirkwood Observatory. He is buried in the Rose Hill Cemetery in Bloomington, Indiana, where Kirkwood Avenue is named for him. *Wik
 *Linda  Hall org

1824 Benjamin Apthorp Gould (27 Sep 1824; 26 Nov 1896) American astronomer whose star catalogs helped fix the list of constellations of the Southern Hemisphere Gould's early work was done in Germany, observating the motion of comets and asteroids. In 1861 undertook the enormous task of preparing for publication the records of astronomical observations made at the US Naval Observatory since 1850. But Gould's greatest work was his mapping of the stars of the southern skies, begun in 1870. The four-year endeavor involved the use of the recently developed photometric method, and upon the publication of its results in 1879 it was received as a signicant contribution to science. He was highly active in securing the establishment of the National Academy of Sciences.*TIS

1876 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California.
Hedrick was born in Union City, Indiana. After undergraduate work at the University of Michigan, he obtained a Master of Arts from Harvard University. With a Parker fellowship, he went to Europe and obtained his PhD from Göttingen University in Germany under the supervision of David Hilbert in 1901. He then spent several months at the École Normale Supérieure in France, where he became acquainted with Édouard Goursat, Jacques Hadamard, Jules Tannery, Émile Picard and Paul Émile Appell, before becoming an instructor at Yale University. In 1903, he became professor at the University of Missouri.
He was involved in the creation of the Mathematical Association of America in 1916 and was its first president.
His work was on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.
He moved in 1920 to UCLA to become head of the department of mathematics. In 1933, he was giving the first graduate lecture on mathematics at UCLA. He became provost and vice-president of the University of California in 1937. He humorously called his appointment The Accident, and told jokingly after this event, "I no longer have any intellectual interests —I just sit and talk to people." He played in fact a very important role in making of the University of California a leading institution. He retired from the UCLA faculty in 1942 and accepted a visiting professorship at Brown University. Soon after the beginning of this new appointment, he suffered a lung infection. He died at the Rhode Island hospital in Providence, Rhode Island. Two UCLA residence halls are named after him: Hedrick Hall in 1963, and Hedrick Summit in 2005.
Earle Raymond Hedrick worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics. *Wik

1843 Gaston Tarry was a French combinatorialist whose best-known work is a method for solving mazes.  The problem as stated by Euler is as follows:-
How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular 6 × 6 array such that no row or column duplicates a rank or a regiment?
Although an amateur mathematician, Tarry had an amazing ability to analyse combinatorial problems. One has simply to feel amazement at some of the problems he solved using purely combinatorial and calculating skills. We give some examples below to illustrate both the type of problem which interested him and also to illustrate his undoubted genius. Even more surprising is the fact that his mathematical achievements came after the age of fifty.
He published a solution to the problem of finding the way out of a maze in 1895, a problem which had been of interest from classical times. Tarry was not the first to give a systematic method so solve a maze, for Trémaux had found a method which was reported by Lucas in 1881. However, the method given by Tarry gave a different approach with an algorithm which, in today's terminology, would be described as depth-first search algorithm. It is particularly suitable to computer implementation. Tarry also gave a general method for finding the number of Euler circuits, and found lots of results pertaining to magic squares..

*SAU

1855 Paul Appell (27 September 1855 – 24 October 1930), also known as Paul Émile Appel, was a French mathematician and Rector of the University of Paris. The concept of Appell polynomials is named after him, as is rue Paul Appell in the 14th arrondissement of Paris.*Wik

1876 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California. He worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.*Wik

1879 Hans Hahn was an Austrian mathematician who is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass. *SAU

1892 Mykhailo Pilipovich Krawtchouk (27 Sept 1892 in Chovnitsy, (now Kivertsi) Ukraine - 9 March 1942 in Kolyma, Siberia, USSR) In 1929 Krawtchouk published his most famous work, Sur une généralisation des polynômes d'Hermite. In this paper he introduced a new system of orthogonal polynomials now known as the Krawtchouk polynomials, which are polynomials associated with the binomial distribution.
However his mathematical work was very wide and, despite his early death, he was the author of around 180 articles on mathematics. He wrote papers on differential and integral equations, studying both their theory and applications. Other areas he wrote on included algebra (where among other topics he studied the theory of permutation matrices), geometry, mathematical and numerical analysis, probability theory and mathematical statistics. He was also interested in the philosophy of mathematics, the history of mathematics and mathematical education. Krawtchouk edited the first three-volume dictionary of Ukrainian mathematical terminology. *SAU

1919 James Hardy Wilkinson (27 September 1919 – 5 October 1986) was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.
He received the Turing Award in 1970 "for his research in numerical analysis to facilitate the use of the high-speed digital computer, having received special recognition for his work in computations in linear algebra and 'backward' error analysis." In the same year, he also gave the John von Neumann Lecture at the Society for Industrial and Applied Mathematics.   The J. H. Wilkinson Prize for Numerical Software is named in his honour.*Wik

DEATHS

1783 Étienne Bézout was a French mathematician who is best known for his theorem on the number of solutions of polynomial equations.*SAU Bézout's theorem for polynomials states that if P and Q are two polynomials with no roots in common, then there exist two other polynomials A and B such that AP+BQ=1. *Wik

1997 William Edge graduated from Cambridge and lectured at Edinburgh University. He wrote many papers in Geometry. He became President of the EMS in 1944 and an honorary member in 1983. *SAU

2014 Jacqueline Anne ( Barton)Stedall (4 August 1950; Romford, Essex, U.K.–27 September 2014; Painswick, Gloucestershire) was a well-known historian of mathematics. Although her career as a researcher, scholar and university teacher lasted less than 14 years, it was greatly influential. Her nine books, more than 20 articles, input to the online edition of the manuscripts of Thomas Harriot, journal editorships and contributions to Melvyn Bragg’s Radio 4 programme In Our Time showed her exceptional breadth of scholarship.
Jackie Stedall came to Oxford in October 2000 as Clifford-Norton Student in the History of Science at Queen’s College. She held degrees of BA (later MA) in Mathematics from Cambridge University (1972), MSc in Statistics from the University of Kent (1973), and PhD in History of Mathematics from the Open University (2000). She also had a PGCE in Mathematics (Bristol Polytechnic 1991). In due course she became Senior Research Fellow in the Oxford Mathematical Institute and at Queen’s College, posts from which, knowing that she was suffering from incurable cancer, she took early retirement in December 2013.
This was her fifth career. Following her studies at Cambridge and Canterbury she had been three years a statistician, four years Overseas Programmes Administrator for War on Want, seven years a full-time parent, and eight years a schoolteacher before she became an academic. *Obituaries at The Guardian, Oxford Mathemtics, and Wik

2020 John David Barrow FRS (29 November 1952 – 26 September 2020) is an English cosmologist, theoretical physicist, and mathematician. He was currently Research Professor of Mathematical Sciences at the University of Cambridge. Barrow is also a writer of popular science and an amateur playwright.
In 1981 he joined the University of Sussex and rose to the rank of Professor and Director of the Astronomy Centre. In 1999, he became Professor in the Department of Applied Mathematics and Theoretical Physics and a fellow in Clare Hall at Cambridge University. He is Director of the Millennium Mathematics Project. From 2003–2007 he was Gresham Professor of Astronomy at Gresham College, London, and he has been appointed as Gresham Professor of Geometry from 2008–2011; only one person has previously held two different Gresham chairs. In 2008, the Royal Society awarded him the Faraday Prize.
Barrow died on 27 September 2020 from  colon cancer at the age of 67.  *Wik

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