Pat'sBlog

Saturday, 26 November 2022

On This Day in Math - November 26

One of the chief duties of a mathematician in acting as an advisor to scientists is to discourage them from expecting too much of mathematicians.
~Norbert Wiener

The 330th day of the year; if all the diagonals of an eleven sided regular polygon were drawn, they would have 330 internal intersections.

330 is the last year day which is a pentagonal number. It is the sum of fifteen consecutive integers starting with the integer 15. (All Pentagonal numbers follow a similar pattern) The average of all the pentagonal numbers up to 330 is the 15th triangular number.

A set of 11 points around a circle provide the vertices for 330 quadrilaterals.

EVENTS
1607 John Harvard, founder of Harvard College, born in London. Harvard, the oldest university in the U.S., was named for him in 1639. *VFR (The college was actually founded almost two years before Harvard made his deathbed bequest to fund it. The grateful colony changed the name of the college to honor its benefactor.)

1750 Euler presents his famous “Gem”; Vertices + Faces -2 = Edges, in two papers Euler presented several results relating the number of plane angles of a solid to the number of faces, edges, and vertices (he referred to “solid angles”). Euler also classified polyhedra by the number of solid angles they had. According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on November 26, 1750. The proofs were contained in a second paper. According to C. G. J. Jacobi, it might have been read to the Berlin Academy on September 9, 1751. According to the records there, it was presented to the St. Petersburg Academy on April 6, 1752. (There seems to be some question as to whether or not this theorem appears in Descartes. There is no question, it seems that he made statements that directly lead to the theorem, but Polya, Lakatos, and many others don't find an actual statement of the theorem in his work. I leave this question to the knowledgeable historians of the period to work out the intricacies .)

1789 President George Washington proclaimed Thanksgiving day the ﬁrst national holiday, acknowledging the nation’s “many and signal favors of Almighty God.” *VFR Washington declared the holiday in an Oct 3 declaration. Other Presidents throughout the years up to the civil war declared days of thanksgiving, not always in the fall. By 1858 proclamations appointing a day of thanksgiving were issued by the governors of 25 states and two territories. President Abraham Lincoln, prompted by a series of editorials written by Sarah Josepha Hale(she is known also as the author of "Mary Had a Little Lamb"), proclaimed a national Thanksgiving Day, to be celebrated on the final Thursday in November 1863. *Wik

1857 An amendment to the Sadlerian Chair to allow teaching of other modern topics beyond Algebra led to an application the same day for the position form Arthur Cayley. His Quickly published resume for the job included 318 of his publications. *A. J. Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age

1864 Charles Dodgson gives Alice Liddell (rhymes with “ﬁddle”) a hand-printed copy of Alice’s Adventures under Ground, a work he wrote for her. This was reproduced by Dover in 1965. See 4 July 1862. *VFR

In 1885, the first meteor trail was photographed in Prague, Czechoslovakia. This was part of the Andromedid meteor shower also known as the Bielids because they were caused by Comet Biela. William F. Denning (Bristol, England) noted the activity with rates averaging 100 per hour. On the next evening, 27 Nov, he declared "meteors were falling so thickly as the night advanced that it became almost impossible to enumerate them." Observers with especially clear skies had rates of about one meteor/second or 3600/hour. Meteor showers are produced by small fragments of cosmic debris entering the earth's atmosphere at extremely high speed. The debris originates from the intersection between a planet's orbit and a comet's orbit. *TIS If someone can supply a digital copy of this first photo, I would be greatly pleased.

1885 Smith Prize winners under new regulations announced in Nature Magazine. A. N. Whitehead gets only honorable mention in the new essay-based Smith's Prize.
And the winners are...."awarded to two essays declared equal in merit, viz. that of Mr. H. E. G. Gallop, Fellow of Trinity College, Second Wrangler in 1883, 1st Division in Part III., 1884, subject, “The Distribution of Electricity on the Circular Disk and Spherical Bowl”; and that of Mr. R. Lachlan, Fellow of Trinity College, 3rd Wrangler, 1883, 1st Division in Part III., 1884, subject “Systems of Circles.” It is further announced that the essay by Mr. C. Chree, Fellow of King’s College, on “Elastic Solids,” and that of Mr. A. N. Whitehead, Fellow of Trinity College, on the “General Equations of Hydrodynamics,” deserved honourable mention." *nature.com

BIRTHS
1894 Norbert Wiener (26 Nov 1894; 18 Mar 1964) U.S. mathematician, who established the science of cybernetics, a term he coined, which is concerned with the common factors of control and communication in living organisms, automatic machines, and organizations. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century. His work on generalised harmonic analysis and Tauberian theorems won the Bôcher Prize in 1933 when he received the prize from the American Mathematical Society for his memoir Tauberian theorems published in Annals of Mathematics in the previous year. His extraordinarily wide range of interests included stochastic processes, quantum theory and during WW II he worked on gunfire control. *TIS Cybernetics, published in 1948, was a major influence on later research into artificial intelligence. In the book, Wiener drew on World War II experiments with anti-aircraft systems that anticipated the course of enemy planes by interpreting radar images. Wiener also did extensive analysis of brain waves and explored the similarities between the human brain and a modern computing machine capable of memory association, choice, and decision making.*CHM (Wiener is somewhat revered as the ultimate absent-minded professor. An anecdote, almost certainly exaggerated, I used to share with my classes went something like this: Wiener had moved to a new address, and his wife knowing of his forgetfulness wrote a note with his new address and put it in his coat pocket. During the day struck by a mathematical muse he whipped out the piece of paper and scribbled notes on the back, then realizing his idea had been wrong, he tossed the piece of paper away and went about his day. In the afternoon he returned to his old house out of habit and coming up to the empty house remembered that he had moved, but not where. As he started to leave a young girl walked up and he stopped here. "Young lady, I am the famous mathematician Wiener. Do you know where I live?" The lass replied, "Yes, father, I'll show you the way home."... )

1895 Bertil Lindblad (26 Nov 1895; 26 Jun 1965) Swedish astronomer who contributed greatly to the theory of galactic structure and motion and to the methods of determining the absolute magnitude (true brightness, disregarding distance) of distant stars. He theorized that the areas around the center of a galaxy revolve and this is why it was flattened. Oort later proved that does indeed happen. He studied the structure and dynamics of star clusters, estimated the Milky Way's galactic mass, the period of our Sun's orbit, confirmed Harlow Shapley's direction and approximate distance to the center of the Galaxy, and developed spectroscopic means of distinguishing between giant and main sequence stars.*TIS

1940 Enrico Bombieri (26 Nov 1940, )Italian mathematician who was awarded the Fields Medal in 1974 for his major contributions to the study of the prime numbers, to the study of univalent functions and the local Bieberbach conjecture, to the theory of functions of several complex variables, and to the theory of partial differential equations and minimal surfaces. "Bombieri's mean value theorem", which concerns the distribution of primes in arithmetic progressions which is obtained by an application of the methods of the large sieve. Between 1979 and 1982 Bombieri served on the executive committee of the International Mathematical Union. Bombieri now works in the United States. In 1996 Bombieri was elected to membership of the National Academy of Sciences.*TIS

DEATHS
1896 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

1965 Zoárd Geöcze (1873–1916) was a Hungarian mathematician famous for his theory of surfaces (Horváth 2005:219ff). He was born August 23, 1873 in Budapest, Hungary and died November 26, 1916 in Budapest. *Wik

1968 Georgii Nikolaevich Polozii (23 April 1914 in Transbaikal, Russia - 26 Nov 1968 in Kiev, Ukraine) Georgii Polozii studied at Saratov University which had been founded in 1919. He graduated in 1937 and then was appointed to the teaching staff of the university. In 1949 Polozii was appointed to the University of Kiev and he remained at Kiev until his death in 1968.
Polozii's major pure mathematical contributions were to the theory of functions of a complex variable, approximation theory, and numerical analysis. He also made major contributions to mathematical physics and applied mathematics in particular working on the theory of elasticity. *SAU

1977 Ruth Moufang (10 Jan 1905 in Darmstadt, Germany - 26 Nov 1977 in Frankfurt, Germany) Moufang studied projective planes, introducing Moufang planes and non-associative systems called Moufang loops. *SAU

1981 Machgielis Euwe (20 May 1901 in Watergraafsmeer, near Amsterdam, Netherlands
- 26 Nov 1981 in Amsterdam, Holland) Machgielis Euwe is better known by the name Max Euwe, and he is better known as the world chess champion from 1935 to 1937 than as a mathematician. However, Euwe was indeed a very fine mathematician who concentrated more on his mathematics throughout his life than on his chess. In 1929 he published a mathematics paper in which he constructed an infinite sequence of 0's and 1's with no three identical consecutive subsequences of any length. He then used this to show that, under the rules of chess that then were in force, an infinite game of chess was possible. It had always been the intention of the rules that this should not be possible, but the rule that a game is a draw if the same sequence of moves occurs three times in succession was not, as Euwe showed, sufficient. *SAU

1990 Richard Alan Day (9 Oct 1941 in Sault Ste Marie, Ontario, Canada - 26 Nov 1990 in Thunder Bay, Ontario, Canada) He spent his whole career at Lakeland University in Thunder Bay, being promoted to Associate Professor in 1975 and to full professor five years later.
Day made many major contributions to lattice theory. One of the first was in the paper A simple solution to the word problem for lattices (1970) where he gave a simple solution to the word problem in free lattices. This paper introduced Day famous doubling construction. *SAU

2015 Amir D. Aczel (November 6, 1950 – November 26, 2015) was an Israeli-born American lecturer in mathematics and the history of mathematics and science, and an author of popular books on mathematics and science.
Aczel was born in Haifa, Israel. Aczel's father was the captain of a passenger ship that sailed primarily in the Mediterranean Sea. When he was ten, Aczel's father taught his son how to steer a ship and navigate. This inspired Aczel's book The Riddle of the Compass.
When Aczel was 21 he studied at the University of California, Berkeley. He graduated with a BA in mathematics in 1975, and received a Master of Science in 1976. Several years later Aczel earned a Ph.D. in statistics from the University of Oregon.
Aczel taught mathematics at universities in California, Alaska, Massachusetts, Italy, and Greece. He married his wife Debra in 1984 and has one daughter, Miriam, and one stepdaughter. He accepted a professorship at Bentley College in Massachusetts where he taught classes on the history of science and the history of mathematics. While teaching at Bentley, Aczel wrote several non-technical books on mathematics and science, as well as two textbooks. His book, Fermat's Last Theorem (ISBN 978-1-56858-077-7), was a United States bestseller and was nominated for a Los Angeles Times Book Prize. Aczel appeared on CNN, CNBC, The History Channel, and Nightline. Aczel was a 2004 Fellow of the John Simon Guggenheim Memorial Foundation and Visiting Scholar in the History of Science at Harvard University (2007). In 2003 he became a research fellow at the Boston University Center for Philosophy and History of Science, and in Fall 2011 was teaching mathematics courses at University of Massachusetts Boston.
He died of cancer on Nov. 26, 2015 in Nîmes, in the south of France. He was 65. *Wik, *Obit
His most recent book was Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers

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

Friday, 25 November 2022

On This Day in Math - November 25

The capacity to blunder slightly is the real marvel of DNA.
Without this special attribute, we would still be anaerobic bacteria
and there would be no music.

— Lewis Thomas

The 329th day of the year; 329 is the sum of three consecutive primes. 329 is the number of forests (trees and disconnected trees) possible with ten vertices.

329 is the sum of three consecutive primes. 107 + 109 + 113

329 is also a happy number, since the iteration of the sums of the squares of its digits includes 1, $3^2 + 2^2 + 9^2 = 94, 9^2 + 4^2 = 97, 9^2 + 7^2 = 130, 1^2 +3^2+0^2 = 10, and 1^2 + 0^2 = 1 $

EVENTS
1658 The prize committee for Pascal’s cycloid problems (see 1 October 1658) decided not to give the prize of sixty Spanish gold doubloons to anyone. [DSB 7, 583] *VFR
In 1658, four years after renouncing mathematics as a vainglorious pursuit, Pascal found himself one day suffering from a painful toothache, and in desperation began to think about the cycloid to take his mind off the pain. Quickly the pain abated, and Pascal interpreted this as a sign from the Almighty that he should proceed to study the cycloid, which he did intensively for the next eight days. During this period he rediscovered most of what had already been learned about the cycloid, and several results that were new. Pascal decided to propose a set of challenge problems, with the promise of a first and second prize to be awarded for the best solutions. Roberval was named as one of the judges. Only two sets of solutions were received, one from Antoine de Lalouvere and another from John Wallis, but Pascal and Roberval decided that neither of the entries merited a prize, so no prizes were awarded. Instead, Pascal published his own solutions, along with an essay on the "History of the Cycloid". *www.mathpages.com

1731 A letter from Euler to Goldbach on this day includes the first use by Euler of continued fractions. Prior to his use continued fractions had made only scattered appearences. In the same letter he introduced the letter e as the base for the natural logarithms, "(e denotat hic numerum, cujus logarithmus hyperbolicus est=1.)," which Google translates as "(e denotes here the number of out of which the hyperbolic logarithm is equal to 1.)"
According to Maor's book e: The story of a number,:

Euler had already used the letter e to represent the number 2.71828... in one of his earliest works, a manuscript entitled "Meditation upon Experiments made recently on the firing of Cannon," written in 1727 when he was only twenty years old (it was not published until 1862, eighty years after his death). In a letter written in 1731 the number e appeared again in connection with a certain differential equation; Euler defines it as "that number whose hyperbolic logarithm is=1." The earliest appearance in a published work was in Euler's Mechanica (1736), in which he laid the foundations of analytical mechanics.

(My thanks to Dave Richeson who provided resources and tied all this information together for me.)

1804 Gauss, in a letter to his close friend Farkas Bolyai, explains that he does not agree with Bolyai's claim that he had put Euclidean Geometry on Solid Ground, "Bolyai has communicated to Gauss his claim that he has put Euclidean geometry on solid ground."

You desire only my careful and unfettered judgment: it is that your explanation does not satisfy me. I will try to explain the issue (it belongs to the same set of reefs on which my attempts have run aground) with as much clarity as possible. To be sure, I still have hope that, before my time is up, these reefs will permit passage. For the time being I have so many other tasks at hand that I cannot think about this; believe me, it would really make me happy if you were to pull ahead of me and overcome all obstacles. I would then undertake with the greatest joy, with all that is in my power, to defend your accomplishment and bring it to the light of day.

*Stan Burris, Notes on Non-Euclidean Geometry

1901 Richardson's law; Owen Willans Richardson read a paper before the Cambridge Philosophical Society which first announced his work on thermionic emission (the release of electrons from hot metals) and in particular a law which mathematically described how the amount of electron current increased as the temperature of the hot surface was raised. (He had been working at the Cavendish Laboratory only one year since his graduation from Cambridge University.) As recorded in the published Proceedings, in Richardson's words: "If then the negative radiation is due to the corpuscles coming out of the metal, the saturation current s should obey the law s = AT^1/2e^-b/T." The discovery of Richardson's law earned him the 1928 Nobel Prize for Physics.*TIS

1906 First Audion tube. The first triode was ordered by Lee de Forest who instructed the New York automobile lamp maker, H. W. Candless, to make a glass bulb containing a "grid" wire between a filament and an electrode plate. These specifications extended the Fleming two-element diode valve design previously published in the Proceedings of the Royal Society. The third element - the grid wire - regulated the flow of electrons between the filament and the anode plate, producing an amplification of the variations in a signal voltage applied to the grid. De Forest named his invention the "Audion." Within a few years (1913-1917) he was able to profit from his patents that he sold to AT&T for a total of $390,000.*TIS

1907 First general meeting of the Warsaw Scientiﬁc Society. Among the 14 founders of the Society were the two mathematicians Samuel Dickstein (1851–1939) and WLladysLlaw Gosiewski (1844– 1911). [Kuratowski, A Half Century of Polish Mathematics, p. 17] *VFR

1915 Albert Einstein completed his general theory of relativity. [A. Hellemans and B. Bunch, The Timetables of Science, p 429].*VFR

1952 Portugal issued two stamps commemorating the centenary of the birth of the mathematician Francisco Gomes Teixeira (1851-1932). [Scott #751-2]. *VFR

1997 Pixar’s A Bug’s Life and Geri’s Game is released. Pixar Animation Studio released their second feature-length animated film, “A Bug’s Life,” on this day in 1997, preceding it with a computer animated short, “Geri’s Game.” A Bug’s Life, following on the success of Pixar’s Toy Story, was the story of a rag-tag group of bugs who band together to defeat a group of invading grasshoppers. The film would make more than $160 million in its initial US release. Geri’s Game would go on to win the Academy Award for Best Animated Short Film. *CHM

BIRTHS
1783 Claude-Louis Mathieu (25 Nov 1783; 5 Mar 1875) French astronomer and mathematician who worked particularly on the determination of the distances of the stars. He began his career as an engineer, but soon became a mathematician at the Bureau des Longitudes in 1817 and later professor of astronomy in Paris. For many years Claude Mathieu edited the work on population statistics L'Annuaire du Bureau des Longitudes produced by the Bureau des Longitudes. His work in astronomy focussed on determining the distances to stars. He published L'Histoire de l'astronomie au XVIII siècle in 1827. *TIS

1814 (Julius) Robert Mayer (25 Nov 1814; 20 Mar 1878) a German physicist. While a ship's doctor sailing to Java, he considered the physics of animal heat. In 1842, he measured the mechanical equivalent of heat. His experiment compared the work done by a horse powering a mechanism which stirred paper pulp in a caldron with the temperature rise in the pulp. He held that solar energy was the ultimate source of all energy on earth, both living and nonliving. Mayer had the idea of the conservation of energy before either Joule or Helmholtz. The prominence of these two scientists, however, diminished credit for Mayer's earlier insights. James Joule presented his own value for the mechanical equivalent of heat. Helmhotlz more systematically presented the law of conservation of energy. *TIS

1816 Lewis Morris Rutherfurd (25 Nov 1816; 30 May 1892) American spectroscopist, astrophysicist and photographer, born in Morrisania, NY, who made the first telescopes designed for celestial photography. He produced a classification scheme of stars based on their spectra as similarly developed by the Italian astronomer. Rutherfurd spent his life working in his own observatory, built in 1856, where he photographed (from 1858) the Moon, Jupiter, Saturn, the Sun, and stars down to the fifth magnitude. While using photography to map star clusters, he devised a new micrometer to measure distances between stars with improved accuracy. When Rutherford began (1862) spectroscopic studies, he devised highly sophisticated diffraction gratings.*TIS

1841 Friedrich Wilhelm Karl Ernst Schröder (25 Nov 1841 in Mannheim, Germany - 16 June 1902 in Karlsruhe, Germany) His important work is in the area of algebra, set theory and logic. His work on ordered sets and ordinal numbers is fundamental to the subject. *SAU

1913 Lewis Thomas (25 Nov 1913; 3 Dec 1993) American physician, researcher, author, and teacher best known for his reflective essays on a wide range of topics in biology. While his specialities are immunology and pathology, in his book, Lives of a Cell, his down-to-earth science writing stresses that what is seen under the microscope is similar to the way human beings live, and he emphasizes the interconnectedness of life. As a research scientist, Thomas made an impact by suggesting that an immunosurveillance mechanism protects us from the possible ravages of mutant cells, an idea later championed by Macfarlane Burnett. He also proposed that viruses have played a major role in the evolution of species by their ability to move pieces of DNA from one individual or species to another. *TIS

1987 Evelyn Merle Nelson (November 25, 1943 – August 1, 1987), born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science. Nelson's teaching record was, according to one colleague, "invariably of the highest order". However, before earning a faculty position at McMaster, prejudice against her lead to doubts about her teaching ability. Nelson published over 40 papers during her 20-year career before she died from cancer in 1987.
She, along with Cecilia Krieger, is the namesake of the Krieger–Nelson Prize, awarded by the Canadian Mathematical Society for outstanding research by a female mathematician. *Wik

DEATHS
1694 Ismael Boulliau (28 Sept 1605 , 25 Nov 1694) was a French clergyman and amateur mathematician who proposed an inverse square law for gravitation before Newton. Boulliau was a friend of Pascal, Mersenne and Gassendi and supported Galileo and Copernicus. He claimed that if a planetary moving force existed then it should vary inversely as the square of the distance (Kepler had claimed the first power), "As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d². *SAU

1913 Sir Robert Stawell Ball (1 July 1840 – 25 November 1913) was an Irish astronomer. He worked for Lord Rosse from 1865 to 1867. In 1867 he became Professor of Applied Mathematics at the Royal College of Science in Dublin. In 1874 Ball was appointed Royal Astronomer of Ireland and Andrews Professor of Astronomy in the University of Dublin at Dunsink Observatory. In 1892 he was appointed Lowndean Professor of Astronomy and Geometry at Cambridge University at the same time becoming director of the Cambridge Observatory.[(not exactly at the same time)In 1892 John Couch Adams, the Lowndean Professor of Astronomy and Geometry at Cambridge and the director of the Cambridge Observatory, died. Ball applied ... and was appointed as Lowndean Professor of Astronomy and Geometry but disputes with the university meant that he had to wait a year before he was appointed director of the Cambridge Observatory.*SAU] His lectures, articles and books (e.g. Starland and The Story of the Heavens) were mostly popular and simple in style. However, he also published books on mathematical astronomy such as A Treatise on Spherical Astronomy. His main interest was mathematics and he devoted much of his spare time to his "Screw theory". He served for a time as President of the Quaternion Society. His work The Story of the Heavens is mentioned in the "Ithaca" chapter of James Joyce's Ulysses. *Wik

1936 Édouard (-Jean-Baptiste) Goursat (21 May 1858, 25 Nov 1936) French mathematician and theorist whose contribution to the theory of functions, pseudo- and hyperelliptic integrals, and differential equations influenced the French school of mathematics. The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour. Cauchy had established the theorem with the added condition that the derivative of the function was continuous. In 1891, he wrote Leçons sur l'intégration des équations aux dérivées partielles du premier ordre. Goursat's best known work is Cours d'analyse mathématique (1900-10) which introduced many new analysis concepts. *TIS
It is almost certain that l'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point, is so named because Goursat named the rule after de l'Hôpital in his Cours d'analyse mathématique . Certainly the rule appears in earlier texts (for example it appears in the work of Euler), but Goursat is the first to attach de l'Hôpital's name to it.*SAU

1937 Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.*Wik

1952 Edward Vermilye Huntington (April 26 1874, Clinton, New York, USA -- November 25, 1952, Cambridge, Massachusetts, USA) was an American mathematician.
Huntington's primary research interest was the foundations of mathematics. He was one of the "American postulate theorists" (the term is Scanlan's), American mathematicians active early in the 20th century (including E. H. Moore and Oswald Veblen) who proposed axiom sets for a variety of mathematical systems. In so doing, they helped found what are now known as metamathematics and model theory.
Huntington was perhaps the most prolific of the American postulate theorists, devising sets of axioms (which he called "postulates") for groups, abelian groups, geometry, the real number field, and complex numbers. His 1902 axiomatization of the real numbers has been characterized as "one of the first successes of abstract mathematics" and as having "filled the last gap in the foundations of Euclidean geometry". Huntington excelled at proving axioms independent of each other by finding a sequence of models, each one satisfying all but one of the axioms in a given set. His 1917 book The Continuum and Other Types of Serial Order was in its day "...a widely read introduction to Cantorian set theory." (Scanlan 1999) Yet Huntington and the other American postulate theorists played no role in the rise of axiomatic set theory then taking place in continental Europe.
In 1904, Huntington put Boolean algebra on a sound axiomatic foundation. He revisited Boolean axiomatics in 1933, proving that Boolean algebra required but a single binary operation (denoted below by infix '+') that commutes and associates, and a single unary operation, complementation, denoted by a postfix prime. The only further axiom Boolean algebra requires is: (a '+b ')'+(a '+b)' = a, now known as Huntington's axiom.
Revising a method from Joseph Adna Hill, Huntington is credited with the Method of Equal Proportions or Huntington-Hill method of apportionment of seats in the U.S. House of Representatives to the states, as a function of their populations determined in the U.S. census. This mathematical algorithm has been used in the U.S. since 1941 and is currently the method used.
In 1919, Huntington was the first President of the Mathematical Association of America, which he helped found. He was elected to the American Academy of Arts and Sciences in 1913, and to the American Philosophical Society in 1933.*Wik

1978 Eduard L. Stiefel (21 April 1909, Zürich – 25 November 1978, Zürich) was a Swiss mathematician. Together with Cornelius Lanczos and Magnus Hestenes, he invented the conjugate gradient method, and gave what is now understood to be a partial construction of the Stiefel–Whitney classes of a real vector bundle, thus co-founding the study of characteristic classes.
Stiefel achieved his full professorship at ETH Zurich in 1948, the same year he founded the Institute for Applied Mathematics. The objective of the new institute was to design and construct an electronic computer (the Elektronische Rechenmaschine der ETH, or ERMETH). *Wik

1988 Dmitrii Evgenevich Menshov (18 April 1892 in Moscow, Russia - 25 Nov 1988)
For his work on the representation of functions by trigonometric series, Menshov was awarded a State Prize in 1951. He was then elected a Corresponding Member of the USSR Academy of Sciences in 1953. In 1958 Menshov attended the International Congress of Mathematicians in Edinburgh and he was invited to address the Congress with his paper On the convergence of trigonometric series. *SAU

2008 Beno Eckmann (March 31, 1917, Bern – November 25, 2008, Zurich) was a Swiss mathematician who was a student of Heinz Hopf.
Born in Bern, Eckmann received his master's degree from Eidgenössische Technische Hochschule Zürich (ETH) in 1931. Later he studied there under Heinz Hopf, obtaining his Ph.D. in 1941. Eckmann was the 2008 recipient of the Albert Einstein Medal.
Calabi–Eckmann manifolds, Eckmann–Hilton duality, the Eckmann–Hilton argument, and the Eckmann–Shapiro lemma are named after Eckmann.*Wik

Thursday, 24 November 2022

Typing Monkeys

More observations stimulated by John Barrows new book (see my recent blog) Everybody has heard the suggestion that a million (or some other number) of monkeys typing continuously for many millenia would eventually produce a) Shakespeare, b) all of known science, c) the bible, d) all of the above).

It began with Jonathon Swift and Gulliver's Travels, 1872, according to Professor Barrow. In the tale "a mythical professor of the Grand Academy of Lagado who aims to generate a catalogue of all scientific knowledge by having his students continuously generate random strings of letters..." (I think, see emphasis in the excerpt below, that it was random strings of words).. Anyway, according to the good Professor Barrow, the story was embellished in different forms until French Mathematician Emile Borel{there is a street and a square named for him in the 17th District in Paris} suggested that random typing monkeys could duplicate the French national library. A few years later(1929), Arthur Eddington Anglicised that to "books in the British Museum." By 1972, Arthur Koestler writing in The Case of the Midwife Toad, New York, 1972, page 30, refers to Monkeys typing Shakespeare as "proverbial":"Neo-Darwinism does indeed carry the nineteenth-century brand of materialism to its extreme limits--to the proverbial monkey at the typewriter, hitting by pure chance on the proper keys to produce a Shakespeare sonnet." Ok, so eventually someone had to put this to a more scientific test, and they did. "A website entitled The Monkey Shakespeare Simulator, launched on July 1, 2003, contained a Java applet that simulates a large population of monkeys typing randomly, with the stated intention of seeing how long it takes the virtual monkeys to produce a complete Shakespearean play from beginning to end. For example, it produced this partial line from Henry IV, Part 2, reporting that it took "2,737,850 million billion billion billion monkey-years" to reach 24 matching characters:"RUMOUR. Open your ears; 9r5j5&?OWTY Z0d... " Even more impressive, to me, is the fact that 'in another part of that book, Swift tells of how the astronomers on the flying island of Laputia had: "discovered two lesser stars, or satellites, which revolve around Mars, whereof the innermost is distant from the center of the primary exactly three of his diameters, and the outermost five: the former revolves in the space of ten hours, and the latter in twenty-one and a half". Swift wrote this in 1726, but it was not until 1877 that Asaph Hall discovered the two moons of Mars.'... I just did a little checking on the orbit and periods he "predicted?" and the actual periods are about 7 hours for Phobos, and about 30 for Deimos... and their distance from the planet were about 9 x 10³km and 23.5 x 10³km. Mars has a diameter of 6.794 x 10³km so they are closer to 1.5 and 3 radii away it seems, but wow, for 100 years before the actual discovery??? Don't you wonder what made him use Mars instead of Venus or ??? Wait, maybe authors typing randomly can describe the true nature of the universe (with some limits of error)... ------------------------------------------------------------------------------------------ Ok best guess, Swift had heard of a misinterpretation of Johannes Kepler. He had interpreted the anagram that Galileo Galilei sent to him in 1609 to tell him about the discovery of the phases of Venus as the discovery of two moons of Mars.

If you have your copy, here is what I found in Chapter Five of Gulliver's Travels. The whole thing is available at the Guttenburg Project. "The first professor I saw, was in a very large room, with forty pupils about him. After salutation, observing me to look earnestly upon a frame, which took up the greatest part of both the length and breadth of the room, he said, "Perhaps I might wonder to see him employed in a project for improving speculative knowledge, by practical and mechanical operations. But the world would soon be sensible of its usefulness; and he flattered himself, that a more noble, exalted thought never sprang in any other man's head. Every one knew how laborious the usual method is of attaining to arts and sciences; whereas, by his contrivance, the most ignorant person, at a reasonable charge, and with a little bodily labour, might write books in philosophy, poetry, politics, laws, mathematics, and theology, without the least assistance from genius or study." He then led me to the frame, about the sides, whereof all his pupils stood in ranks. It was twenty feet square, placed in the middle of the room. The superfices was composed of several bits of wood, about the bigness of a die, but some larger than others. They were all linked together by slender wires. These bits of wood were covered, on every square, with paper pasted on them; and on these papers were written all the words of their language, in their several moods, tenses, and declensions; but without any order. The professor then desired me "to observe; for he was going to set his engine at work." The pupils, at his command, took each of them hold of an iron handle, whereof there were forty fixed round the edges of the frame; and giving them a sudden turn, the whole disposition of the words was entirely changed. He then commanded six-and-thirty of the lads, to read the several lines softly, as they appeared upon the frame; and where they found three or four words together that might make part of a sentence, they dictated to the four remaining boys, who were scribes. This work was repeated three or four times, and at every turn, the engine was so contrived, that the words shifted into new places, as the square bits of wood moved upside down. Six hours a day the young students were employed in this labour; and the professor showed me several volumes in large folio, already collected, of broken sentences, which he intended to piece together, and out of those rich materials, to give the world a complete body of all arts and sciences; which, however, might be still improved, and much expedited, if the public would raise a fund for making and employing five hundred such frames in Lagado, and oblige the managers to contribute in common their several collections. He assured me "that this invention had employed all his thoughts from his youth; that he had emptied the whole vocabulary into his frame, and made the strictest computation of the general proportion there is in books between the numbers of particles, nouns, and verbs, and other parts of speech."

The Monkeys, well, they showed up a little later. (Félix-Édouard-Justin-) Émile Borel (7 Jan 1871; 3 Feb 1956) was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory. In 1913, in one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library). This is now popularly known as the infinite monkey theorem.

On This Day in Math - November 24

Albertus Magnus

To call in the statistician after the experiment is done may be no more than asking hm to perform a postmortem examination: he may be able to say what the experiment died of.
~Fisher, Ronald Aylmer

The 328th day of the year; 328 is the sum of the first fifteen primes. No year day can has more.
It is also is a tau-number since it is divisible by the number of divisors it has.

328 reversed is prime, and it is the sum of the first 15 primes. It is the last day of the year that will be the sun of the first n primes.

$328 =18^2 + 2^2 $ and

$328 = 6^2 + 6^2 + 16^2$

EVENTS

1639 British astronomers Jeremiah Horrocks and William Crabtree became the first observers to record a transit of Venus. Horrocks was just a teenager, and would die at the tender age of twenty-two, but before he did, he ran up several impressive notches in his scientific portfolio. For more on this event, see

this blog by The Renaissance Mathematicus. Applying Kepler's prediction that in 1631, Venus would transit the Sun, Horrocks calculated that these transits occurred not singly but in pairs eight years apart. Thus, Horrocks prepared his equipment for the next transit he had thus predicted for this day. His simple telescope was mounted on a wooden beam, so he could project a solar image onto a piece of paper marked with a six inch graduated circle. From this, he made measurements and calculated that the value for the solar parallax was smaller than previously recorded, and so concluded that the Sun was further away from the Earth than previously thought. *TIS As the image shows, the observation was made at Carr House where he lived at the time. "Horrocks returned to Toxteth Park (Liverpool) sometime in the summer of 1640 and died suddenly and from unknown causes on 3 January 1641, aged only 22. As expressed by Crabtree, "What an incalculable loss!" *John Wallis The image is from the lancashire.gov.uk

1713 As the 18th century began, even the devoted Newton supporters were finding themselves drawn to the Leibniz notation used on the continent, although the real break would not come for another hundred years. But in 1713, even the most devout Newtonians were wavering. On this date, John Kell, a bitter opponent of Leibniz, would use the $ \int $ for integration, but fiercely continued to use the "pricked numerals" of Newton. $ \dot {x}$ . *Philosophical Transactions

1759 Lagrange wrote Euler that he believes that he had developed the true metaphysics of the calculus; at that time he seems to have been convinced that the use of inﬁnitesimals was rigorous. Lagrange attempted to prove Taylor’s theorem (the power of which he was the ﬁrst to observe) and then to develop the entire calculus from it. (Cajori, History of Mathematics, 257) *VFR

1789 Lagrange ﬁnished his M´ecanique analytique. In this he lays down the law of virtual work, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole of mechanics, both of solids and fluids.
The object of the book is to show that the subject is implicitly included in a single principle, and to give general formulae from which any particular result can be obtained. The method of generalized co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he showed that, if we determine its configuration by a sufficient number of variables whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation. *Wik

1831 Michael Faraday reads the first of a series of papers on "Experimental Research into Electricity." *Phil. Trans. R. Soc. Lond. January 1, 1832 122:125-162;

1836 A total lunar eclipse occurred which Gauss had promised to show, through the observatory telescope to his friend Ribbentrop, conﬁrmed bachelor, campus eccentric, and absent-minded professor of law. Although it was pouring rain that evening Ribbentrop appeared. Gauss explained that observation was impossible, but Ribbentrop countered, “No, I have my umbrella.” [Eves, Squared, 191◦] *VFR

1845 After Faraday’s discovery of the a between light and magnetism was announced in the papers, Mrs. Jane Marcet, whose book, Conversations on Chemistry, had been influential in Faraday's youth, wrote to ask Faraday for more information. " I have kept back the proof sheets of the ‘Conversation on Electricity,’ which I was this morning revising, until I receive your answer, in hopes of being able to introduce it in that sheet."
The two kept up correspondence throughout her life, and she would contact him for information on the most recent developments in order to update her "Conversations." The last new edition of Conversations on Chemistry came out in 1853, when Marcet was 84 years old!
A more complete story of the influence she had on Faraday, and their relationship is at the *skullsinthestars blogsite.

1847 Barrister to barrister math; 1837's second Wrangler to 1842's Senior Wrangler: J. J. Sylvester writes to Arthur Cayley to inform him that while reading the second volume of Theorie des Nombres that he had found two examples by Legendre that he thought might be "very congenial" to Cayley's present line of thought, "not doubting that it will turn to good account in your able hands." Although their communication was stil in the "My Dear Sir" stage, Sylvester felt he had found a kindred spirit. *Karen Hunger Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World

In 1859, The Origin of Species by Means of Natural Selection, Darwin's groundbreaking book, was published in England to great acclaim. The British naturalist, Charles Darwin detailed the scientific evidence he had collected since his voyage on the Beagle in the 1830's. He presented his idea that species are the result of a gradual biological evolution in which nature encourages, through natural selection, the propagation of those species best suited to their environments. He had been prompted to publish at this time by Charles Lyell, who advised him that Alfred Russel Wallace, a naturalist working in Borneo, was approaching the same conclusions. Lyell believed Darwin should publish without further delay to establish priority. *TIS

1864 So as not to miss a lecture, George Boole walked the three miles from his home in Ballintemple to Queen’s College in Cork, Ireland, in a pouring rain. He lectured in wet clothes, caught a cold, and died two weeks later at age 49. [MacHale, George Boole, His Life and Work, p 24]. *VFR

1858 Dedekind discovers his cuts and thereby provides the ﬁrst correct definition of continuity. [Dauben, p. 48] *VFR

1888 On Thanksgiving Day, six members of the mathematics department at Columbia University met to form a society for the purpose of discussing mathematics and reading papers of mathematical interest. A month later they christened it the New York Mathematical Society. By 1894 the society had attained a national character, so its name was changed to the American Mathematical Society. The six were J. H. Van Amring, the ﬁrst president, Thomas Scott Fiske, Rees (a professor), Jacoby and Stabler (fellow students with Fiske) and Maclay (a graduate student). *P. Duren (ed), A Century of Mathematics in America, vol. I, pp. 5, 13.

1918 Richard Courant sat down with Ferdinand Springer and signed a contract for the series of books now famous as the “Yellow Series.” *Constance Reid, Courant in Gottingen and New York, p. 72

1982 Sweden issued ﬁve stamps honoring Nobel Prize winners Niels Bohr, Erwin Schrodinger, Louis de Broglie, Paul Dirac and Werner Heisenberg. [Scott #1425-9] *VFR Bohr also appears on 500-krone banknote with the portrait of Bohr smoking a pipe since 1997.

2015 President Barack Obama awarded the presidential medal of freedom—America’s highest civilian honor—to a 97-year-old mathematician named Katherine Coleman Goble Johnson. You might not have heard her name in history class, but Katherine did some life-saving work back in 1962. In her job at NASA, she calculated the trajectory for astronaut John Glenn's pioneering space mission to orbit Earth. Katherine co-authored the research and equations that laid out how to send Glenn into orbit and how to bring him back home safely. Johnson is just one part of a cadre of African American women who did crucial calculations for the space workforce during the Cold War. */bitchmedia.org

BIRTHS

1879 Duncan MacLaren Young Sommerville (24 Nov 1879 in Beawar, Rajasthan, India - 31 Jan 1934 in Wellington, New Zealand) Sommerville studied at St Andrews and then had a post as a lecturer there. He left to become Professor of Pure and Applied mathematics at Victoria College, Wellington New Zealand. He worked on non-Euclidean geometry and the History of Mathematics. He became President of the EMS in 1911. *SAU

1909 Gerhard Gentzen (24 Nov 1909 in Greifswald, Germany - 4 Aug 1945 in Prague, Czechoslovakia) Gentzen invented a 'natural deduction' which provided a logic closer to mathematical reasoning than the systems proposed by Frege, Russell and Hilbert.*SAU

1912 Dr. Lyle B. Borst, (Nov 24, 1912 - July 30, 2002) was a nuclear physicist who helped build Brookhaven National Laboratory's nuclear reactor and was an early member of the Manhattan Project.
In 1950, Dr. Borst led the construction of the Brookhaven Graphite Research Reactor, which was the largest and most powerful reactor in the country and the first to be built solely for research and other peacetime uses of atomic energy.
Within the first nine months of operating the reactor, Dr. Borst announced that it had produced a new type of radioactive iodine, which is used in treating thyroid cancer.
In 1952, based on studies of new types of atomic nuclei created in the reactor, Dr. Borst helped explain the mystery behind giant stars, known as supernovae, that burst with the energy of billions of atomic bombs and flare for several years with the brilliance of several million suns.
Dr. Borst found that beryllium 7, an isotope of beryllium that does not occur naturally on earth, is formed in supernovae by the fusion of two helium nuclei. The fusion takes place after the star has used up its hydrogen supply. This reaction absorbs huge quantities of energy, causing the star to collapse in the greatest cosmic explosion known. *NY Times obit.

1925 Simon van der Meer (24 Nov 1925, )Dutch engineer and physicist who along with Italian physicist Carlo Rubbia, discovered the W particle and the Z particle by colliding protons and antiprotons, for which both men shared the Nobel Prize for Physics. These subatomic particles (units of matter smaller than an atom) transmit the weak nuclear force, one of four fundamental forces in nature. The discovery supported the unified electroweak theory put forward in the 1970's. Working at CERN in Switzerland, Van der Meer improved the design of particle accelerators used produce collisions between beams of subatomic particles. He invented a device that would monitor and adjust the particle beam with correcting magnetic fields by a system of 'kickers' placed around the accelerator ring.*TIS

1926 Tsung Dao Lee (24 Nov 1926, ) Chinese-born American physicist who received (with Chen Ning Yang) the 1957 Nobel Prize for Physics for their "penetrating investigation" of violations of the principle of parity conservation (the quality of space reflection symmetry of subatomic particle interactions), which has led to important discoveries regarding the elementary particles. Conservation of parity had previously been regarded as a "law" of nature. (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.*TIS

1944 Veerabhadran Ramanathan (24 Nov 1944, )Indian atmospheric scientist who in 1999 discovered the "Asian Brown Cloud" - wandering layers of air pollution as wide as a continent and deeper than the Grand Canyon. The dark particles in these brown clouds may reduce rainfall, dry the planet’s surface, cool the tropics and reduce sunlight - Global Dimming. In 1975, Ramanathan was the first to demonstrate that CFCs are major greenhouse gases. His calculations showed each CFC molecule in the atmosphere contributes more to the greenhouse effect that over 10,000 molecules of carbon dioxide. In the 1980s, he led a study discovering numerous trace gases contributing to global warming, and a NASA study that demonstrated that clouds had a net global cooling effect on the planet.*TIS

DEATHS

1930 Prosper-René Blondlot (3 July 1849 – 24 November 1930) was a French physicist, best remembered for his mistaken "discovery" of N rays, a phenomenon that subsequently proved to be illusory.
In order to demonstrate that a Kerr cell responds to an applied electric field in a few tens of microseconds, Blondlot, in collaboration with Ernest Bichat, adapted the rotating-mirror method that Léon Foucault had applied to measure the speed of light. He further developed the rotating mirror to measure the speed of electricity in a conductor, photographing the sparks emitted from two conductors, one 1.8 km longer than the other and measuring the relative displacement of their images. He thus established that the speed of electricity in a conductor is very close to that of light.
In 1891, he made the first measurement of the speed of radio waves, by measuring the wavelength using Lecher lines. He used 13 different frequencies between 10 and 30 MHz and obtained an average value of 297,600 km/s, which is within 1% of the current value for the speed of light. This was an important confirmation of James Clerk Maxwell's theory that light was an electromagnetic wave like radio waves.
In 1903, Blondlot announced that he had discovered N rays, a new species of radiation. The "discovery" attracted much attention over the following year until Robert W. Wood showed that the phenomena were purely subjective with no physical origin. The French Academy of Sciences awarded the Prix Leconte (₣50,000) for 1904 to Blondot, although they hedged on the reason, citing the totality of his work rather than the discovery of N-rays.
Little is known about Blondlot's later years. William Seabrook stated in his Wood biography Doctor Wood, that Blondlot went insane and died, supposedly as a result of the exposure of the N ray debacle: "This tragic exposure eventually led to Blondlot's madness and death." Using an almost identical wording this statement was repeated later by Martin Gardner, possibly without having investigated into the subject: "Wood's exposure led to Blondlot's madness and death." However, Blondlot continued to work as a university professor in Nancy until his early retirement in 1910. He died at the age of 81; at the time of the N-ray affair he was nearly 60 years old. *Wik

1978 Warren Weaver (b. July 17, 1894 in Reedsburg, Wisconsin d. November 24, 1978 in New Milford, Connecticut) was an American scientist, mathematician, and science administrator. He is widely recognized as one of the pioneers of machine translation, and as an important figure in creating support for science in the United States.*Wik

1980 Henrietta Hill Swope(26 October 1902; Saint Louis, Missouri - 24 November 1980; Pasadena, California)was an American astronomer. She was the eldest child of Gerard and Mary Dayton (Hill) Swope; her mother was the daughter of Thomas Hill, president of Harvard University, 1862-1868. She received her A.B. from Barnard College in 1926 and her A.M. from Radcliffe College in 1928. In 1936, while assistant at the Harvard Observatory (1928-1942), she was a member of the expedition sent jointly by the Harvard Observatory and the Massachusetts Institute of Technology to study the solar eclipse in Soviet Central Asia. During World War II she was staff member of the M.I.T. Radiation Laboratory and then served as a mathematician in the Hydrographic Office of the U.S. Department of the Navy. From 1947 to 1952 she taught astronomy at Barnard College and in 1952 was appointed assistant, later research fellow, at the Mt. Wilson and Palomar Observatories in California. After her retirement in 1968, she continued to work at the Observatories.
HHS was a member of the American Astronomical Society; she received the AAS Annie Jump Cannon Prize in 1968 for her research on photometry and variable stars. She was responsible for developing a new yardstick for measuring the universe: calibrating distance by determining the brightness of stars. She received the Distinguished Alumna Award of Barnard College in 1975 and the Barnard Medal of Distinction in 1980.
The Swope Telescope at the Las Campanas Observatory in Chile is named in her honor, as is asteroid 2168 Swope.

1987 Hans Herbert Schubert (1 May 1908 in Weida, Thüringen Germany - 24 Nov 1987 in Halle, Germany) Schubert was a German mathematician who worked on differential equations. *SAU

2008 John Robert Stallings Jr. (July 22, 1935 – November 24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups. Stallings was born in the small town of Morrilton, Arkansas.*Wik