Monday, 1 November 2021

On This Dayin Math - November 2



The Boole Window, Lincoln Cathedral

[Arithmetic] is one of the oldest branches, perhaps the very oldest branch, of human knowledge; and yet some of its most abstruse secrets lie close to its tritest truths.
~Henry Bell

The 306th day of the year; 306 is the sum of four consecutive primes starting with 71.

There are 306 triangular numbers with five digits. (students, how many triangular numbers have 3 digits... Can you calculate without listing them all?)

306 = 92 + 92 + 122; (not impressed?) you can write the same numerals with exponents and 306 =92 + 92 + 122 Really? Still not impressed, how about 306 =82 + 112 + 112 = 82 + 112 + 112


1749 Leonhard Euler wrote (June 28) to the Rev. Mr. Caspar Wetstein, Chaplain to His Royal Highness the Prince of Wales, concerning the Gradual Approach of the Earth to the Sun. Read before the Royal Society Nov 2, 1749. *Philosophical Transactions

1917 The poet Alfred Noyes was present for the "first light" of the Hooker telescope on November 2, 1917. Noyes used this night as the setting in the opening of Watchers of the Sky, the first volume in his trilogy The Torchbearers, an epic poem about the history of science. According to his account of the night, the first object viewed in the telescope was Jupiter and Noyes himself was the first to see one of the planet's moons through the telescope. *Wik The 100 inch telescope on Mount Wilson was the largest telescope in the world until the 200 inch in 1948 at Palomar Observatory. It is the location where Edwin Hubble made the observation that some of the fuzzy blobs in space were actually galaxies like our own. The campus on Mount Wilson is also the place where Michelson made his measurements of the speed of light. *Frederick Pohl, Chasing Science, pg 54

1944 One of the greatest chemists of the century, and one who inadvertently killed more people than any dictator, died on this day of one of his own inventions. Thomas Midgley Jr was instrumental in the discovery and introduction of the gasoline additive tetraethyl lead. He also developed a method to extract large quantities of bromine from seawater when he learned that bromine was needed to prevent tetraethyl lead from corroding engine valves and spark plugs. He also discovered that dichlorodifluoromethane, also known as Freon, could be used as a nontoxic and nonflammable refrigerant.
His work led to the release of large quantities of lead into the atmosphere as a result of the large-scale combustion of leaded gasoline all over the world. High atmospheric lead levels have been linked with serious long-term health problems from childhood, including neurological impairment.
Midgley died three decades before the ozone-depleting and greenhouse gas effects of CFCs in the atmosphere became widely known. Bill Bryson remarks that Midgley possessed "an instinct for the regrettable that was almost uncanny."
In 1940, at the age of 51, Midgley contracted poliomyelitis, which left him severely disabled. This led him to devise an elaborate system of strings and pulleys to help others lift him from bed. This system was the eventual cause of his own death when he was entangled in the ropes of this device and died of strangulation at the age of 55. Tetraethyl lead and CFCs have both become illegal, but I have no evidence that the device that killed him has been banned. *wik, *Priestly Medal bio

1979 Krachian’s ellipse algorithm for linear programming announced in Science. *VFR

1988 Computers in America went mad, thanks to a virus spread by graduate student Robert T. Morris Jr. *VFR Robert Morris, Jr., a graduate student in Computer Science at Cornell, wrote an experimental, self-replicating, self-propagating program called a worm and injected it into the Internet. He chose to release it from MIT, to disguise the fact that the worm came from Cornell. Morris soon discovered that the program was replicating and reinfecting machines at a much faster rate than he had anticipated---there was a bug. Ultimately, many machines at locations around the country either crashed or became ``catatonic.'' When Morris realized what was happening, he contacted a friend at Harvard to discuss a solution. Eventually, they sent an anonymous message from Harvard over the network, instructing programmers how to kill the worm and prevent reinfection. However, because the network route was clogged, this message did not get through until it was too late. Computers were affected at many sites, including universities, military sites, and medical research facilities. *MIT Edu

In 2000, an American astronaut and two Russian cosmonauts became the first permanent residents of the international space station, at the start of their four-month mission. After their Soyuz spacecraft linked up at 11:00am GMT, William Shepherd, Sergei Krikalev and Yuri Gidzenko entered the station, turned on the lights and life support systems, and proceeded to set up a live television link with the Russian mission control to confirm that the move-in was going well. They were confined to two of the space station’s three rooms until space shuttle Endeavor arrived in early Dec. with giant solar panels that would provide all the necessary power. *TIS

2011 The 2011 Rolf Schock Prize in Mathematics is being awarded to Michael Aschbacher for his "fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups, notably his contribution to the quasi-thin case." The $75,000 Rolf Schock Prize in Mathematics is awarded by the Royal Swedish Academy of Sciences. An award ceremony will take place in Stockholm on November 2, 2011.
Aschbacher, the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology, received the AMS's Cole Prize in 1980 and became a member of the National Academy of Sciences in 1990.*MAA


1815 George Boole (2 Nov 1815; 8 Dec 1864) English mathematician who helped establish modern symbolic logic and an algebra of logic, now called Boolean algebra. By replacing logical operations by symbols, Boole showed that the operations could be manipulated to give logically consistent results. Boole's logical algebra is essentially an algebra of classes, being based on such concepts as complement and union of classes.The study of mathematical or symbolic logic developed mainly from his ideas, and is basic to the design of digital computer circuits. Boolean also algebras find important applications in such diverse fields as topology, measure theory, probability and statistics.Boole also wrote important works on differential equations and other branches of mathematics. *TIS

1826 Henry John Stephen Smith (2 Nov 1826 in Dublin, Ireland, 9 Feb 1883 in Oxford, England) was an Irish mathematician whose most important contributions are in number theory where he worked on elementary divisors. He proved that any integer can be expressed as the sum of 5 squares and as the sum of 7 squares, showing in how many ways this could occur. In addition to solving these cases explicitly, he gave a method which would yield the number of ways that an integer can be expressed as the sum of k squares for any fixed k. He published his results in The orders and genera of quadratic forms containing more than three indeterminates published in the Proceedings of the Royal Society in 1867. Eisenstein had earlier proved the result for 3 squares and Jacobi for 2, 4 and 6 squares. Smith also extended Gauss's theorem on real quadratic forms to complex quadratic forms. *SAU

1871 Poul Heegaard (2 Nov 1871 in Copenhagen, Denmark - 7 Feb 1948 in Oslo, Norway) was a Danish mathematician who (with Max Dehn) was the first to classify compact surfaces.*SAU His 1898 thesis introduced a concept now called the Heegaard splitting of a 3-manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincaré. Poincaré had overlooked the possibility of the appearance of torsion in the homology groups of a space.
He later co-authored, with Max Dehn, a foundational article on combinatorial topology, in the form of an encyclopedia entry.
Heegaard studied mathematics at the University of Copenhagen, from 1889 to 1893 and following years of traveling, and teaching mathematics, he was appointed professor at University of Copenhagen in 1910.
Following a dispute with the faculty over, among other things, the hiring of Harald Bohr (The Brother of Niels Bohr, and Olmpic Soccer medalist) as professor at the University (Heegaard was against it); Heegaard accepted a professorship at Oslo in Norway, where he worked till his retirement in 1941.*Wik

1885 Harlow Shapley (2 Nov 1885; 20 Oct 1972) Astronomer, known as "The Modern Copernicus," who discovered the Sun's position in the galaxy. From 1914 to 1921 he was at Mt. Wilson Observatory, where he calibrated Henrietta S. Leavitt's period vs. luminosity relation for Cepheid variable stars and used it to determine the distances of globular clusters. He boldly and correctly proclaimed that the globulars outline the Galaxy, and that the Galaxy is far larger than was generally believed and centered thousands of light years away in the direction of Sagittarius. In the early 1920's, Shapley entered a "Great Debate" with Heber D. Curtis. They truly argued over the "Scale of the Universe." *TIS

1911 Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an American mathematician. He worked on mathematical logic, set theory, geometry, number theory, and combinatorics. Robinson (1937) set out a simpler and more conventional version of John Von Neumann's 1923 axiomatic set theory. Soon after Alfred Tarski joined Berkeley's mathematics department in 1942, Robinson began to do major work on the foundations of mathematics, building on Tarski's concept of "essential undecidability," by proving a number of mathematical theories undecidable. Robinson (1950) proved that an essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample: Robinson arithmetic Q. Q is finitely axiomatizable because it lacks Peano arithmetic's axiom schema of induction; nevertheless Q, like Peano arithmetic, is incomplete and undecidable in the sense of Gödel. Robinson's work on undecidability culminated in his coauthoring Tarski et al. (1953), which established, among other things, the undecidability of group theory, lattice theory, abstract projective geometry, and closure algebras.
Robinson worked in number theory, even employing very early computers to obtain results. For example, he coded the Lucas-Lehmer primality test to determine whether 2n − 1 was prime for all prime n<2304 on a SWAC. In 1952, he showed that these Mersenne numbers were all composite except for 17 values of n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281. He discovered the last 5 of these Mersenne primes, the largest ones known at the time. *Wik

1929 Richard E. Taylor (2 Nov 1929, ) Canadian physicist who in 1990 shared the Nobel Prize for Physics with Jerome Friedman and Henry Kendall for his collaboration in pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics. The team performed a series of experiments that confirmed the hypothesis that protons and neutrons are made up of quarks. This discovery was crucial to the formulation of the currently accepted theoretical description of matter and its interactions, known as the standard model. *TIS

1932 Melvin Schwartz (2 Nov 1932, ) American physicist and entrepreneur who, along with Leon M. Lederman and Jack Steinberger, received the Nobel Prize for Physics in 1988 for their research concerning neutrinos (subatomic particles that have no electric charge and virtually no mass). Using a beam of neutrinos, the team discovered a new kind of neutrino called a muon, and new information about the structure of particles called leptons. Neutrinos are produced when unstable atomic nuclei or subatomic particles disintegrate. Schwartz and his team wanted to study the "weak" nuclear force that creates certain kinds of radioactivity. The team used a particle accelerator to create a high-intensity beam of neutrinos. They studied the reactions produced when this beam hit other matter.*TIS


1914 Heinrich Friedrich Karl Ludwig Burkhardt (10 Oct 1861 in Schweinfurt, Germany
- 2 Nov 1914 in Munich, Germany) His main work was in analysis, particularly the theory of trigonometric series, and on the history of mathematics. Other topics on which Burkhardt published papers included groups, differential equations, differential geometry and mathematical physics. One of his papers, published in 1888, was Hyperelliptic sigma functions. Other papers include: Theorie der Cremonatransformationen (1892), Über Vectoranalysis (1896), Mathematisches und naturwissenschaftliches Denken (1902), Über Reihenentwicklungen nach oszillierenden Funktionen (1903), Zu den Funktionen des elliptischen Zylinders (1906), and Mathematische Miszellen aus der Vorlesungspraxis (1913). *SAU

1966 Petrus (Peter) Josephus Wilhelmus Debye (24 Mar 1884, 2 Nov 1966) was a Dutch physical chemist whose investigations of dipole moments, X rays, and light scattering in gases brought him the 1936 Nobel Prize for Chemistry. Most of his work was in chemical-physics with special interest in electrolytes and dipolar momentum analysis. He established a theory of specific heat with some improvements on that proposed by Einstein. Debye performed important work in the analysis of crystalline powders using X-ray diffraction techniques. He also determined the dimensions of gaseous molecules and the interatomic distances using X-rays.*TIS

1970 Abram Samoilovitch Besicovitch (24 Jan 1891 in Berdyansk, Russia -2 Nov 1970 in Cambridge, Cambridgeshire, England) Besicovitch left Petrograd for Copenhagen in 1924 and there worked with Harald Bohr. He had been awarded a Rockefeller Fellowship but his applications for permission to work abroad had been refused. He escaped across the border with a colleague J D Tamarkin under the cover of darkness. He managed to reach Copenhagen where he was supported financially for a year with the Rockefeller Fellowship. His interest in almost periodic functions came about through this year spent working with Harald Bohr. After he visited Oxford in 1925 Hardy, who quickly saw the mathematical genius in Besicovitch, found a post for him in Liverpool. At Cambridge Besicovitch lectured on analysis in most years but he also gave an advanced course on a topic which was directly connected with his research interests such as almost periodic functions, Hausdorff measure, or the geometry of plane sets. Besicovitch was famous for his work on almost periodic functions, his interest in which, as we mentioned above, came from his time in Copenhagen with Harald Bohr. In 1932 he wrote an influential text Almost periodic functions covering his work in this area.
One of the achievements, with which he will always be associated, was his solution of the Kakeya problem on minimising areas. The problem had been posed in 1917 by a Japanese mathematician S Kakeya and asked what was the smallest area in which a line segment of unit length could be rotated through 2p. Besicovitch proved in 1925 that given any e, an area of less than e could be found in which the rotation was possible. The figures that resulted from Besicovitch's construction were highly complicated, unbounded figures.
Other areas on which Besicovitch worked included geometric measure theory, Hausdorff measure, real function theory, and complex function theory. In addition to this work on deep mathematical theories, Besicovitch loved problems, particularly those which could be stated in elementary terms but which proved resistant to attack. Often he showed that the "obvious solution" to certain problems is false. An example of such a problem is the Lion and the Man problem posed by Richard Rado in the mid 1920s. *SAU

1993 Dura Kurepa (16 Aug 1907 in Majske Poljane near Glina, Croatia - 2 Nov 1993)
The topics which Kurepa investigated are very varied but lie mostly within topology, set theory and number theory. He published over 200 papers but this number rises to over 700 items if we include books, articles and reviews. He was fascinated by the continuum hypothesis and the axiom of choice. Perhaps best known is his work on trees and partitions, especially Aronszajn and Suslin trees. His book The Theory of Sets written in Serbo-Croatian and published in 1951 illustrates his interests in that particular area. After introducing the fundamental concepts and elementary operations in Chapter 1, he looks at cardinal numbers in the second chapter, then partially ordered sets and ordinal numbers in the third. Chapter 4 is on topological and metric spaces, with the fifth and final chapter on limiting processes in analysis, measure theory, Borel and Souslin sets.
In number theory he made many contributions, but perhaps his most famous is his open problem on the left factorial function. In 1971 he published his definition of !n, the left factorial function, defined by

!n = 0! + 1! + 2! + 3! + ... + (n-1)!.

Kurepa conjectured that the greatest common divisor of !n and n! was 2 for all n>1. There are many equivalent forms of the conjecture, but one of the most natural was given by Kurepa in the same 1971 paper, namely that !n is not divisible by n for any n>2. If the left factorial conjecture is false we certainly know that it will fail for n>106. *SAU

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

On This Day in Math - November 1


If you walk along the street you will encounter a number of scientific problems. Of these, about 80 per cent are insoluble, while 19½ per cent are trivial. There is then perhaps half a per cent where skill, persistence, courage, creativity and originality can make a difference. It is always the task of the academic to swim in that half a per cent, asking the questions through which some progress can be made.
~Sir Hermann Bondi

The 305th day of the year; 305 is the smallest odd composite which is the average of two consecutive Fibonacci numbers. *Number Gossip

305 has two representations as a sum of two squares: 305 = 17^2 + 4^2 = 16^2 + 7^2

It also has two representations as the difference of two squares, 153^2 - 152^2 = 33^2 - 28^2 = 305

Math Joke for Halloween: Why do mathematicians confuse Halloween and Christmas? Because Oct 31 = Dec 25 (31 in base 8 (Octal) is the same quantity as 25 in Decimal)

1536 Letter to Copernicus from Cardinal Schoenberg, included by Copernicus in the introduction to On the Revolutions (1543)
".....I beg you most emphatically to communicate your discovery to the learned world, and to send me as soon as possible your theories about the Universe, together with the tables and whatever else you have pertaining to the subject. I have instructed Dietrich von Rheden to make a fair copy of this at my expense and send it to me. If you will do me these favors, you will find that you are dealing with a man who has your interests at heart, and wishes to do full justice to your excellence. Farewell.

1772, Antoine Lavoisier reported in a note to the Secretary of the French Academy of Sciences that in the previous week he had discovered that sulphur and phosphorus when burned increased in weight because they absorbed "air," while the metallic lead formed when litharge was heated with charcoal weighed less than the original litharge because it had lost "air." The exact nature of the airs concerned in the processes he could not yet explain, and he proceeded to study the question extensively. Lavoisier's investigation of the role of air in combustion would change the way chemists viewed combustion. *TIS

1809 Louis Poinsot (1777–1859) named assistant professor of analysis and mechanics at the Ecole Polytechnique. In 1794 he was admitted to the first class at the university despite insufficient knowledge of algebra. *VFR

1812 On 1st November 1812, Davy writes to Jane (his wife), worried that she’ll hear this story from some other source: ‘Yesterday I began some new experiments to which a very interesting discovery & a slight accident put an end. I made one of those compounds more powerful than gunpowder destined perhaps at some time to change the nature of war & influence the state of Society, an explosion took place which has done me no other harm than that of preventing me from working this day & the effects of which will be gone tomorrow & which I should not mention at all, except that you may hear some foolish exaggerated account of it for it really is not worth mentioning’. *Sharon Ruston Blog

1818 Whewell wrote John Herschel that he “would not be surprised if in a short time we were only to read a few propositions of Newton, as a matter of curiosity.” See H. W. Becher, “William Whewell and Cambridge mathematics,” *HSPS, 11(1980), p. 15.

1826 John Boole an amateur mathematician of some ability, would pencil into the cover of the sixth book of Leslie's Geometry, "George Boole finished this book on 1 Nov. 1826." The following day would be George's eleventh birthday. *Desmond MacHale, The Life and Works of George Boole

1844 Gauss in a letter to Schumacher, “I am rather surprised that you expect clarity from a professional philosopher. Muddled concepts and definitions are nowhere more at home than among philosophers who are not mathematicians ... Just look aroung at today’s philosophers, Schelling, Hegel, Nees von Esenbeck and Co. Don’t their definitions make your hair stand on end? Or, in classical philosophy, read the kinds of things which “stars” like Plato and others (I except Aristotle) gave as explanations. Even Kant is often not much better: his distinction between analytic and synthetic propositions is, I believe, one of those which either turns on a triviality or is false.” [The Mathematical Intelligencer, 1(1978), p. 18]*VFR

1884 The International Meridian Conference referenced mean solar time to the 24 standard meridians each of 15 degrees longitude. The international date line was then established to generally follow the 180th meridian in the Pacific Ocean. Previously Lewis Carroll had badgered officials with the question: Leave London at noon and travel with the sun directly overhead, returning the next day. When does the new day begin? *VFR Greenwich Mean Time (GMT) was (more or less) universally adopted at this conference.

1927 40 pfennig violet stamp featuring Leibniz is issued in Germany. According to a 1960 article in Mathematics Magazine by Maxey Brooke of Sweeny Texas this was the first stamp featuring a mathematician in Philatelic history.

1951 Cuba commemorated the 30th anniversary of the winning of the World Chess title by Jose Raul Capablanca by issuing a stamp picturing the resignation play of Dr. Emanuel Lasker (1868-1941). [Scott #C44]. *VFR (The match began March 15, 1921, and ended (prematurely) on April 21, when Lasker retired from the match. At this point he was down 0-4, with 10 draws. Lasker had been champion since 1894. Capablanca retained the title until 1927, when he lost to Alexander Alekhine.)

2017 A nice number fact about today from John Cook at Algebra Fact @AlgebraFact

Today's date is prime if you write it as 11/1/2017, 11/01/2017, or 11/1/17.
i.e. 1112017, 11012017, and 11117 are all prime.


1535 Giambattista della Porta (1 November 1535 Vico Equense (near Naples), Italy
- 4 February 1615 Naples, Italy) was an Italian scholar who worked on cryptography and also on optics. He claimed to be the inventor of the telescope although he does not appear to have constructed one before Galileo.
In 1563, della Porta published De Furtivis Literarum Notis, a work about cryptography. In it he described the first known digraphic substitution cipher.[6] Charles J. Mendelsohn commented, "He was, in my opinion, the outstanding cryptographer of the Renaissance. Some unknown who worked in a hidden room behind closed doors may possibly have surpassed him in general grasp of the subject, but among those whose work can be studied he towers like a giant."
Della Porta invented a method which allowed him to write secret messages on the inside of eggs. During the Spanish Inquisition, some of his friends were imprisoned. At the gate of the prison, everything was checked except for eggs. Della Porta wrote messages on the egg shell using a mixture made of plant pigments and alum. The ink penetrated the egg shell which is semi-porous. When the egg shell was dry, he boiled the egg in hot water and the ink on the outside of the egg was washed away. When the recipient in prison peeled off the shell, the message was revealed once again on the egg white.

Della Porta was the founder of a scientific society called the Academia Secretorum Naturae (Accademia dei Segreti). This group was more commonly known as the Otiosi, (Men of Leisure). Founded sometime before 1580, the Otiosi were one of the first scientific societies in Europe and their aim was to study the "secrets of nature." Any person applying for membership had to demonstrate they had made a new discovery in the natural sciences.
His private museum was visited by travelers and was one of the earliest examples of natural history museums. It inspired the Jesuit Athanasius Kircher to begin a similar, even more renowned, collection in Rome.
*SAU *Wik

1585 Jan Brożek (Ioannes Broscius, Joannes Broscius or Johannes Broscius;) (1 November 1585 – 21 November 1652) was a Polish polymath: a mathematician, astronomer, physician, poet, writer, musician and rector of the Kraków Academy.
Brożek was born in Kurzelów, Sandomierz Province, and lived in Kraków, Staszów, and Międzyrzec Podlaski. He studied at the Kraków Academy (now Jagiellonian University) and at the University of Padua. He served as rector of Jagiellonian University.
He was the most prominent Polish mathematician of the 17th century, working on the theory of numbers (particularly perfect numbers) and geometry. He also studied medicine, theology and geodesy. Among the problems he addressed was why bees create hexagonal honeycombs; he demonstrated that this is the most efficient way of using wax and storing honey.
He contributed to a greater knowledge of Nicolaus Copernicus' theories and was his ardent supporter and early prospective biographer. Around 1612 he visited the chapter at Warmia and with the knowledge of Prince-Bishop Simon Rudnicki took from there a number of letters and documents in order to publish them, which he never did. He contributed to a better version of a short biography of Copernicus by Simon Starowolski. "Following his death, his entire collection was lost"; thus "Copernicus' unpublished work probably suffered the greatest damage at the hands of Johannes Broscius."
Brożek died at Bronowice, now a district of Kraków. One of the Jagiellonian University's buildings, the Collegium Broscianum, is named for him. *Wik

1828 Balfour Stewart (1 Nov 1828; 19 Dec 1887) Scottish meteorologist and geophysicist noted for his studies of terrestrial magnetism and radiant heat. His researches on radiant heat contributed to foundation of spectrum analysis. He was the first to discover that bodies radiate and absorb energy of the same wavelength. In meteorology, he pioneered in ionospheric science, making a special study of terrestrial magnetism. He proposed (1882) that the daily variation in the Earth's magnetic field could be due to air currents in the upper atmosphere, which act as conductors and generate electrical currents as they pass through the Earth's magnetic field. He also investigated sunspots. In 1887, he died, age 59, soon after suffering a stroke while crossing to spend Christmas at his estate in Ireland. *TIS

1828 William Henry Besant FRS (1 November 1828, Portsea, Portsmouth – 2 June 1917, Cambridge) was a British mathematician, brother of novelist Walter Besant.
In a competition, William won a scholarship to Corpus Christi College, Cambridge in 1844. He took part in Cambridge Mathematical Tripos in 1850, gaining the title of Senior Wrangler. He was also winner of Smith's Prize.
In 1853 William became a Fellow of Saint John's College, Cambridge where he was a lecturer in mathematics until 1889. His pupils included William Burnside, A. W. Flux and G. B. Mathews. Besant served as an examiner for Tripos in 1856, 1857, and 1885. He was also an examiner for University of London from 1859 to 1864. Besant was also a coach for students taking the Tripos; twenty-one of his students placed in the ranks of top ten wranglers. According to Mathews, "he had the great advantage (for a coach) of being equally good in geometry, analysis, and dynamics."
In 1859 Besant vacated his Fellowship with Saint John's college to marry Margaret Elizabeth Willis, daughter of Rev. Robert Willis, a professor of natural philosophy at Cambridge. They had two sons and a daughter. In 1863 Besant published Elementary Hydrostatics, a textbook on fluid statics containing mathematical exercises such as students might face in examination. The book was reprinted several times, and revised in 1892. He also wrote Treatise on Hydromechanics (1867) covering fluid mechanics. His book Elementary Conics came out in 1901.
Besant was a Fellow of the Royal Astronomical Society from 10 February 1854. He became a Fellow of the Royal Society in 1871. In 1883 Cambridge University bestowed upon him, and Edward Routh, the degree Sc.D.. He died on 2 June 1917 and is buried at the Parish of the Ascension Burial Ground in Cambridge. He created the term Glissettes for his studies on the objects for Notes on Roulettes and Glissettes(1871). He writes in the preface:

1864 Ludwig Schlesinger was a mathematician, born in what is now Slovakia, who worked on differential equations *SAU

1880 Alfred L. Wegener (1 Nov 1880; Nov 1930) Alfred Lothar Wegener was a German meteorologist and geophysicist who first gave a well-developed hypothesis of continental drift. He suggested (1912) that about 250 million yrs ago all the present-day continents came from a single primitive land mass, the supercontinent Pangaea, which eventually broke up and gradually drifted apart. (A similar idea was proposed earlier by F.B. Taylor in 1910.) Others saw the fit of coastlines of South America and Africa, but Wegener added more geologic and paleontologic evidence that these two continents were once joined. From 1906, interested in paleoclimatology, he went on several expeditions to Greenland to study polar air circulation. He died during his fourth expedition. *TIS (The hypothesis that continents 'drift' was first put forward by Abraham Ortelius in 1596 * Wik)

1913 Andrzej Mostowski was a Polish mathematician who worked on logic and the foundations of mathematics.*SAU

1919 Sir Hermann Bondi (1 Nov 1919; 10 Sep 2005) Austrian-born British mathematician and cosmologist who, with Fred Hoyle and Thomas Gold, formulated the steady-state theory of the universe (1948). Their theory addressed a crucial problem: "How do the stars continually recede without disappearing altogether?" Their explanation was that the universe is ever-expanding, without a beginning and without an end. Further, they said, since the universe must be expanding, new matter must be continually created in order to keep the density constant, by the interchange of matter and energy. The theory was eclipsed in 1965, when Arno Penzias and Robert Wilson discovered a radiation background in microwaves giving convincing support to the "big bang" theory of creation now accepted.*TIS

1920 Claude Ambrose Rogers FRS (1 November 1920 – 5 December 2005) was an English mathematician who worked on analysis and geometry, and in particular found the Rogers bound for dense packings of spheres and a counterexample to the Busemann–Petty problem. *Wik

1950 Robert B. Laughlin (1 Nov 1950, ) American physicist who (with Daniel C. Tsui and Horst Störmer) received the Nobel Prize for Physics in 1998 for research on the fractional quantum Hall effect. In a current-carrying conductor, the classic Hall effect is the voltage produced at right angles to a magnetic field, as first discovered in 1879. A century later the German physicist Klaus von Klitzing discovered that in a powerful magnetic field at extremely low temperatures the Hall resistance of a semiconductor is quantized in integral "steps". Using even stronger magnetic fields and lower temperatures, Störmer and Tsui discovered fractional steps, explained by Laughlin's theory that the electrons can form a new type of quantum fluid with quasiparticles carrying fractions of an electron's charge. *TIS


1884 Thomas MacRobert studied at Glasgow and Cambridge universities. He returned to Glasgow to a series of posts culminating in the professorship. He worked on Complex Analysis. He became President of the EMS in 1921 and was a founder member of the Glasgow Mathematical Association. *SAU

1943 Alexander George McAdie (4 Aug 1863, 1 Nov 1943) American meteorologist who was a pioneer in employing kites in the exploration of high altitude air conditions. As a college graduate, McAdie in Jan 1882 joined the Army Signal Service, which preceded the civilian U.S. Weather Bureau. He invented and patented devices to protect fruit from frost. He examined the influence of smoke pollution on the atmosphere, McAdie studied the relation between atmospheric electricity and auroral phenomena, and wrote about lightning as a hazard both in the air and on the ground. He believed that the units used in meteorology should be standardized by adoption of the metric system. McAdie was a founder of the Seismological Society of America. Mt. McAdie (13,799 ft.) in the Sierra Nevada was named for him.*TIS

1971 Leonard Jimmie Savage (20 November 1917 – 1 November 1971) was an American mathematician and statistician. Nobel Prize-winning economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." His most noted work was the 1954 book Foundations of Statistics, in which he put forward a theory of subjective and personal probability and statistics which forms one of the strands underlying Bayesian statistics and has applications to game theory.
During World War II, Savage served as chief "statistical" assistant to John von Neumann, the mathematician credited with building the first electronic computer.
One of Savage's indirect contributions was his discovery of the work of Louis Bachelier on stochastic models for asset prices and the mathematical theory of option pricing. Savage brought the work of Bachelier to the attention of Paul Samuelson. It was from Samuelson's subsequent writing that "random walk" (and subsequently Brownian motion) became fundamental to mathematical finance.
In 1951 he introduced the minimax regret criterion used in decision theory.
The Hewitt–Savage zero-one law is (in part) named after him, as is the Friedman–Savage utility function. *Wik

1989 Gerrit Bol (May 29, 1906 in Amsterdam, Nov 1, 1989) was a Dutch mathematician, who specialized in geometry. He is known for introducing Bol loops in 1937, and Bol’s conjecture on sextactic points.
Bol earned his PhD in 1928 at Leiden University under Willem van der Woude. In the 1930s, he worked at the University of Hamburg on the geometry of webs under Wilhelm Blaschke and later projective differential geometry. In 1931 he earned a habilitation.
In 1942–1945 during World War II, Bol fought on the Dutch side, and was taken prisoner. On the authority of Blaschke, he was released. After the war, Bol became professor at the Albert-Ludwigs-University of Freiburg, until retirement there in 1971. *Wik

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