Wednesday 8 November 2023

On This Day in Math - November 8


Algebra exists only for the elucidation of geometry.
~William Edge

The 312th day of the year; the number is expressed 2222 in base five. [It is also a Zuckerman number (a number that is divisible by the product of its digits) Thanks to David Brooks].

312 = 0!*5! + 1!*4! + 2!*3! + 3!*2! + 4!*1! + 5!*0! *Derek Orr

and 3122 is the sum of the cubes of the integers from 14 to 25. 3122=n=1425n3 *

312 is between two twin primes 311 and 313.  Prime Curios points out that the next "see and say" number after 312 shares this quality, that is 131112 ("one three, one one, and one two") is between a pair of twin primes as well .
Patrick Honaker says this is the smallest such example.  


*Wik The library in 1566, drawn by John Bereblock and given to Queen Elizabeth I as part of a book when she first visited Oxford

1602 The Bodleian Library was established in Oxford, England. Whilst the Bodleian Library, in its current incarnation, has a continuous history dating back to 1602, its roots date back even further. The first purpose-built library known to have existed in Oxford was founded in the fourteenth century by Thomas Cobham, Bishop of Worcester. This small collection of chained books was situated above the north side of the University Church of St Mary the Virgin on the High Street. This collection continued to grow steadily, but when, between 1435 and 1437 Humphrey, Duke of Gloucester (brother of Henry V of England), donated a great collection of manuscripts, the space was deemed insufficient and a larger building was required. A suitable room was finally built above the Divinity School, and completed in 1488. This room continues to be known as Duke Humfrey’s Library.
The late sixteenth century saw the library go through a period of decline (to the extent that the library’s furniture was sold, and only three of the original books belonging to Duke Humfrey remained in the collection). It was not until 1598 that the library began to thrive once more, when Thomas Bodley (a former fellow of Merton College) wrote to the Vice Chancellor of the University offering to support the development of the library: "where there hath bin hertofore a publike library in Oxford: which you know is apparent by the rome it self remayning, and by your statute records I will take the charge and cost upon me, to reduce it again to his former use." Duke Humfrey’s Library was refitted, and Bodley donated a number of his own books to furnish it. The library was formally re-opened on 8 November 1602 under the name “Bodleian Library” (officially Bodley's Library) *Wik

1795   A letter from Miss Caroline Herschel to Sir Joseph Banks informs him that on the evening of the seventh she had observed a new comet.  "As the appearance of one of these objects is almost become a novelty,  I flatter myself that this intelligence will not be uninteresting to astronomers." *Phil. Trans. R. Soc. Lond. 1796 86, 131-134

1895 Wilhelm Conrad RÖNTGEN discovers x-rays. He followed his mentor August Kundt and became assistant at the University of Würzburg in 1872 (or 1871) but was not offered a post. He then worked at Strasbourg and Giessen, but returned in 1888 as Professor of Physics and Head of the Physikal Institut, then Rector of the University in 1894. There he discovered X-rays on the evening of Friday 8 Nov 1895 'at a late hour when assistants were no longer to be found in the laboratory'. He investigated the phenomenon in secret, taking an X-ray of his wife's hand, and first announced it in a paper, "Ein neue Art von Strahlen", to the Würzburg Physical-Medical-Society on 28 Dec and it appeared in their 1895 proceedings. By January he was famous. In the next year some 50 books and 1000 papers appeared on the subject! A journal devoted to the subject was founded in May 1896. The techniques of barium meals and enemas were developed in 1896. He left Würzburg for Munich in 1900, shortly before receiving the first Nobel Prize in Physics in 1901. He donated the prize money to the University of Würzburg. [Bowers. Darius, p. 48-49. Pengelley & Pengelley, pp. 155-157.] The Physikal Institut is at Röntgenring 8b and has a plaque on the outside. Röntgen's laboratory is now a modern physics laboratory, but the Institut has three display cases of memorabilia, including the X-ray of his wife's hand, his Nobel Prize certificate and a commendation from the German Physics Society, signed by Einstein and Planck. A lecture room that Röntgen used is preserved more or less as in his day. [Pengelley & Pengelley, pp. 158-159.]

1949 Claude Shannon's paper "Programming a Computer for Playing Chess", seminal in the development of computer chess and introducing the Shannon number is received by the Philosophical Magazine. It will be published in March of 1950. The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess. Shannon calculated it as an aside in his 1950 paper

In 1980, scientists at the Jet Propulsion Laboratory in California announced the discovery of a 15th moon orbiting the planet Saturn, courtesy of Voyager I.*TIS

2011 An asteroid the size of an aircraft carrier, asteroid 2005 YU55, passes close by the Earth. OK, it will miss Earth by at least 201,700 miles, but in astronomical terms that distance is not great. The moon is further away from us than that.*Indiana Public Media Moment of Science


1656 Edmund Halley born. He is best known for his accurate prediction that the comet of 1682 would return in 1758. The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet.*VFR (Image at top is from a St Helena stamp commemorating the tercentennial of Halley's visit.)
He became professor of geometry at Oxford and was later appointed the second Astronomer Royal. After originating the question that prodded Newton to write the Principia, Halley edited and arranged the publication of this seminal work. Halley identified the proper motion of stars, studied the moon's motion and tides, realized that nebulae were clouds of luminous gas among the stars, and that the aurora was associated with the earth's magnetism. His prediction of the transit of Venus led to Cook's voyage to Tahiti.*TIS
Halley was buried in the graveyard of the old church of St. Margaret, Lee (in London). In the same vault is Astronomer Royal John Pond; the unmarked grave of Astronomer Royal Nathaniel Bliss is nearby. *Wik

1843 Moritz Pasch (8 Nov 1843 in Breslau, Germany (now Wrocław, Poland)
- 20 Sept 1930 in Bad Homburg, Germany) mathematician who worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before. Pasch's analysis relating to the order of points on a line and in the plane is both striking and pertinent to its understanding. Every student can draw diagrams and see that if a point B is between A and a point C, then C is not between A and B, or that every line divides a plane into two parts. But no one before Pasch had laid a basis for dealing logically with such observations. These matters may have been considered too obvious; but the result of such neglect is the need to refer constantly to intuition, so that the logical status of what is being done cannot become clear. *SAU

1846 Eugenio Bertini (8 Nov 1846 in Forli, Italy - 24 Feb 1933 in Pisa, Italy) was an Italian mathematician who worked in projective and algebraic geometry. His work in algebraic geometry extended Cremona's work. He studied geometrical properties invariant under Cremona transformations and used the theory to resolve the singularities of a curve. A paper by Kleiman studies what the authors calls the two fundamental theorems of Bertini. These two fundamental theorems are among the ones most used in algebraic geometry. The first theorem is a statement about singular points of members of a pencil of hypersurfaces in an algebraic variety. The second theorem is about the irreducibility of a general member of a linear system of hypersurfaces. *SAU

1848 (Friedrich Ludwig) Gottlob Frege (8 Nov 1848; 26 July 1925) was a German mathematician and logician, founder of modern symbolic logic and first to put forward the view that mathematics is reducible to logic. He extended Boole's work by inventing logical symbols (symbols for "or"," if-then", etc.) that improved on the syllogistic logic it replaced. He also worked on general questions of philosophical logic and semantics. His theory of meaning, based on making a distinction between what a linguistic term refers to and what it expresses, is still influential. Frege tried to provide a rigorous foundation for mathematics on the basis of purely logical principles, but abandoned the attempt when Bertrand Russell, on whose work he had a profound influence, pointed out a paradox that made the system inconsistent. *TIS Frege's influence in the short term came through the work of Peano, Wittgenstein, Husserl, Carnap and Russell. In the longer term, however, Frege has become a major influence on the development of philosophical logic and the man who seems to have been largely ignored by his contemporaries has been avidly read by many in the second half of the twentieth century, particularly after his works were translated into English. *SAU

1854 Johannes Robert Rydberg (8 Nov 1854; 28 Dec 1919) Swedish physicist, known for the Rydberg constant in his empirical formula that related the wave numbers of the spectral lines of an element (1890). This formula expressed fundamental relationships in those lines, which he presumed were the result of the inner nature and structure of an element's atoms. In 1897, he suggested that an atomic number for each of the elements, rather than atomic weights, would be a better means for organizing the elements and their periodicity of their characteristics. His work did provided the basis for discovering the electron shell structure of the atom. It was later established that the integer number of positive charges on an element's nucleus (its number of protons) corresponded to his idea of atomic number. *TIS

1868 Felix Hausdorff (8 Nov 1868 in Breslau, Germany (now Wrocław, Poland)
- 26 Jan 1942 in Bonn, Germany) worked in topology creating a theory of topological and metric spaces. He also worked in set theory and introduced the concept of a partially ordered set.
As a Jew his position became more and more difficult. In 1941 he was scheduled to go to an internment camp but managed to avoid being sent.
Bonn University requested that the Hausdorffs be allowed to remain in their home and this was granted. By October 1941 they were forced to wear the "yellow star" and around the end of the year they were informed that they would be sent to Cologne.
They were not sent to Cologne but in January 1942 they were informed that they were to be interned in Endenich. Together with his wife and his wife's sister, he committed suicide on 26 January. He wrote to a friend on Sunday 25 January:
Dear Friend Wollstein
By the time you receive these lines, we three will have solved the problem in another way - in the way which you have continually attempted to dissuade us. ...
What has been done against the Jews in recent months arouses well-founded anxiety that we will no longer be allowed to experience a bearable situation. ...
Forgive us, that we still cause you trouble beyond death; I am convinced that you will do what you are able to do (and which perhaps is not very much). Forgive us also our desertion! We wish you and all our friends will experience better times
Yours faithfully
Felix Hausdorff
On the night of Sunday 25 January all three took barbiturates. Both Hausdorff and his wife Charlotte were dead by the morning of the 26 January. Edith, Charlotte's sister, survived for a few days in a coma before dying. *SAU
Example of non-integer dimensions. The first four iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses the scale factor (S = 3) and the number of self-similar objects (N = 4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26  *Wik  

1904 William Leonard Edge (8 Nov 1904 in Stockport, England - 27 Sept 1997 in Bonnyrigg, Scotland) graduated from Cambridge and lectured at Edinburgh University. He wrote many papers in Geometry. He became President of the EMS in 1944 and an honorary member in 1983. Edge wrote nearly 100 papers and his mastery of the area ranks him with Coxeter as one of the leading geometers of the 20th century. His work was a continuation of work started by the great geometers of the late 19th and early 20th centuries, in particular Castelnuovo, Cayley, Clebsch, Cremona, Fano, Fricke, Humbert, Klein, Plücker and Schläfli. Edge investigated a pencil of canonical curves of genus 6 on a del Pezzo quintic surface in a 5-dimensional projective space. He investigated the group of self-projectivities of the space, which is isomorphic to the symmetric group S5. He also used geometrical configurations to investigate groups and, although his work was out of fashion at a time when group theorists were moving towards the classification of finite simple groups, his work did provide a deeper understanding of some of these groups, for example Conway's simple groups. Edge was not someone uninterested in modern techniques, however, and it may come as a surprise to some that in a 1991 paper he included computer-drawn pictures.
Other topics Edge worked on, all of which exhibit his mastery of the subject, include nets of quadric surfaces, the geometry of the Veronese surface, Klein's quartic, Maschke's quartic surfaces, Kummer's quartic, the Kummer surface, Weddle surfaces, Fricke's octavic curve, the geometry of certain groups, finite planes and permutation representations of groups arising from geometry. *SAU

1914 George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.
Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and his work with linear programming, some years after it was invented by the Soviet mathematician & economist Leonid Kantorovich. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman.
Dantzig was the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford.*TIS

Dantzing is known for the "accidental" solution of two unsolved problems which he mistook for homework.  


1633 Xu Guang-qi was a Chinese mathematician who made Western mathematics available by translating works into Chinese.*SAU

1703 John Wallis (3 Dec 1616- 8 Nov 1703) English mathematician. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Wallis was part of a group interested in natural and experimental science who started to meet in London. This group became the Royal Society (1663), with Wallis as a founder member and one of its first Fellows. He contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. Wallis introduced our the symbol infinity for infinity (1656), and exponents using negative or fractional numbers (such as 1/x2 = x-2 or sqrt(x)=x^(1/2). In 1668, he was the first to suggest the law of conservation of momentum for colliding bodies, the first of all-important conservation laws.*TIS

1719 Michel Rolle, (21 April 1652 – 8 November 1719)whose favorite area of research was the theory of equations. He introduced the symbol we use for nth roots. *VFR (famous to Calculus I students for Rolle's Theorem... and I always tell my students he had a daughter named Tootsie) . He also deserves to be known as the co-inventor in Europe of Gaussian elimination.In 1690, Rolle published Traité d'Algebre. It contains the first published description in Europe of the Gaussian elimination algorithm, which Rolle called the method of substitution. *Wik

1858 George Peacock (9 Apr 1791 - 8 Nov 1858) English mathematician who, with fellow Cambridge undergraduates Charles Babbage and John Herschel brought reform to nomenclature in English mathematics. They formed the Analytical Society (1815) whose aims were to bring the advanced methods of calculus from Europe to Cambridge to replace the increasingly stagnant notation of Isaac Newton from the previous century. The Society produced a translation of a book of Lacroix in the differential and integral calculus. In 1830, he published Treatise on Algebra which attempted to give algebra a logical treatment, and which went at least partway toward the establishment of symbolic algebra. Instead of using only numbers he used objects, and showed the associativity and commutativity of these objects.*TIS
A really enjoyable book covering this development in English Mathematics is The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World
, by Laura Snyder.

1952 Gino Fano (5 January 1871 – 8 November 1952) died in Verona, Italy. This geometer created a finite geometry that is now a common classroom example. *VFR  Fano worked on projective and algebraic geometry; the Fano postulate, Fano plane, Fano fibration, Fano surface, and Fano varieties are named for him. *Wik

1969 Vesto Melvin Slipher (11 Nov 1875, 8 Nov 1969) American astronomer whose systematic observations (1912-25) of the extraordinary radial velocities of spiral galaxies provided the first evidence supporting the expanding-universe theory. Died at Flagstaff, Ariz. *TIS

2001 Albrecht Fröhlich (22 May 1916 – 8 November 2001) was a German mathematician who made important contributions to group theory*SAU  He was most well known for his major results and conjectures on Galois module theory in the Galois structure of rings of integers. *Wik

2004 Melba Newell Phillips (February 1, 1907 - November 8, 2004) was an American physicist and science educator. She completed her doctoral studies under J. Robert Oppenheimer and was also known for refusing to testify before a U.S. Senate Judiciary Committee's subcommittee on internal security, her actions leading to her dismissal by Brooklyn College. (Phillips appeared before a subcommittee hearing in New York and agreed to answer questions relating to her work as a scientist and physics educator, she invoked her Fifth Amendment rights when asked about other topics, including questions about whether she was a member of the Communist party.)
(In 1987 Brooklyn College publicly and personally apologized to Phillips for her dismissal from the College in 1952.)
Melba Phillips was born in Hazleton, Indiana. She graduated from high school at the age of 15 and went on to study Mathematics at Oakland City College, Indiana graduating in 1926. She received a master's degree in physics from Battle Creek College of Michigan in 1928 and her doctorate in physics in 1933 at the University of California, Berkeley.
Phillips's supervisor at Berkeley was J. Robert Oppenheimer, who would later become scientific head of the Allied atomic bomb effort, the Manhattan Project. Together they described the Oppenheimer-Phillips effect explaining the behavior of accelerated nuclei of radioactive hydrogen atoms in 1935. *Wik

2009 Vitaly Lazarevich Ginzburg, ( October 4, 1916 – November 8, 2009) was a Soviet and Russian theoretical physicist, astrophysicist, Nobel laureate, a member of the Soviet and Russian Academies of Sciences and one of the fathers of Soviet hydrogen bomb.[2][3] He was the successor to Igor Tamm as head of the Department of Theoretical Physics of the Academy's physics institute *Wik & *TIS

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

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