Tuesday, 12 January 2021

On This Day in Math - Jan 12


Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
~Hermann Minkowski

The 12th day of the year; 12 is the smallest abundant number (number whose proper factors add up to more than the number itself). It is also the largest number of spheres that may be in contact with a given sphere in 3-D (This is not trivial, Newton couldn't prove it). See Kissing Number.

Behold the Oreo, it's a tasty treat and a duodecimal sensation. Each has 12 dashes, 12 dots, and 12 flowers around the periphery. Observe... dip in the milk... ahhhhh

And for chess buffs, it takes 12 knights to attack/occupy every square on chessboard. And there are 12 ways for 8 queens to be placed on a chess board so that none attacks another.

And Fermat was wrong, at least for the 12th dimension. 1782¹² + 1841¹² = 1922¹² (Well, almost; and  from the 1995 Halloween "Treehouse of Horror" series on The Simpsons). *Simon Singh

The 12 letter word "tattarrattat" is the longest palindrome in the Oxford English Dictionary, coined by James Joyce in Ulysses for a knock on the door

There is only one number that is spelled with twelve different letters. If you can't think of it, check the bottom of the post below credits. *Pi Guy@grey_matter

In 1913 R. D. Carmichael proved his conjecture that for any Fibonacci Number F(n), with n greater than 12, has at least one prime factor that is not a factor of any earlier Fibonacci number. 


1721 John Hadley showed up at a meeting of the Royal Society with a reflecting telescope six feet long which magnified 200 times and was made according to Newton’s plan. *VFR Thony Christie has a nice post about Hadley and his brothers contributions.

1812 Thomas Jefferson writes to his old friend John Adams about his life after the Presidency, "I have given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid; and I find myself much the happier."  *Steven Strogatz, The Joy of X

1817 Thomas Young writes to Arago to explain his theory of transverse vibration to explain polarization.  He had struggled for six years to find a way to explain polarization with a wave theory of light.  *A history of physics in its elementary branches By Florian Cajori

1820 Founding of the Royal Astronomical Society of England. Charles Babbage was one of the founding members. *Goldstine, The Computer from Pascal to von Neumann, p. 10 *VFR.
  The 'Astronomical Society of London' was conceived on 12 January 1820 when 14 gentlemen sat down to dinner at the Freemason's Tavern, in Lincoln's Inn Fields, London. After an unusually short gestation the new Society was born on 10 March 1820 with the first meeting of the Council and the Society as a whole. An early setback, when Sir Joseph Banks induced the Duke of Somerset to withdraw his agreement to be the first President, was overcome when Sir William Herschel agreed to be the titular first President, though he never actually took the Chair at a meeting. *Royal Astronomical Society

1875 The aerophore, an apparatus to enable a person to enter a noxious, inflammable atmosphere, was successfully tested at Chatham, 12-14 Jan 1875. Invented by Louis Denayrouze, a naval lieutenant, it comprised an air-pump, lamp, and flexible tubing*. Air in cylinders at a pressure of 300-350 lb/in2, reduced through a valve to atmospheric pressure, supported respiration. The apparatus was heavy and unmanageable for more than an hour's supply. He and Benoit Rouquayrol, a French mining engineer, had patented an underwater aerophore (1865), a steel tank filled with compressed air carried on a diver's back, connected through valves to a mouthpiece. It was the predecessor of contemporary scuba equipment. *TIS

1896, the first x-ray photograph in the U.S. was taken by Dr. Henry Louis Smith, a professor of physics and astronomy at Davidson College, Davidson, NC. It showed the location of a bullet in the hand of a corpse, using a 15 minute exposure. Immediately after he first heard of Roentgen's discovery in Germany, Smith obtained the hand of the corpse, and fired a bullet into it, for this experiment. In Feb 1896, he published this X-Ray photograph in the Charlotte Observer. He was subsequently elected president of Davidson College in 1901. In 1905, Smith established the first electric light plant in the town of Davidson.*TIS

1898 Charlotte Agnes Scott wrote to to M. Carey Thomas: “I am most disturbed and disappointed at present to find you taking the position that intellectual pursuits must be ‘watered down’ to make them suitable for women and that a lower standard must be adopted in a woman’s college than in a man’s.” At the time Scott, who received a “First Class” D.Sc. from the University of London in 1885, was a faculty member at Bryn Mawr. Thomas was president of Bryn Mawr and the first American woman to earn a doctorate in any field (linguistics from Zurich in 1882). *Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell, 196-197 *VFR

1924 The first U.S. History of Science Society was organized in Boston “to encourage and maintain active interest in the history of science and the various sciences in particular.” The movement to form the society was begun by David Eugene Smith and today is the most important historical society in the world. *VFR
1997 The fictional HAL 9000 computer becomes operational, according to Arthur C. Clarke's 2001: A Space Odyssey. In the 1968 movie adaptation, the computer's statement -- I am a HAL 9000 computer, Production Number 3. I became operational at the HAL Plant in Urbana, Illinois, on January 12, 1997 -- put his birthdate in 1992. Both dates have now passed with no super-intelligent, human-like HAL computer in sight. *CHM

1937 Solomon Lefschetz writes to John F. O'Hara, president of Notre Dame, to suggest the hiring of Emil Artin, a professor at Hamburg with a wife who was half Jewish. Within two weeks Hitler would make a proclamation that anyone with a spouse declared Jewish would also lose their jobs. "
1 October 1937, Artin and his family arrived in America. Notre Dame had recently hired Karl Menger and Lefshetz wrote:

Volume 50, Number 2, April 2013, Pages 321–330


1716 Antonio de Ulloa (12 Jan 1716; 5 Jul 1795) Spanish scientist and naval officer who discovered the element platinum (atomic number 78). In 1735, the French and Spanish governments sent an scientific expedition to Peru and Equador to measure a degree of meridian at Quinto, close to the equator. Ulloa was one of the officers appointed to take charge of the expedition. In 1744, the ship on which he returned was captured by the British, and he was taken prisoner, though treated respectfully by the English naval officers for they "were not at war with the arts and sciences." The log of his voyage to Peru published in 1748 contains a description of platinum. He established the first museum of natural history and the first metallurgical laboratory in Spain, as well as the Cadiz observatory.*TIS

1853 Gregorio Ricci-Curbastro (12 Jan 1853; 6 Aug 1925) Italian mathematician instrumental in the development of the absolute differential calculus (also called the Ricci calculus), now known as tensor analysis. Ricci-Curbastro's early work was in mathematical physics, particularly on the laws of electric circuits and differential equations. He changed area somewhat to undertake research in differential geometry and was the inventor of the absolute differential calculus between 1884 and 1894. Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity. As a councillor for his home town of Lugo, he was involved in many projects relating to the supply of water and to swamp drainage.*TIS

1857 Knut Johan Angstrom (12 Jan 1857; 4 Mar 1910) Swedish physicist, son of Anders Angstrom, who invented an electric compensation pyrheliometer and other devices for infra-red photography. With these, he studied the sun's heat radiation*TIS

1888 Sir Thomas Ralph Merton KBE, DSc, FRS (12 January 1888–10 October 1969) was an English physicist, inventor and art collector. He is particularly noted for his work on spectroscopy and diffraction gratings. Diffraction gratings were one of his lifelong interests and here his inventive genius best showed itself. The rarity and expense of good diffraction gratings led him to devise, in 1935, a method of copying them without loss of optical quality, by applying a thin layer of a cellulose ester solution to an original plane grating. When the solvent had evaporated he detached this pellicle and applied its grooved surface to a moist gelatine film on a glass plate. When dry, the gelatine bore a faithful record of the original rulings.
In 1948 Merton made an important basic advance in the art of ruling diffraction gratings. Since 1880 these had been ruled groove by groove by the method used by Rowlands. In place of this, Merton ruled a very fine helix continuously on a steel cylinder which he then opened out upon a plane gelatine-coated surface by his copying method. No lathe could, however, rule a helix free from errors of pitch and these Merton eliminated by an ingenious device. It consisted of a ‘chasing lathe’ by which he cut a secondary helix on the same cylinder with a tool mounted on a ‘nut’ lined with strips of cork pressed upon the primary lathe-cut helix. Periodic errors were thus averaged and eliminated by the elasticity of the cork.
In 1947 Merton bought Stubbings House, at Maidenhead Thicket, Berkshire. Its spacious rooms made an appropriate setting for his collection of pictures. As a man of considerable wealth, he maintained what was probably the last private physics laboratory in Britain. Papers and patents continued to appear, based on his researches there. In 1957 he had several serious operations and thereafter he rarely left his home, where he died on 10 October 1969.*Wik

1896 David Wechsler (12 Jan 1896; 2 May 1981) U.S. psychologist and inventor of several widely used intelligence tests for adults and children. During WW I, while assisting Edwin Garrigues Boring (1886-1968) in testing army recruits, Wechsler realized the inadequacies of the Army Alpha Tests (designed to measure abilities of conscripts and match them to suitable military jobs). He concluded that academically defined "intelligence" did not apply to "real life" situations. After leaving the military and more years of research, he developed the Wechsler Adult Intelligence Scale, and introduced deviation scores in intelligence tests. He developed the Wechsler Memory Scale in 1945, Wechsler Intelligence Scale for Children (1949), and Wechsler Preschool and Primary Scale of Intelligence (1967).*TIS

1903 Igor Vasilyevich Kurchatov (12 Jan 1903; 7 Feb 1960) Soviet nuclear physicist who from 1932 conducted nuclear science research in the Soviet Union, during which time his team built a cyclotron, a proton accelerator and studied artificial radioactivity and neutron-proton interactions. During WW II, he was chosen as director for the development of his country's first atomic bomb, detonated 29 Aug 1949. Meanwhile, in Dec 1946, Kurchatov demonstrated a working prototype reactor, though limited to producing only a few watts and by Jun 1948, a plutonium production reactor. He subsequently produced the world's first practical thermonuclear bomb (1952). Before 1978, the Soviet name for element-104 was kurchatovium (Ku), though subsquently rutherfordium (Rf) became the accepted name. *TIS

1906 Kurt Hirsch (12 Jan 1906 in Berlin, Germany - 4 Nov 1986 in London, England) worked in various areas of Group Theory.*SAU

1915 Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician who did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still (as of 2007) in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping).*WIK


1665 Pierre de Fermat, age 65, died without publishing a single mathematical work. However, because of his correspondence he was known as one of he best mathematicians in Europe. *VFR
(17 Aug 1601, 12 Jan 1665)French mathematician, often called the founder of the modern theory of numbers. Together with Rene Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. He anticipated differential calculus with his method of finding the greatest and least ordinates of curved lines. He proposed the famous Fermat's Last Theorem while studying the work of the ancient Greek mathematician Diophantus. He wrote in pencil in the margin, "I have discovered a truly remarkable proof which this margin is too small to contain," that when the Pythagorean theorem is altered to read an + bn = cn, the new equation cannot be solved in integers for any value of n greater than 2. *TIS The quote in the margin is given this way by *SAU : "To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it."
The exact dates of his birth, (and death?) are somewhat contested.  A seemingly new tombstone erected shows his date of death as 13 January, an older tombstone dedicated by his son gives the 12th.  For instance, " His tombstone in the church of the Augustines in Toulouse (later in the museum) gives the date of death as above, and the age as fifty-seven [57] years" was sent to the Math History archives at the Math Forum by Julio Gonzalez Cabillon, and supported by other such references. 

1849 James Thomson (13 Nov 1786 in Annaghmore, near Ballynahinch, Co. Down, Ireland - 12 Jan 1849 in Glasgow, Scotland) campaigned to reform Glasgow University. He wrote many textbooks. He was the father of Lord Kelvin.*SAU

1909 Hermann Minkowski (22 Jun 1864, 12 Jan 1909) German mathematician who developed the geometrical theory of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity. By 1907, Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-euclidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional "space-time continuum". Minkowski worked out a four-dimensional treatment of electrodynamics. His idea of a four-dimensional space (since known as "Minkowski space"), combining the three dimensions of physical space with that of time, laid the mathematical foundation of Albert Einstein's general theory of relativity.*TIS  Minkowski had won his first cash prize at the age of 16 in his first semester at University in Berlin, but then gave the cash to a needy student and never mentioned it to friends or family(his family found out when told by the brother of the student who had received the money). At the age of 17 he set his eyes on the Grand Prix of the Paris Academy. The problem was to prove the the number of representations of a number as the sum of five squares. (Unknown to the committee the problem had been solved an published by H J S Smith When Smith wrote Hermite that he had published a general solutions several years earlier, Hermite acknowledged that the committee was unaware of his work, and asked him to spare them embarrassment by writing up his work and submitting for the prize. Smith agreed and published his work, but Hermite later admitted he forgot to notify the prize committee of the contact with Smith.) Minkowski, meanwhile had become so involved in the problem that he went on to extend and generalize his solution to the point that he neglected to translate his paper into French, as required by the rules.  He submitted it anyway, with a short preface that indicated his neglect was due to his attraction to the topic.  When the prize was awarded, Minkowski, still only eighteen was named as a co-winner with Smith, who had died in February.  Minkowski died at noon on a Tuesday following an attack of appendicitis, and an operation on Sunday.  It was the practice of his associates to walk and talk together each Thursday at 3pm, and so on Thursday January 14th, Klein, Hilbert, Runge and the other mathematics professors walked together to carry Hermann Minkowski to his grave, at exactly 3pm.  *Constance Reid, Hilbert; pg 11

1996 Bartel Leendert van der Waerden (February 2, 1903, Amsterdam, Netherlands – January 12, 1996, Zürich, Switzerland) was a Dutch mathematician and historian of mathematics. Van der Waerden is mainly remembered for his work on abstract algebra. He also wrote on algebraic geometry, topology, number theory, geometry, combinatorics, analysis, probability and statistics, and quantum mechanics (he and Heisenberg had been colleagues at Leipzig). In his later years, he turned to the history of mathematics and science. His historical writings include Ontwakende wetenschap (1950), which was translated into English as Science Awakening (1954), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).*Wik

2001 William (Redington) Hewlett (20 May 1913, 12 Jan 2001) was an American electrical engineer who co-founded the Hewlett-Packard Company, a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with David Packard, a friend and Stanford classmate. (The order of their names was determined by a coin toss.) HP's first product was an audio oscillator based on a design developed by Hewlett when he was in graduate school. Eight were sold to Walt Disney for Fantasia. Lesser-known early products were: bowling alley foul-line indicator, automatic urinal flusher, weight-loss shock machine. The company's first "plant" was a small garage in Palo Alto, with $538 initial capital.*TIS

2004 Olga Aleksandrovna Ladyzhenskaya (March 7, 1922, Kologriv – January 12, 2004, St. Petersburg) was a Soviet and Russian mathematician. She was known for her work on partial differential equations (especially Hilbert's 19th problem) and fluid dynamics. She provided the first rigorous proofs of the convergence of a finite difference method for the Navier-Stokes equations. She was a student of Ivan Petrovsky. She was awarded the Lomonosov Gold Medal in 2002.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Five thousand

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