## Tuesday, 11 February 2020

### On This Day in Math - February 11

Good teachers deserve apples; great teachers deserve chocolate.
(A favorite quotation, written in calligraphy on his office door.)
~Richard Hamming

The 42nd day of the year; in The Hitchhiker's Guide to the Galaxy, the Answer to the Ultimate Question of Life, The Universe, and Everything is 42. The supercomputer, Deep Thought, specially built for this purpose takes 7½ million years to compute and check the answer. The Ultimate Question itself is unknown.

There is only one scalene triangle in simplest terms with integer sides and integer area of 42, it's perimeter is also 42. (There are only three integer (non-right) triangles possible with area and perimeter equal and all integer sides.)

42 is between a pair of twin primes (41,43) and its concatenation with either of them (4241, 4243) is also a prime, which means that 4242 is also between twin primes.

On September 6, 2019, Andrew Booker, University of Bristol, and Andrew Sutherland, Massachusetts Institute of Technology, found a sum of three cubes for $42= (–80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3$. This leaves 114 as the lowest unsolved case. At the beginning of 2019, 33 was the lowest unsolved case, but Booker solved that one earlier in 2019.

EVENTS

1144 "On the 11th February 1144 the Hellenistic science of alchemy entered medieval Europe by way of the Islamic empire. In his translation of Liber de compositione alchemiae (Book about the composition of alchemy) Robert of Chester wrote the following:
"I have translated this Book because, what alchemy is, and what its composition is, almost no one in our Latin [that is: Western] world knows. finished February 11th anno 1144."
From a blog at *RMAT

1635 Sir Charles Cavendish writes to William Oughtred to thank him for teaching him, "the way of calculating the divisions of your guaging rod." He also passes on praise for Oughtred’s, “Clavis is in great estimation amongst the mathematicians at Paris.“ *Augustus De Morgan, Correspondence of scientific men of the seventeenth century ..., Volume 1

In 1801, Giuseppe Piazzi made a 24th observation of the position of Ceres, the asteroid he discovered between the orbits of Mars and Jupiter, on 1 Jan 1801. It was the first and largest of the dwarf planets now known. After this, it moved into the light of the Sun, and was lost to view for most of the rest of the year. To mathematically relocate Ceres, Carl Gauss, age 24, took up the challenge to calculate its orbital path, based on the limited number of observations available. His method was tedious, requiring 100 hours of calculation. He began with a rough approximation for the unknown orbit, and then used it to produce a refinement, which became the subject of another improvement.. And so on. Astronomers using them found his results in close agreement as they located Ceres again 25 Nov-31 Dec 1801.« *TIS

1825 Charles Bonnycastle arrives in America to take up position as Professor of Natl. Philosophy at newly founded Univ of Virginia. He was found on the arrivals manifest of the ship Competitor from London captained by E.P. Godby which arrived in the District of Norfolk & Portsmouth. Passengers included Robley & Harriet Dungleson (Dr of Medicine), Chas Bonnycastle 27 Profr of Natl Philosophy, Thomas H & Sarah Key (Profr of Mathematics), Robert Lee 16, and F.W. Colquhoun 15. All intended to become inhabitants of the United States

1826 Founding of the University College of London. UCL was the first university institution to be founded in London and the first in England to be established on an entirely secular basis, to admit students regardless of their religion and to admit women on equal terms with men.
First professor of mathematics at UCL was  Augustus De Morgan.

1897 Indiana bill to ﬁx the value of π was introduced to the state senate, and referred to committee. It speciﬁed several values for π to simplify computation. On the 13th a bill to postpone consideration of the bill passed, and the bill has never been reintroduced. The official history of the Indiana General Assembly (p. 429) gives the credit to Professor Waldo for his intervention.(see my blog)

In 1939, the journal Nature published a theoretical paper on nuclear fission. The term was coined by the authors Lise Meitner and Otto Frisch, her nephew. They knew that when a uranium nucleus was struck by neutrons, barium was produced. Seeking an explanation, they used Bohr's "liquid drop" model of the nucleus to envision the neutron inducing oscillations in a uranium nucleus, which would occasionally stretch out into the shape of a dumbbell. Sometimes, the repulsive forces between the protons in the two bulbous ends would cause the narrow waist joining them to pinch off and leave two nuclei where before there had been one. They calculated calculated the huge amounts of energy released. This was the basis for nuclear chain reaction. *TIS (see Szilard below) (I was informed by Daniel Fischer@cosmos4u that this paper is now available here.

1948 Richard Duffin writes a recommendation for John Nash. Duffin was inducted to the National Academy of Sciences in 1972 and to the American Academy of Arts and Sciences in 1984. He was joint winner of the 1982 John von Neumann Theory Prize, and winner of Sigma Xi's Monie A. Ferst Award for 1984 in recognition of his ability as a teacher and communicator. This recommendation tends to emphasize his ability to communicate with few words. *HT to Sarah Crook@SarahRoseCrook

1966 The RAND Coporation Takes JOSS Out of Service:
The RAND Corporation takes the Johnniac Open Shop System (JOSS) out of service. JOSS was a conversational time-sharing service that eased the bottleneck experienced by programmers in the batch environment--typical of the time--in which long delays existed between sending information to the computer and getting results back. Timesharing aimed to bring the user back into contact with the machine for online debugging and program development. *CHM

1986 Soviet Jewish dissident, mathematician and computer expert, Anatoly Shcharansky was released by the Soviet Union in an East-West spy swap. Shcharansky, who helped run a committee monitoring human rights abuse in the Soviet Union, had been jailed since 1978 on charges of spying for the CIA. [UPI press release] *VFR

1999 Nature Magazine publishes an article on how to dunk a biscuit, by UK/Australian scientist, Len Fisher. The article, : "Physics Takes the Biscuit", would also win Professor Fisher an Ignoble Prize on September 30 at at the annual presentation at Harvard. Fisher followed with a Book on the topic, adjusted perhaps for American Audiences, called How to Dunk a Doughnut: The Science of Everyday Life, which includes other explanations of "everyday" science. You can read the chapter on dunking at Fisher's blog site, along with many other wonderful treats.*lenfisherscience.com, .improbable.com

2003 NASA's WMAP satellite completes the first detailed cosmic microwave background radiation map of the universe. The image reveals the universe is 13.7 billion years old (within one percent error) and provides evidence that supports the inflationary theory.*Wik

BIRTHS
1657  Bernard Le Bovier, sieur de Fontenelle (11 Feb 1657, 9 Jan 1757) French scientist and author, whose Conversations on the Plurality of Worlds (1686), was one of the first works to present science for the lay reader. He popularized the astronomical theories of Descartes. Many of the characteristic ideas of the Enlightenment are found in embryonic form in his works. From 1697 he became permanent secretary to the Académie des Sciences. He held the office for 42 years, and in this official capacity, he wrote the Histoire du renouvellement del Académie des Sciences (Paris, 3 vols., 1708, 1717, 1722) containing extracts and analyses of the proceedings, written with great simplicity and delicacy. Fontenelle presented many obituary notices to the Académie, including those of Newton and Leibniz. *TIS

1800 William Henry Fox Talbot (11 Feb 1800; 17 Sep 1877 at age 77)
English inventor, mathematician, chemist, physicist, philologist and Egyptologist who invented the negative-positive photographic process. He improved Thomas Wedgewood's discovery (1802) that brushing silver nitrate solution onto paper produces a light-sensitive medium able to record negative images, but Wedgewood was unable to control the darkening. In February 1835, Fox Talbot found that a strong solution of salt fixed the image. Using a camera obscura to focus an image onto his paper to produce a negative, then - by exposing a second sheet of paper to sunlight transmitted through the negative - he was the first to produce a positive picture of which he was able to make further copies at will. His Pencil of Nature (1844) was the first photographically illustrated book to be commercially published.. *TIS Talbot's family estate, the site of Lacock Abbey, was used for scenes from several of the Harry Potter films.

1839 Josiah Willard Gibbs (11 Feb 1839; 28 Apr 1903 at age 64)
was an American mathematical physicist and chemist known for contributions to vector analysis and as one of the founders of physical chemistry. In 1863, He was awarded Yale University's first engineering doctorate degree. His major work was in developing thermodynamic theory, which brought physical chemistry from an empirical inquiry to a deductive science. In 1873, he published two papers concerning the fundamental nature of entropy of a system, and established the “thermodynamic surface,” a geometrical and graphical method for the analysis of the thermodynamic properties of substances. His famous On the Equilibrium of Homogeneous Substances, published in 1876, established the use of “chemical potential,” now an important concept in physical chemistry.*TIS Gibbs studied at Yale, Paris, Berlin, and Heidelberg before becoming Professor of Mathematical Physics at Yale. He was one of the inventors of vector analysis, and discussed the “Gibbs Phenomenon” in the theory of Fourier Series. *VFR

1854 Benjamin Osgood Peirce (11 February 1854 Beverly, Massachusetts, USA — 14 January 1914 Cambridge, Massachusetts, USA) was an American mathematician and a holder of the Hollis Chair of Mathematics and Natural Philosophy at Harvard from 1888 until his death in 1914.*Wik

1862 Francis Sowerby Macaulay FRS (11 February 1862 – 9 February 1937) was an English mathematician who made significant contributions to algebraic geometry. He is most famous for his 1916 book, The Algebraic Theory of Modular Systems, which greatly influenced the later course of algebraic geometry. Both Cohen-Macaulay rings and the Macaulay resultant are named for Macaulay.
Macaulay was educated at Kingswood School and graduated with distinction from St John's College, Cambridge.  He taught top mathematics class in St Paul's School in London from 1885 to 1911. His students included J. E. Littlewood and G. N. Watson.*Wik Littlewood consulted the examinations record and wrote, "In the 25 years from [Macaulay's] appointment to St Paul's in 1885 to his resignation in 1911 there were 41 scholarships (34 at Cambridge) and 11 exhibitions; and in the 20 years available there were 4 senior wranglers, one second, and one fourth among his former pupils." *SAU

1887 John Jackson (11 Feb 1887 in Paisley, Renfrewshire, Scotland - 9 Dec 1958 in London, England) graduated from Glasgow and Cambridge. He went to the Royal Observatory at Greenwich but his career there was interrupted by World War I. He was then appointed HM Astronomer at the University of Cape Town. *SAU

1898 Leo Szilard (11 Feb 1898; 30 May 1964 at age 66) Hungarian-American physicist who, with Enrico Fermi, designed the first nuclear reactor that sustained nuclear chain reaction (2 Dec 1942). In 1933, Szilard had left Nazi Germany for England. The same year he conceived the neutron chain reaction. Moving to N.Y. City in 1938, he conducted fission experiments at Columbia University. Aware of the danger of nuclear fission in the hands of the German government, he persuaded Albert Einstein to write to President Roosevelt, urging him to commission American development of atomic weapons. In 1943, Major General Leslie Groves, leader of the Manhattan Project designing the atomic bomb, forced Szilard to sell his atomic energy patent rights to the U.S. government. *TIS Frederik Pohl , talks about Szilard's epiphany about chain reactions in Chasing Science (pg 25),
".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."

1891 Ivan Ivanovich Privalov (13 Feb 1891 in Nizhny Lomov, Penza guberniya (now oblast), Russia - 13 July 1941 in Moscow, USSR) Privalov, often in collaboration with Luzin, studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals. He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere. In 1934 he studied subharmonic functions, building on the work of Riesz. He published the monograph Subharmonic Functions in 1937 which gave the general theory of these functions and contained many results from his papers published between 1934 and 1937. *SAU

1897 Emil Leon Post (February 11, 1897, Augustów – April 21, 1954, New York City) was a mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. In 1936, Post developed, independently of Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewriting and developed by Post in the 1920s but first published in 1943. Post's rewrite technique is now ubiquitous in programming language specification and design, and so with Church's lambda-calculus is a salient influence of classical modern logic on practical computing. Post devised a method of 'auxiliary symbols' by which he could canonically represent any Post-generative language, and indeed any computable function or set at all.
The unsolvability of his Post correspondence problem turned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages.
In an influential address to the American Mathematical Society in 1944, he raised the question of the existence of an uncomputable recursively enumerable set whose Turing degree is less than that of the halting problem. This question, which became known as Post's problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
Post made a fundamental and still influential contribution to the theory of polyadic, or n-ary, groups in a long paper published in 1940. His major theorem showed that a polyadic group is the iterated multiplication of elements of a normal subgroup of a group, such that the quotient group is cyclic of order n − 1. He also demonstrated that a polyadic group operation on a set can be expressed in terms of a group operation on the same set. The paper contains many other important results.*Wik

1909 Claude Chevalley (11 Feb 1909 in Johannesberg, Transvaal, South Africa - 28 June 1984 in Paris, France had a major influence on the development of several areas of mathematics including Ring Theory and Group Theory *SAU

1915 Richard Wesley Hamming (11 Feb 1915, 7 Jan 1998)  was an American mathematician who devised computer Hamming codes - error-detecting and correcting codes (1947). These add one or more bits to the transmission of blocks of data, used for a parity check, so that errors can be corrected automatically. By making a resend of bad data unnecessary, efficiency improved for modems, compact disks and satellite communications. He also worked on programming languages, numerical analysis and the Hamming spectral window (used to smooth data before Fourier analysis is carried out). He taught at University of Louisville, then during WW II worked (1945) on computers with the Manhattan Project creating the atomic bomb. From 1946, he spent 30 years with Bell Telephone Labs, eventually becoming head of computing science research.*TIS

1917 Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach. *Wik

DEATHS
1141 Hugh of St. Victor died. For him the word “mathematica” had two meanings: When the ‘t’ is not aspirated it means “the superstition of those who place the destiny of men in the constellations” of the heavens; when the ‘t’ is aspirated it means the science of “abstract quantity.” *VFR

1555 Giovanni Antonio Magini (in Latin, Maginus) (June 13, 1555; Padua, Italy – February 11, 1617; Bologna, Italy) was an Italian astronomer, astrologer, cartographer, and mathematician.
Dedicating himself to astronomy, in 1582 he wrote Ephemerides coelestium motuum, translated into Italian the following year.
In 1588 he was chosen over Galileo to occupy the chair of mathematics at the University of Bologna after the death of Egnatio Danti.
Magini supported a geocentric system of the world, in preference to Copernicus's heliocentric system. Magini devised his own planetary theory, in preference to other existing ones. The Maginian System consisted of eleven rotating spheres, which he described in his Novæ cœlestium orbium theoricæ congruentes cum observationibus N. Copernici (Venice, 1589).
In his De Planis Triangulis (1592), he described the use of quadrants in surveying and astronomy. In 1592 Magini published Tabula tetragonica, and in 1606 devised extremely accurate trigonometric tables. He also worked on the geometry of the sphere and applications of trigonometry, for which he invented calculating devices. He also worked on the problem of mirrors and published on the theory of concave spherical mirrors.
He also published a commentary on Ptolemy’s Geographia (Cologne, 1596).
As a cartographer, his life's work was the preparation of Italia or the Atlante geografico d'Italia (Geographic Atlas of Italy), printed posthumously by Magini's son in 1620. This was intended to include maps of every Italian region with exact nomenclature and historical notes. A major project, its production (begun in 1594) proved expensive and Magini assumed various additional posts in order to fund it, including becoming tutor in mathematics to the sons of Vincenzo I of Gonzaga, Duke of Mantua, a major patron of the arts and sciences. He also served as court astrologer. The Duke of Mantua, to whom the atlas is dedicated, assisted him with this project and allowed for maps of the various states of Italy to be brought to Magini. The governments of Messina and Genoa also assisted Magini financially in this project. Magini did not do any of the mapping himself.
He was also interested in pursuits which today would be considered pseudoscientific. A strong supporter of astrology, he defended its use in medicine in his De astrologica ratione (Venice, 1607). Magini collaborated closely with Valentine Naibod, and in this book he published De annui temporis mensura in Directionibus and De Directionibus from Naibod's unfinished manuscript Claudii Ptolemaei Quadripartitae Constructionis Apotelesmata Commentarius novus et Eiusdem Conversio nova. He was also interested in metoposcopy.
He corresponded with Tycho Brahe, Clavius, Abraham Ortelius, and Johann Kepler.
*Wik

1626 Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate. Cataldi discovered the sixth and seventh Mersenne primes by 1588. He held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered 231 - 1 was the eighth Mersenne prime.*Wik
(It is known now that "J Scheybl gave the sixth perfect number in 1555 in his commentary to a translation of Euclid's Elements. This was not noticed until 1977 and therefore did not influence progress on perfect numbers." *SAU )

1650 René Descartes (31 March 1596 in La Haye (now Descartes),Touraine, France
- 11 Feb 1650 in Stockholm, Sweden)was a French philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian geometry. His work had a great influence on both mathematicians and philosophers. La Géométrie is by far the most important part of this work. Scott summarises the importance of this work in four points:

He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.
Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all.
Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method.
Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.
*SAU  His lifelong habit of laying abed till noon was interrupted by Descartes’ new employer, the athletic, nineteen-year-old Queen Christiana of Sweden, who insisted he tutor her in philosophy in an unheated library early in the morning. This change of lifestyle caused the illness that killed him. [Eves, Circles, 177◦]*VFR

1868 Jean Bernard Léon Foucault (18 Sep 1819; 11 Feb 1868) French physicist whose Foucault Pendulum experimentally proved that the Earth rotates on its axis (6 Jan 1851). Using a long pendulum with a heavy bob, he showed its plane rotated at a rate related to Earth's angular velocity and the latitude of the site. He studied medicine and physics and became an assistant at the Paris Observatory (1855). He invented an accurate test of a lens for chromatic and spherical aberations. Working with Fizeau, and also independently, he made accurate measurements of the absolute velocity of light. In 1850, Foucault showed that light travels slower in water than in air. He also built a gyroscope (1852), the Foucault's prism (1857) and made improvements for mirrors of reflecting telescopes. *TIS (a brief biography of Foucault is here)

1914 Alexander Ross Clarke (16 Dec 1828; 11 Feb 1914) English geodesist with the Army Ordnance Survey who made calculations of the size and shape of the Earth (the Clarke ellipsoid) were the first to approximate accepted modern values with respect to both polar flattening and equatorial radius. The figures from his second determination (1866) became a standard reference for U.S. geodesy for most of the twentieth century until satellites could improve accuracy. In 1880, Clarke coined the term "Geodesy" when he published his famous book by that title. He wrote articles on mathematical geography and geodesy and also contributed "The Figure of the Earth" in the Encyclopedia Britannica. His military service with the Ordnance Survey lasted 27 years.*TIS

1923 Wilhelm Karl Joseph Killing (10 May 1847 in Burbach (near Siegen), Westphalia, Germany - 11 Feb 1923 in Münster, Germany) introduced Lie algebras independently of Lie in his study of non-euclidean geometry. His classification of the simple Lie algebras was one of the finest achievements in the whole of mathematical research.*SAU

1942 Egbert van Kampen,(28 May 1908 in Berchem, Antwerp, Belgium - 11 Feb 1942 in Baltimore, Maryland, USA) In 1908 he left Europe and traveled to the United States to take up the position which he had been offered at Johns Hopkins University in Baltimore, Maryland. There he met Oscar Zariski who had taught at Johns Hopkins University as a Johnston Scholar from 1927 until 1929 when he had joined the Faculty. Zariski had been working on the fundamental group of the complement of an algebraic curve, and he had found generators and relations for the fundamental group but was unable to show that he had found sufficient relations to give a presentation for the group. Van Kampen solved the problem, showing that Zariski's relations were sufficient, and the result is now known as the Zariski–van Kampen theorem. This led van Kampen to formulate and prove what is nowadays known as the Seifert–van Kampen theorem. *Wik

1959  Hardy Cross (10 Feb 1885; died 11 Feb 1959 at age 73) U.S. professor of civil and structural engineering whose outstanding contribution was a method of calculating tendencies to produce motion (moments) in the members of a continuous framework, such as the skeleton of a building. By the use of Cross's technique, known as the moment distribution method, or simply the Hardy Cross method, calculation can be carried to any required degree of accuracy by successive approximations, thus avoiding the immense labour of solving simultaneous equations that contain as many variables as there are rigid joints in a frame. He also successfully applied his mathematical methods to the solution of pipe network problems that arise in municipal water supply design; these methods have been extended to gas pipelines. *TIS

1973  Johannes Hans Daniel Jensen (25 Jun 1907, 11 Feb 1973 at age 65) was a German physicist who proposed the shell theory of nuclear structure of nucleons - protons and neutrons - grouped in onion-like layers of concentric shells. He suggested that the nucleons spun on their own axis while they moved in an orbit within their shell and that certain patterns in the number of nucleons per shell made the nucleus more stable. Scientists already knew that the electrons orbiting the nucleus were arranged in different shells. For his model of the nucleus, Jensen shared the 1963 Nobel Prize in physics (with Maria Goeppert-Mayer, who arrived at the same hypothesis independently in the U.S.; and Eugene P. Wigner for unrelated work.) Through the 1950s, Jensen worked on radioactivity.
*TIS

1974 Vladimir Ivanovich Smirnov  (10 June 1887 – 11 February 1974) was a Russian mathematician who made significant contributions in both pure and applied mathematics, and also in the history of mathematics.
Smirnov worked on diverse areas of mathematics, such as complex functions and conjugate functions in Euclidean spaces. In the applied field his work includes the propagation of waves in elastic media with plane boundaries (with Sergei Sobolev) and the oscillations of elastic spheres.
Smirnov is also widely known among students for his five volume book A Course in Higher Mathematics (the first volume was written jointly with Jacob Tamarkin).*Wik

1976 Dorothy Maud Wrinch (12 September 1894 – 11 February 1976) married names Nicholson, Glaser) was a mathematician and biochemical theorist best known for her attempt to deduce protein structure using mathematical principles. *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