## Thursday, 8 February 2018

### On This Day in Math - February 8

 Edgeworth box; *daviddfriedman.com

The most important and urgent problems of the technology of today are no longer the satisfactions of the primary needs or of archetypal wishes, but the reparation of the evils and damages by technology of yesterday.
~Dennis Gabor

The 39th day of the year; 39 is the smallest number with multiplicative persistence 3. [Multiplicative persistence is the number of times the digits must be multiplied until they produce a one digit number; 3(9)= 27; 2(7) = 14; 1(4)=4. Students might try to find the smallest number with multiplicative persistence of four, or prove that no number has multiplicative persistence greater than 11]

For the 39th day: 39 = 3¹ + 3² + 3³ *jim wilder ‏@wilderlab

An Armstrong (or Pluperfect digital invariant) number is a number that is the sum of its own digits each raised to the power of the number of digits. For example, 371 is an Armstrong number since $3^3+7^3+1^3 = 371$. The largest Armstrong number in decimal numbers has 39 digits. (115,132,219,018,763,992,565,095,597,973,522,401 is the largest)
(Armstrong numbers are named for Michael F. Armstrong who named them for himself as part of an assignment to his class in Fortran Programming at the University of Rochester \)

I find it interesting that 39 = 3*13, and is the sum of all the primes from 3 to 13, 39=3+5+7+11+13

EVENTS
1587 Mary, Queen of Scots, was beheaded after Sir Francis Walsingham did a frequency count on Mary’s cipher, read her message, and uncovered her plot to assassinate Elizabeth I, Queen of England. *VFR  a more complete version of the "Babington Plot" and Walsingham's work in deciphering the code is here

In 1672, Isaac Newton's first paper on optics read before Royal Society in London. He had been elected a member only the previous month, recognizing his original design of the first reflecting telescope. Newton had already spent several years investigating optics, beginning in 1665. His studies of the colors from glass prisms with their dispersion of light were recorded in his essay New Theory about Light and Colors (1672), and expanded later in Opticks (1704).*TIS (Always sensitive to criticism, the controversy over his theories and experiments in light would lead to his not publishing on the topic until 1704.) Thony Christie has a nice post about Newton's research on color and light here.

In 1865, Gregor Mendel, aged 42, who first discovered the laws of genetics, read his first scientific paper to the Brünn Society for the study of Natural Sciences in Moravia (published 1866). He described his investigations with pea plants. Although he sent 40 reprints of his article to prominent biologists throughout Europe, including Darwin, only one was interested enough to reply. Most of the reprints, including Darwin's, were discovered later with the pages uncut, meaning they were never read. Fortunately, 18 years after Mendel's death, three botanists in three different countries researching the laws of inheritance, in spring 1900, came to realize that Mendel had found them first. Mendel was finally acknowledged as a pioneer in the field which became known as genetics*TIS

1913 Hardy wrote a letter to Ramanujan, (actually Littlewood wrote the letter, but surely speaking their joint interest) expressing his interest for his work. Hardy also added that it was "essential that I should see proofs of some of your assertions". *Wik

1945 A Patent is Filed for the Harvard Mark I. C.D Lake, H.H. Aiken, F.E. Hamilton, and B.M. Durfee file a calculator patent for the Automatic Sequence Control Calculator, commonly known as the Harvard Mark I. The Mark I was a large automatic digital computer that could perform the four basic arithmetic functions and handle 23 decimal places. A multiplication took about five seconds. *CHM (We've come a long way, baby.)

In 1969, pieces of a large meteorite were recovered in Chihuahua, Mexico. It fell at 1:05 am as a huge fireball that scattering several tons of material over an area measuring 48 by 7 km. Named after the nearby village of Allende, samples of this carbonaceous chondrite stone contain an aggregated mass of particles several of which can be easily identified as chondrules. This ancient material comes from before our Solar System formed, thus over 4.6 billion years old. Since these remnants represent the most primitive geological material from which planets were formed, and carry information to help explain the evolution of the our galaxy, Allende is one of the most studied meteorites in the world.*TIS

1978 The first issue of the CSHPM (Canadian Society for History and Philosophy of Mathematics) newsletter is issued. The issue announced the establishment of a fund as a memorial to Ken May. The fund will be used to underwrite the Kenneth O. May Lecture series. May had been one of the primary agents in the creation of the CSHPM. *CSHPM newsletter

BIRTHS

411 Proclus Diadochus (8 Feb 411 in Constantinople (now Istanbul), Byzantium (now Turkey) - 17 April 485 in Athens, Greece) was a Greek philosopher who became head of Plato's Academy and is important mathematically for his commentaries on the work of other mathematicians. *SAU

1627 Jonas Moore (8 Feb 1627 in Whitelee, Pendle Forest, Lancashire, England - 25 Aug 1679 in Godalming, England) was an English man of science important for his support of mathematics and astronomy.*SAU He seems to have been the first to use "cot" for the cotangent function. He also founded the Royal Mathematical School at Christ's Hospital with Samual Pepys to train young men in the mathematics of navigation. *Wik He made critical contributions to the draining of the fens in England (making my daily drive from Lakenheath to Stoke Ferry much easier) and was instrumental in convincing Charles II to create the Royal Observatory and appoint Flamsteed as Astronomer Royal. *The day that Jonas died, Renaissance Mathematicus.

1630 Pierre-Daniel Huet (8 Feb 1630, 26 Jan 1721) French scholar, antiquary, scientist, and bishop whose incisive skepticism, particularly as embodied in his cogent attacks on René Descartes, greatly influenced contemporary philosophers. Huet wrote a number of philosophical works that asserted the fallibility of human reason in addition to scientific work in the fields of astronomy, anatomy, and mathematics. *TIS

1677 Jacques Cassini (8 February 1677 – 16 April 1756) was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini.
Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. Having succeeded to his father's position at the observatory in 1712, he measured in 1713 the arc of the meridian from Dunkirk to Perpignan, and published the results in a volume entitled Traité de la grandeur et de la figure de la terre (1720). He also wrote Eléments d'astronomie (1740), and died at Thury, near Clermont. He published the first tables of the satellites of Saturn in 1716.*Wik

1700 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

1834 Dmitry Ivanovich Mendeleev (8 Feb 1834; 2 Feb 1907 at age 73) (Also spelled Mendeleyev) Russian chemist who developed the periodic classification of the elements. In his final version of the periodic table (1871) he left gaps, foretelling that they would be filled by elements not then known and predicting the properties of three of those elements.*TIS

1845 Francis Ysidro Edgeworth FBA (8 February 1845, Edgeworthstown – 13 February 1926, Oxford) was an Irish philosopher and political economist who made significant contributions to the methods of statistics during the 1880s. Edgeworth was a highly influential figure in the development of neo-classical economics. He was the first to apply certain formal mathematical techniques to individual decision making in economics. He developed utility theory, introducing the indifference curve and the famous Edgeworth box, which is now familiar to undergraduate students of microeconomics. He is also known for the Edgeworth conjecture which states that the core of an economy shrinks to the set of competitive equilibria as the number of agents in the economy gets large. In statistics Edgeworth is most prominently remembered by having his name on the Edgeworth series. *Wik In 1881 he published Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences. This work, really on economics, looks at the Economical Calculus and the Utilitarian Calculus. In fact most of his work could be said to be applications of mathematical psychics which Edgeworth saw as analogous to mathematical physics. They were applied to the measure of utility, the measure of ethical value, the measure of evidence, the measure of probability, the measure of economic value, and the determination of economic equilibria. He formulated mathematically a capacity for happiness and a capacity for work. His conclusions that women have less capacity for pleasure and for work than do men would not be popular today. *SAU

1853 Alexander Ziwet (February 8, 1853 - No vember 18, 1928) born in Breslau. He became professor at the University of Michigan, an editor of the Bulletin of the AMS, and a collector of mathematics text who enriched the Michigan library. *VFR His early education was obtained in a German gymnasium. He afterwards studies in the universities of Warsaw and Moscow, one year at each, and then entered the Polytechnic School at Karlsruhe, where he received the degree of Civil Engineer in 1880.
He came immediately to the United States and received employment on the United States Lake Survey. Two years later he was transferred to the United States Coast and Geodetic Survey, computing division, where he remained five years.
In 1888 he was appointed Instructor in Mathematics in the University of Michigan. From this position he was advanced to Acting Assistant Professor in 1890, to Assistant Professor in 1891, to Junior Professor in 1896, and to Professor of Mathematics in 1904.
He was a member of the Council of the American Mathematical Society and an editor of the "Bulletin" of the society. In 1893-1894 he published an "Elementary Treatise on Theoretical Mechanics" in three parts, of which a revised edition appeared in 1904. He also translated from the Russian of I. Somoff "Theoretische Mechanik" (two volumes, 1878, 1879).
*Burke A. Hinsdale and Isaac Newton Demmon, History of the University of Michigan (Ann Arbor: University of Michigan Press, 1906), pp. 320-321.

1875 Thomas John l'Anson Bromwich (8 Feb 1875 in Wolverhampton, England - 26 Aug 1929 in Northampton, England) He worked on infinite series, particularly during his time in Galway. In 1908 he published his only large treatise An introduction to the theory of infinite series which was based on lectures on analysis he had given at Galway. He also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest. In a series of papers he put Heaviside's calculus on a rigorous basis treating the operators as contour integrals*SAU G. H. Hardy described him as the “best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians.” *VFR

1928 Ennio de Giorgi (Lecce, February 8, 1928 – Pisa, October 25, 1996) was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.*SAU

DEATHS

1909 Giacinto Morera (born Novara, 18 July 1856 – died Turin, 8 February 1909), was an Italian engineer and mathematician. He is remembered for Morera's theorem in the theory of functions of a complex variables and for his work in the theory of linear elasticity. *Wik

1957 John von Neumann (28 Dec 1903, 8 Feb 1957 at age 53)Hungarian-American mathematician who made important contributions in quantum physics, logic, meteorology, and computer science. He invented game theory, the branch of mathematics that analyses strategy and is now widely employed for military and economic purposes. During WW II, he studied the implosion method for bringing nuclear fuel to explosion and he participated in the development of the hydrogen bomb. He also set quantum theory upon a rigorous mathematical basis. In computer theory, von Neumann did much of the pioneering work in logical design, in the problem of obtaining reliable answers from a machine with unreliable components, the function of “memory,” and machine imitation of “randomness.”*TIS

1974 Fritz Zwicky (14 Feb 1898, 8 Feb 1974 at age 76) Swiss-American astronomer and physicist who proposed dark matter exists in the universe, and made valuable contributions to the theory and understanding of supernovas (stars that for a short time are far brighter than normal).*TIS

1979 Dennis Gabor (5 Jun 1900, 8 Feb 1979 at age 78)  Hungarian-born British electrical engineer who won the Nobel Prize for Physics in 1971 for his invention of holography, a system of lensless, three-dimensional photography that has many applications. He first conceived the idea of holography in 1947 using conventional filtered-light sources. Because such sources had limitations of either too little light or too diffuse, holography was not commercially feasible until the invention of the laser (1960), which amplifies the intensity of light waves. He also did research on high-speed oscilloscopes, communication theory, physical optics, and television. Gabor held more than 100 patents. *TIS

2005 Germund Dahlquist (January 16, 1925 – February 8, 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations.*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