## Tuesday 16 January 2018

### On This Day in Math - January 16

*hastac.org

“It has nothing to do with defending our country, except to make it worth defending.”
~Robert R Wilson, 1969 (at Senate Hearing to justify Fermilab funding)

The 16th day of the year; 16 is the only number that can be written as ab = ba when a and b are not equal.

16 and its next smaller square, 9,  form a square when added or multiplied: 16+9=25, 16x9=144

16 is the smallest number which is the sum of two distinct primes in two ways,  16 = 3 + 13 = 5 + 11

Jim Wilder pointed out that 1616 ends in 1616 , 18446744073709551616

EVENTS

1741 John Harrison receives a 500 Pound grant from the Board of Longitude, "on account of his making a Machine with Improvements upon two Others before contrived by him." *Derek Howse, Britain's Board of Longitude:the Finances, 1714-1828

1777 Euler last attended a meeting of the St. Petersburg Academy on this date, after which he sent his papers in to the Academy with his assistants. *Ed Sandifer

1826 Neils Henrik Abel wrote his teacher and friend Holmboe: “The divergent series are the invention of the devil.” *VFR

1831 In an audience with the King of Sardinia, Cauchy answered ﬁve questions with “I expected Your Majesty would ask me this, so I have prepared to answer it.” Then he took a memoir from his pocket and read it. *VFR

1832 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

1865 Founding of the London Mathematical Society. Despite its name, the London Mathematical Society (LMS) has, almost since its foundation, served as the national society for the British mathematical community. Its establishment in 1865 made Britain one of the first countries in the world to have such an organisation. What was to become the London Mathematical Society arose from a chance remark in a conversation between two former students of University College London in the summer of 1864. The two young men were Arthur Cowper Ranyard and George Campbell De Morgan, the son of one of the most influential British mathematicians of the day. Augustus De Morgan was the founding professor of mathematics at University College, which he had single-handedly established as the home of advanced mathematical education in London. Conscious of the key role the Professor's reputation could play in attracting members to the Society, it was agreed that George should ask his father to take the chair at the first meeting.
Agreeing to this, the senior De Morgan apparently insisted that their tentative title of The London University Mathematics Society, be changed, first to the University College Mathematical Society, and then, in order to widen the scope of the society's membership, to the London Mathematical Society. The newly-retitled society held its inaugural meeting at University College London on Monday, January 16th 1865, with De Morgan as its first president giving the opening address. Within months, it had attracted over 60 new members from around the country, including many of the leading British mathematicians of the 19th century, such as Arthur Cayley, James Joseph Sylvester, Henry John Stephen Smith, George Salmon, William Kingdon Clifford and James Clerk Maxwell. *A Brief History of the London Mathematical Society

1910 At six o’clock in the evening, Richard Courant was scheduled to be examined for his Ph.D. by Hilbert in mathematics, Voight in physics, and Husserl in philosophy. Hilbert arrived early and was anxious to get on with it so he could go home, but the others did not appear. Since Courant had written his dissertation under Hilbert, he had no need to probe Courant’s mathematical knowledge, so they talked about non-mathematical things. After forty minutes, Husserl appeared. Hilbert excused himself and went home. After Husserl asked one question, Courant asked him to explain a delicate point in phenomenology. This took the remainder of the alloted time. Voight never appeared. Later several friends rented a horse-drawn carriage and hauled Courant around the quiet town of Gottingen while they blared over megaphones: “Dr. Richard Courant summa cum laude!” [Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician (Springer 1976), pp. 33-34] *VFR

1913 Srinivasa Ramanujan, a 23 year old clerk in Madras, India, wrote G. H. Hardy, Professor at Cambridge, sending “a few examples of my theorems,” and asking for advice. Although he was inclined to dismiss it as a letter from a crank, Hardy and his colleague J. E. Littlewood puzzled out some of the 120 formulas in the letter after dinner and concluded that Ramanujan was a mathematical genius. Hardy immediately invited Ramanujan to England, where they collaborated on a number of important papers in number theory. *VFR ( Hardy figured that Ramanujan's theorems "must be true, because, if they were not true, no one would have the imagination to invent them".)

1956 The U.S. government's Semi-Automatic Ground Environment (SAGE) is disclosed to the public. SAGE, an air defense system, linked hundreds of radar stations in the United States and Canada in the first large-scale computer communications network. With the increasing possibility of a large-scale bomber attack on the United States in the mid-1950s, it became evident that further improvements in the nation's defense capability were needed. MIT's Lincoln Laboratory was commissioned to develop an automated nationwide computer-based air defense system. SAGE was completed in the early 1960s, revolutionizing air defense and civilian air traffic control. In 1979 SAGE was replaced by Regional Operations Control Centers (ROCC).*CHM

2015 The London Mathematical Society begins its 150th Anniversary Celebrations. The Launch event tok place at the prestigious Goldsmiths’ Hall, London. *London Mathematical Society

BIRTHS

1477 Johannes Schöner (16 Jan 1477; 16 Jan 1547) German geographer who is noted for making and printing geographical globes. A notable work from 1515 is one of the earliest surviving globes produced following the discovery of new lands by Christopher Columbus. It was the first to show the name America that had been suggested by Waldseemüller. Tantalizingly, it also depicts a passage around South America before it was recorded as having been discovered by Magellan. Schöner was a professor mathematics at the University of Nuremberg and was the author of numerous mathematical, astronomical and geographical works. In his first career, he was an ordained Roman Catholic priest, which he gave up on becoming a university professor and converted to a Lutheran. *TIS
Only one specimen of the famous Waldseemüller map survives. It once was owned by Schöner and was rediscovered in 1901 at Schloss Wolfegg in Upper Swabia. Since 2003 it is in possession of the Library of Congress.
It is best to refer to him using the usual 16th-century Latin term "mathematicus", as the areas of study to which he devoted his life were very different from those now considered to be the domain of the mathematician. He was a priest, astronomer, astrologer, geographer, cosmographer, cartographer, mathematician, globe and scientific instrument maker and editor and publisher of scientific tests. In his own time he enjoyed a European wide reputation as an innovative and influential globe maker and cosmographer and as one of the continents leading and most authoritative astrologers. Today he is remembered as an influential pioneer in the history of globe making and as a man who played a significant role in the events that led up to the publishing of Copernicus' "De revolutionibus" in Nürnberg in 1543. In 1538, Georg Joachim Rheticus, a young professor of mathematics at Wittenberg, stayed for some time with Schöner who convinced him to visit Nicolaus Copernicus in Frauenburg. In 1540, Rheticus dedicated the first published report of Copernicus work, the Narratio prima, to Schöner. As this was well received, Copernicus finally agreed to publish his main work, and Rheticus prepared Copernicus' manuscript for printing. *Wik
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1730 Jean-Baptiste-Gaspard Bochart de Saron (16 Jan 1730; 20 Apr 1794) French lawyer and natural scientist who pursued his interest in astronomy both as a productive amatuer and a patron. He assembled a significant collection of astronomical instruments made by renowned craftsmen. He both utilized then himself and gave access to his academic colleagues. In collaboration with Charles Messier, who provided the data, he calculated orbits of comets, helping his friend find them again after they had disappeared behind the sun. He funded the publication of Laplace's Theory of the Movement and Elliptic Figure of the Planets (1784). Bochart made calculations for what was at first called Herschel's comet, supposing a circular orbit at twelve time the Sun-Saturn distance. This was refined by Laplace, and contributed to the discovery of Uranus. Bochart died as a politician guillotined during the French Revolution.*TIS

1801 Thomas Clausen. (16 Jan 1801 in Snogbaek, Denmark - 23 May 1885 in Dorpat, Russia (now Tartu, Estonia)) In 1854 he factored the Fermat number F (6) = 226 +1 as 274177 times 67280421310721, thus providing another counterexample to a conjecture of Fermat. (Euler factored F(5) in 1732.)*VFR Clausen wrote over 150 papers on pure mathematics, applied mathematics, astronomy and geophysics and worked with some of the best mathematicians of his day. *SAU

1807 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

1906 Erich Kähler (16 January 1906, Leipzig – 31 May 2000, Wedel) was a German mathematician with wide-ranging geometrical interests.
As a mathematician he is known for a number of contributions: the Cartan–Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Élie Cartan.
Kähler manifolds — complex manifolds endowed with a Riemannian metric and a symplectic form so that the three structures are mutually compatible — are named after him.
The K3 surface is named after Kummer, Kähler, and Kodaira.
His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted.*Wik

1925 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

DEATHS

1547 Johannes Schöner (16 Jan 1477; 16 Jan 1547) See births above, born and died on the same calendar day.

1834 Jean Nicolas Pierre Hachette was a French mathematician who worked on descriptive geometry. When the Ecole Polytechnique was established, he was appointed along with Monge over the department of descriptive geometry. There he instructed some of the ablest Frenchmen of the day, among them SD Poisson, François Arago and A Fresnel. *Wik

1887 Edward Olney (ALL-nee*) (July 24, 1827 - January 16, 1887) was born in Moreau, Saratoga County, New York. His ancestry can be traced back to Thomas Olney who accompanied Roger Williams in founding the city of Providence and colony of Rhode Island. Benjamin Olney's family moved to Oakland County, Michigan, in 1833 and, a few months later, settled on a farm in Weston, Wood County, Ohio.
Olney was largely self-taught. Calloway tells about Edward hiring a neighbor boy to drive the team of oxen on the Olney farm so that he could attend school for six weeks in order to master Day's Algebra. During this time he also ran an arithmetic school at home in the evenings in order to earn the money to pay for his substitute driver.
At age 19, Olney began his career as a teacher in the local elementary schools, while studying mathematics, natural science, and languages on his own. Cajori reports that "though he had never studied Latin, he began teaching it and kept ahead of the class because he 'had more application'." In 1848 Olney was hired as a teacher in the district school at Perrysburg, Ohio. The following year he was named principal of the grammar department in the new Union School. Over the next five years he would become the school's superintendent, marry Miss Sarah Huntington (a teacher at the school), and receive an honorary A. M. degree from Madison University (now Colgate University) in Hamilton, New York. Today there is an Olney School in Lake Township, Wood County, named after him.
In 1853 Olney was appointed Professor of Mathematics at Kalamazoo College, Michigan, where he remained for ten years and established the first mathematics curriculum at that institution. He inspired his colleagues and students alike with "his high Christian aims; his generous, self-sacrificing spirit; his thoroughness in government and discipline; and the inspiration which attended him." Although he insisted that his students recite using exact and correct language, he always tried to simplify the explanations of concepts and processes and make them more understandable. Kalamazoo college later conferred the honorary degree, LL. D. upon him.
In 1863 Olney was named Professor of Mathematics at the University of Michigan, succeeding George P. Williams, whose title was then changed to Professor of Physics. In those days the freshmen at Michigan were taught by inexperienced instructors, but once a week they had to recite for Professor Olney. His reputation for being a stern disciplinarian and a stickler for correct details earned him the nickname "Old Toughy." Nevertheless, he took great pains to see that the poorer students obtained help in making up their deficiencies. According to a former student, G. C. Comstock, "He was not a harsh man, and although the students stood in awe of him, I think that he was generally liked by them."
While he was at Michigan, Professor Olney began writing a series of successful mathematics textbooks for use in both grammar schools and colleges. In many places these displaced the works of such highly regarded authors as Charles Davies and Elias Loomis. Among the titles are: Elements of Arithmetic for Intermediate, Grammar, and Common Schools (1877), A University Algebra (1873), Elementary Geometry (1883), Elements of Trigonometry (1870), and A General Geometry and Calculus (1871) (online). Olney's treatment of calculus was criticized for using infinitesimal methods, but praised for giving "the elegant method, discovered by Prof. James C. Watson [Professor of Astronomy at Michigan], of demonstrating the rule for differentiating a logarithm without the use of series." It is said that Olney preferred geometry to analysis, and when teaching calculus, he would attempt to translate analytical expressions into their geometrical equivalents. This, along with his own struggles in self-education, contributed to his great success as a teacher and textbook author. Edward Olney died on January 16, 1887, after suffering for three years from the effects of a stroke. *David E. Kullman

1922 Pierre René Jean Baptiste Henri Brocard (12 May 1845 in Vignot (part of Commercy), France - 16 Jan 1922 in Bar-le-Duc, France) mathematician best known for his discovery of the so-called Brocard points of a triangle. His two major publications were the two volumes of Notes de bibliographie des corbes géométriques (1897, 1899) and the two volumes of Courbes géométriques remarkables the first of which was published in 1920, the second in 1967 long after his death. This last work was written in collaboration with T Lemoyne. The Notes may be regarded as a source book of geometric curves, with a painstakingly prepared index containing more than a thousand named curves. The text consists of brief descriptive paragraphs, with diagrams and equations of these curves. *SAU

1938 William Henry Pickering (15 Feb 1858, 16 Jan 1938) American astronomer who discovered Phoebe, the ninth moon of Saturn (1899). This was the first planetary satellite with retrograde motion to be detected, i.e., with orbital motion directed in an opposite sense to that of the planets. He set up a number of observing stations for Harvard. He made extensive observations of Mars and claimed, like Lowell, that he saw signs of life on the planet by observing what he took to be oases in 1892. He went further than Lowell however when in 1903 he claimed to observe signs of life on the Moon. By comparing descriptions of the Moon from Giovanni Riccioli's 1651 chart onward, he thought he had detected changes that could have been due to the growth and decay of vegetation.*TIS

1941 Charles Thurstan Holland (Mar 1863, 16 Jan 1941) English radiologist who pioneered the clinical use of X-rays in the UK, beginning shortly after Roentgen announced their discovery. He was present at the first clinical use of X-rays in England, (7 Feb 1896) in the laboratory of Oliver Lodge, head of the physics department at Liverpool University. The wrist of a 12-year-old boy who had shot himself the previous month was examined. The boy had been brought there by surgeon Sir Robert Jones who with Lodge reported the case in the 22 Feb 1896 of The Lancet. Jones subsequently financed an X-ray apparatus for Holland to pioneer radiology at Royal Southern Hospital, Liverpool. During WWI, he perfected methods of detecting bullets and shell fragments in patients' bodies. *TIS

1967 Robert Jemison Van de Graaff (20 Dec 1901; 16 Jan 1967) American physicist and inventor of the Van de Graaff generator, a type of high-voltage electrostatic generator that can be used as a particle accelerator in atomic research. The potential differences achieved in modern Van de Graaff generators can be up to 5 MV. It is a principle of electric fields that charges on a surface can leap off at points where the curvature is great, that is, where the radius is small. Thus, a dome of great radius will inhibit the electric discharge and added charge can reach a high voltage. This generator has been used in medical (such as high-energy X-ray production) and industrial applications (sterilization of food). In the 1950s, Van de Graaff invented the insulating core transformer able to produce high voltage direct current.*TIS

2000 Robert Rathbun Wilson (4 Mar 1914, 16 Jan 2000) was an American physicist who was the first director of Fermilab. From 1967, he led the design and construction of Fermilab (the Fermi National Accelerator Laboratory) near Chicago, Illinois. He also improved the environment by restoring prairie at the site. It began operating in 1972 with the world's most powerful particle accelerator. With later improvements, it retained that status for well over three decades until it was superceded by the LHC (Large Hadron Collider) at the CERN laboratory in Geneva, Switzerland. Wilson is remembered for his justification of the needed financing at a Senate hearing in 1969, where he said “It has nothing to do with defending our country, except to make it worth defending.” He resigned in 1978 because he did not believe the government was giving it sufficient funding for its research mission.*TIS

2002 Robert Hanbury Brown (31 Aug 1916, 16 Jan 2002) English astronomer who was a pioneer in radar and observational astronomy. During and after WW II he worked with R.A. Watson-Watt and then E.G. Bowen to develop radar for uses in aerial combat. In the 1950s he applied this experience to radio astronomy, developing radio-telescope technology at Jodrell Bank Observatory and mapping stellar radio sources. He designed a radio interferometer capable of resolving radio stars while eliminating atmospheric distortion from the image (1952). With R.Q. Twiss, Brown applied this method to measuring the angular size of bright visible stars, thus developing the technique of intensity interferometry. They set up an intensity interferometer at Narrabri in New South Wales, Australia, for measurements of hot stars.*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