## Tuesday 13 December 2022

### On This Day in Math - December 13

 Scottish Café (Polish: Kawiarnia Szkocka) in Lwów

Once a sage asked why scholars always flock to the doors of the rich, whilst the rich are not inclined to call at the doors of scholars. "The scholars" he answered, "are well aware of the use of money, but the rich are ignorant of the nobility of science".
al-Biruni

The 347th day of the year; 347 is a safe prime, one more than twice a Sophie Germain Prime, 173. There is only one more safe prime this year.
And from Derek at @MathYearRound, "Adding 2 to any digit of 347 keeps it prime (547, 367 and 349 are prime)."

Derek's comment also points out that 347 is the smaller of a pair of twin primes. I just found out that, "(p, p+2) are twin primes if and only if p + 2 can be represented as the sum of two primes. Brun (1919)" (Brun showed that even if there are an infinity of prime pairs, the sum of their reciprocals converges.)

There are 347 even digits before the 347th odd digit of π. (How often is it true that after 2n digits of π there are n even and n odd digits?)

### Events

 Not the Actual Aurora from 1128  ;-}

1128 “In the third year of Lothar, emperor of the Romans, in the twenty-eighth year of King Henry of the English…on Saturday, 8 December, there appeared from the morning right up to the evening two black spheres against the sun.” This description of sunspots, and the earliest known drawing of sunspots, appears in John of Worcester’s Chronicle recorded in 1128. On the night of 13 December 1128, astronomers in Songdo, Korea, witnessed a red vapour that “soared and filled the sky” from the northwest to the southwest. A delay of five days is the average delay between the occurrence of a large sunspot group near the center of the Sun – exactly as witnessed by John of Worcester – and the appearance of the aurora borealis in the night sky at relatively low latitudes *Joe Hanson, itsokaytobesmart.com

1883 Felix Klein notes in his references, "Received call to go to Baltimore. Great desire to go there -- at the least a new start." He had received an offer to replace J. J. Sylvester as the Professor of Mathematics at Johns Hopkins University in the form of a telegram from Danial Colt Gilman, President of the University. Klein's response contains two demands. The first is that he will not take less than the salary of the departing Sylvester, (\$1000 a year more than the initial offer) and the second that his need for the economic security of his family should be somehow met (in Germany tenured positions included a pension that passed to the wife after the professor's death). Neither demand was met, and eventually Klein would go to Gottingen to develop his famous math institute. *Constance Reid, The Road Not Taken, Mathematical Intelligencer, 1978

1907 Emmy Noether received her Ph.D. degree, summa cum laude, from the University of Erlangen, for a dissertation on algebraic invariants directed by Paul Gordan. She went on to become the world’s greatest woman mathematician. [DSB 10, 137 and A. Dick, p. xiii] *VFR

In 1920, first U.S. measurement of the size of a fixed star was made on Betelgeuse, the bright red star in the right shoulder of Orion, which was found to be 260 million miles in diameter - 150 times greater than the Sun. Dr. Francis G. Pease made the measurement on the 100-inch telescope at the Mount Wilson Observatory using a beam interferometer designed by Professor A. A. Michelson. Betelgeuse was selected as the first test object since theoretical calculations had suggested that the star was unusually great in size. The apparent angular size of Betelgeuse was found to average about .044 arcseconds. Direct interferometer measurements can only be used with large stars. The majority of stars rely upon more indirect methods of determining stellar sizes. *TIS

1943 Croatia issued a pair of stamps to honor the Serbo-Croation mathematician and physicist Fr. Rugjer Boscovich (1711–1787). [Scott #59-60].*VFR

1957 Niels Bohr comes to Univ of Oklahoma for lecture on "Atoms and Human Knowledge." Jens Rud Nielsen, who joined the OU Physics Department in 1924, was an undergraduate student of Bohr in Denmark. Bohr, one of the founders of quantum mechanics, made two trips to the University of Oklahoma, first in 1937 and again in 1957. *U of Ok digital collection

1991 Stanford Linear Accelerator Center launches first Web site outside Europe
On December 13, 1991 the Stanford Linear Accelerator Center (SLAC) put up the first Web site outside Europe. It let physicists browse the full text of pre-publication scientific papers on SLAC's SPIRES database directly over the Web. This was a radical improvement over the old system, which involved submitting requests and waiting for fax or email versions to be sent back. As a vital service for the international physics community, the SLAC site became an important early step in helping the World Wide Web live up to its ambitious name *CHM

BIRTHS

1724 Franz Maria Ulrich Theodor Hoch Aepinus (13 Dec 1724; 10 Aug 1802.)
Dutch physicist whose Tentamen theoriae electricitatis et magnetismi (1759; "An Attempt at a Theory of Electricity and Magnetism") was the first work to apply mathematics to the theory of electricity and magnetism. Aepinus' experiments led to the design of the parallel-plate capacitor, a device used to store energy in an electric field. He also discovered the electric properties of the mineral tourmaline and investigated pyroelectricity, the state of electrical polarization produced in tourmaline and various other crystals by a change of temperature. Other achievements of Aepinus include improvements to the microscope, and his demonstration of the effects of parallax in the transit of a planet across the Sun's disk (1764). *TIS

1753 William Nicholson (13 December 1753 – 21 May 1815) was a renowned English chemist and writer on "natural philosophy" and chemistry, as well as a translator, journalist, publisher, scientist, inventor, patent agent and civil engineer.
In 1797 he began to publish and contribute to the Journal of Natural Philosophy, Chemistry and the Arts, generally known as Nicholson's Journal, the earliest monthly scientific work of its kind in Great Britain— the publication continued until 1814. The journal included the first comprehensive descriptions of aerodynamics with George Cayley's "On Aerial Navigation", which inspired the Wright brothers a hundred years later. In May 1800 he with Anthony Carlisle discovered electrolysis, the decomposition of water into hydrogen and oxygen by voltaic current. The two were then appointed to a chemical investigation committee of the new Royal Institution. But his own interests shortly turned elsewhere.
Besides considerable contributions to the Philosophical Transactions, Nicholson wrote translations of Fourcroy's Chemistry (1787) and Chaptal's Chemistry (1788), First Principles of Chemistry (1788) and a Chemical Dictionary (1795); he also edited the British Encyclopaedia, or Dictionary of Arts and Sciences (6 vols., London, 1809).
Nicholson died in Bloomsbury at the age of 61 on 21 May 1815. *Wik

1759 John Hailstone (13 Dec, 1759– 9 June, 1847), English geologist, born near London, was placed at an early age under the care of a maternal uncle at York, and was sent to Beverley school in the East Riding. Samuel Hailstone was a younger brother. John went to Cambridge, entering first at Catharine Hall, and afterwards at Trinity College, and was second wrangler and second in the Smith Prize of his year (1782). He was second in both competitions to James Wood who became master of Saint Johns, and Dean of Ely. Hailstone was elected fellow of Trinity in 1784, and four years later became Woodwardian Professor of Geology, an office which he held for thirty years.
He went to Germany, and studied geology under Werner at Freiburg for about twelve months. On his return to Cambridge he devoted himself to the study and collection of geological specimens, but did not deliver any lectures. He published, however, in 1792, ‘A Plan of a course of lectures.’
He married, and retired to the vicarage of Trumpington, near Cambridge, in 1818, and worked zealously for the education of the poor of his parish. He devoted much attention to chemistry and mineralogy, as well as to his favourite science, and kept for many years a meteorological diary. He made additions to the Woodwardian Museum, and left manuscript journals of his travels at home and abroad, and much correspondence on geological subjects. He was elected to the Linnean Society in 1800, and to the Royal Society in 1801, and was one of the original members of the Geological Society. Hailstone contributed papers to the ‘Transactions of the Geological Society’ (1816, iii. 243–50), the ‘Transactions of the Cambridge Philosophical Society’ (1822, i. 453–8), and the British Association (Report, 1834, p. 569). He died at Trumpington in his eighty-eighth year. *Wik

1805 Johann von Lamont (13 Dec 1805; 6 Aug 1879) Scottish-born German astronomer noted for discovering (1852) that the magnetic field of the Earth fluctuates with a 10.3-year activity cycle, but does not correlate it with the period of the sunspot cycle. From 1 Aug 1840, Johann von Lamont (as director of the Royal Astronomical Observatory in Munich) started regular and permanent observations of the earth's magnetic field. In the 1850's he started making regional magnetic surveys in the kingdom of Bavaria, later extended to other states in south Germany, France, Holland, Belgium, Spain, Portugal, Prussia and Denmark. His central European maps with isolines of geomagnetic elements, reduced to 1854, were the first worldwide. *TIS

1887 George Pólya (13 Dec 1887 in Budapest, Hungary - 7 Sept 1985 in Palo Alto, California, USA) Pólya was arguably the most influential mathematician of the 20th century. His basic research contributions span complex analysis, mathematical physics, probability theory, geometry, and combinatorics. He was a teacher par excellence who maintained a strong interest in pedagogical matters throughout his long career. Before going to the United States Pólya had a draft of a book How to solve it written in German. He had to try four publishers before finding one to publish the English version in the United States but it sold over one million copies over the years and has been translated in 17 languages. Schoenfeld described its importance, "For mathematics education and the world of problem solving it marked a line of demarcation between two eras, problem solving before and after Pólya."
Pólya explained in How to solve it that to solve problems required the study of heuristic"The aim of heuristic is to study the methods and rules of discovery and invention .... Heuristic, as an adjective, means 'serving to discover'. ... its purpose is to discover the solution of the present problem. ... What is good education? Systematically giving opportunity to the student to discover things by himself."
He also gave the wise advice, "If you can't solve a problem, then there is an easier problem you can't solve: find it."
Pólya published further books on the art of solving mathematical problems. For example Mathematics and plausible reasoning (1954), and Mathematical discovery which was published in two volumes (1962, 1965).*SAU (The student or teacher who has not read any of these books should go immediately and read them.)

1908 Leon Bankoff (December 13, 1908, New York City, NY -February 16, 1997, Los Angeles, CA), was an American dentist and mathematician.
After a visit to the City College of New York, Bankoff studied dentistry at New York University. Later, he moved to Los Angeles, California, where he taught at the University of Southern California; while there, he completed his studies. He practiced over 60 years as a dentist in Beverly Hills. Many of his patients were celebrities.
Along with Bankoff's interest in dentistry were the piano and the guitar. He was fluent in Esperanto, created artistic sculptures, and was interested in the progressive development of computer technology. Above all, he was a specialist in the mathematical world and highly respected as an expert in the field of flat geometry. Since the 1940s, he lectured and published many articles as a co-author. Bankoff collaborated with Paul Erdős in a mathematics paper and therefore has an Erdős number 1.
From 1968 to 1981, Bankoff was the editor of the Problem Department of Pi Mu Epsilon Journals, where he was responsible for the publication of some 300 top problems in the area of plane geometry, particularly Morley's trisector theorem, and the arbelos of Archimedes. Among his discoveries with the arbelos was the Bankoff circle, which is equal in area to Archimedes' twin circles. Martin Gardner called Bankoff, “one of the most remarkable mathematicians I have been privileged to know.” *Wik

1910 Charles Alfred Coulson FRS (13 December 1910, Dudley, England – 7 January 1974, Oxford, England) was a British applied mathematician, theoretical chemist and religious author.
His major scientific work was as a pioneer of the application of the quantum theory of valency to problems of molecular structure, dynamics and reactivity. He shared his deep religious belief, as a Methodist lay preacher, with the general public in radio broadcasts, served on the World Council of Churches from 1962 to 1968 and was Chairman of Oxfam from 1965 to 1971.
Coulson was a Senior Lecturer in the Mathematics Department of University College, Dundee, which was administratively part of the University of St. Andrews from 1938 to 1945. He held a Fellowship at the University of Oxford from 1945 to 1947, when he took up the newly appointed Chair of Theoretical Physics at King's College London. He returned to Oxford in 1952 as Rouse Ball Professor of Mathematics and Fellow of Wadham College. He set up and directed the Mathematical Institute. In 1972 he was appointed to the newly created Chair of Theoretical Chemistry, which has since been named for him.
He was elected a Fellow of the Royal Society of Edinburgh in 1941 and a Fellow of the Royal Society of London in 1950. He was awarded the Davy Medal of the Royal Society in 1970, the Faraday and Tilden Medals of the Chemical Society in 1968 and 1969 respectively, and received a dozen honorary degrees from English and other universities. He was a member of the International Academy of Quantum Molecular Science.
In each of his successive appointments, Coulson attracted an active and enthusiastic group of graduate students, short and long term visitors, many of whom held senior university and industrial positions in England and other countries. Many of his students went on to make major contributions in several fields of endeavour.
Coulson was an excellent cricketer and chess player, a warm family man and had a strong sense of humour. He and Eileen were gracious hosts to his students and his associates. The conference in his honour at Brasenose College in 1967 had an impressive international attendance, despite the difficulty of organizing it during a postal strike. *Wik

1921 David Gale (December 13, 1921 – March 7, 2008) was a distinguished American mathematician and economist. He was a Professor Emeritus at University of California, Berkeley, affiliated with departments of Mathematics, Economics, and Industrial Engineering​ and Operations Research. He has contributed to the fields of mathematical economics, game theory, and convex analysis.*Wik

1923 Philip Warren Anderson (13 Dec 1923, ) is an American physicist who (with John H. Van Vleck and Sir Nevill F. Mott) received the 1977 Nobel Prize for Physics for his research on semiconductors, superconductivity, and magnetism. He made contributions to the study of solid-state physics, and research on molecular interactions has been facilitated by his work on the spectroscopy of gases. He conceived a model (known as the Anderson model) to describe what happens when an impurity atom is present in a metal. He also investigated magnetism and superconductivity, and his work is of fundamental importance for modern solid-state electronics, making possible the development of inexpensive electronic switching and memory devices in computers. *TIS

DEATHS

1048 Abu Arrayhan Muhammad ibn Ahmad al-Biruni (15 Sept 973 in Kath, Khwarazm (now Kara-Kalpakskaya, Uzbekistan) - 13 Dec 1048 in Ghazna (now Ghazni, Afganistan)) one of the major figures of Islamic mathematics. He contributed to astronomy, mathematics, physics, medicine and history. the mathematical contributions of al-Biruni. These include: theoretical and practical arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes' theorems, trisection of the angle and other problems which cannot be solved with ruler and compass alone, conic sections, stereometry, stereographic projection, trigonometry, the sine theorem in the plane, and solving spherical triangles.
Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century (see [50]). His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge. Not all, however, were measured by al-Biruni himself, some being taken from a similar table given by al-Khwarizmi. The author of [27] remarks that al-Biruni seemed to realize that for places given by both al-Khwarizmi and Ptolemy, the value obtained by al-Khwarizmi is the more accurate.
Al-Biruni also wrote a treatise on time-keeping, wrote several treatises on the astrolabe and describes a mechanical calendar. He makes interesting observations on the velocity of light, stating that its velocity is immense compared with that of sound. He also describes the Milky Way as, "... a collection of countless fragments of the nature of nebulous stars. "
Topics in physics that were studied by al-Biruni included hydrostatics and made very accurate measurements of specific weights. He described the ratios between the densities of gold, mercury, lead, silver, bronze, copper, brass, iron, and tin. Al-Biruni displayed the results as combinations of integers and numbers of the form 1/n, n = 2, 3, 4, ... , 10. *SAU

1557 Niccolò Fontana Tartaglia (1499, 13 Dec 1557) Italian mathematician who originated the science of ballistics. His proper name was Niccolo Fontana although he is always known by his nickname, Tartaglia, which means the "stammerer." When the French sacked Brescia in 1512, soldiers killed his father and left young Tartaglia for dead with a sabre wound that cut his jaw and palate. In 1535, by winning a competition to solve cubic equations, he gained fame as the discoverer of the formula for their algebraic solution (which was published in Cardan's Ars Magna, 1545) Tartaglia wrote Nova Scientia (1537) on the application of mathematics to artillery fire. He described new ballistic methods and instruments, including the first firing tables. He was the first Italian translator and publisher of Euclid's Elements (1543).*TIS

1565 Conrad Gessner (Konrad Gessner, Conrad Geßner, Conrad von Gesner, Conradus Gesnerus, Conrad Gesner; 26 March 1516 – 13 December 1565) was a Swiss naturalist and bibliographer. His five-volume Historiae animalium (1551–1558) is considered the beginning of modern zoology, and the flowering plant genus Gesneria (Gesneriaceae) is named after him. He is denoted by the author abbreviation Gesner when citing a botanical name. Gessner in 1551 was the first to describe adipose tissue; and in 1565 the first to document the pencil. *Wik See more at The Renaissance Mathematicus blog.

1603 Seigneur (lord) De La Bigotiere François Viète (1540, 13 Dec 1603) French mathematician who introduced the first systematic algebraic notation and contributed to the theory of equations. As Henry IV's cryptographer, he broke an elaborate cipher used by Spanish agents. In algebra, he made a number of innovations in the use of symbolism and several technical terms still in use (e.g., coefficient) were introduced by him. By using algebraic rather than geometric methods, Viète was able to solve a number of geometrical problems. In his In artem analyticam isagoge (1591) Viète introduced such basic algebraic conventions as using letters to represent both known and unknown quantities, while improving the notation for the expression of square and cubic numbers. *TIS

1870 William Chauvenet (24 May 1820, Milford, Pennsylvania - 13 December 1870, St. Paul, Minnesota) was an early American educator. A professor of mathematics, astronomy, navigation, and surveying, he was always known and well liked among students and faculty. In 1841 he was appointed a professor of mathematics in the United States Navy, and for a while served on Mississippi. A year later, he was appointed to the chair of mathematics at the naval asylum in Philadelphia, Pennsylvania. He was instrumental in the founding of the United States Naval Academy at Annapolis, Maryland. In 1859, he was offered a professorship at his alma mater at the same time he was offered a position at Washington University in St. Louis as professor of mathematics and astronomy. He chose St. Louis over New Haven and brought with him a deep love of music and a familiarity with the classics, in addition to being an outstanding figure in the world of science, noted by many historians as one of the foremost mathematical minds in the U.S. prior to the Civil War. It was Chauvenet who mathematically confirmed James B. Eads' plans for the first bridge to span the Mississippi River at St. Louis. The directors of the University chose him to be chancellor when his friend and Yale classmate Joseph Hoyt died in 1862. He came to his chancellorship in the midst of the Civil War in a state divided by the question of slavery.
Washington University went through a great period of growth during his chancellorship, adding dozens of professors, hundreds of students, and several new programs, including the establishment in 1867 of the law school. He served terms as vice president of the United States National Academy of Sciences and president of the American Association for the Advancement of Science, and was a member of both the American Philosophical Society and the American Academy of Arts and Sciences. After his death, the Mathematical Association of America established a prestigious prize in his honor, the Naval Academy named a mathematics building for him, and the U.S. Navy christened two ships Chauvenet.
*Wik

1921 Max Noether (24 Sept 1844 in Mannheim, Baden, Germany - 13 Dec 1921 in Erlangen, Germany) was one of the leaders of nineteenth century algebraic geometry. Although himself a very distinguished mathematician, his daughter Emmy Noether was to bring greater innovation to mathematics than did her father.*SAU

1950 Abraham Wald (October 31, 1902 – December 13, 1950) was a mathematician born in Cluj, in the then Austria–Hungary (present-day Romania) who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis. He spent his researching years at Columbia University.Wald applied his statistical skills in World War II​ to the problem of bomber losses to enemy fire. A study had been made of the damage to returning aircraft and it had been proposed that armor be added to those areas that showed the most damage. Wald's unique insight was that the holes from flak and bullets on the bombers that returned represented the areas where they were able to take damage. The data showed that there were similar patches on each returning B-29 where there was no damage from enemy fire, leading Wald to conclude that these patches were weak spots and that they must be reinforced. *Wik

2004 David Wheeler, Inventor of the Closed Subroutine, Dies. Wheeler, born February 9, 1927, was Emeritus Professor of Computer Science at Cambridge University and a computer science pioneer. He worked on the original Cambridge EDSAC computer and wrote the first computer program to be stored in a computer’s memory. He pioneered the use of subroutines and data compression. He earned his Ph.D. in 1951 from Cambridge’s Computer Laboratory. (reputed to be the first Ph.D. in computer science) He spent time at the University of Illinois where he made contributions to the architecture of the ILLIAC system there. He later returned to the Cambridge Computer Laboratory and invented the Cambridge Ring and advanced methods of computer testing. He continued to work there until his death, a decade after he had officially retired. *CHM

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