Pat'sBlog

Thursday, 14 December 2017

The 348th day of the year; 348 is the sum of four consecutive primes. It is the last day of the year that is of such distinction.

348 is the smallest number whose fifth power contains exactly the same digits as another fifth power... find it.

EVENTS

1498 Luca Pacioli was professor in Milan 1496-1499. He was inspired to start his Divina Proportione on 9 Feb 1498 and completed it on 14 Dec 1498, though it was not published (in an expanded form) until 1509 . The period in Milan was the high point of his career, being a leading member of the glittering intellectual court of Lodovico Sforza. He lived at the monastery of San Simpliciano, writing his Divina Proportione, and De Viribus Quantitatis here . He was a good friend of LEONARDO DA VINCI who drew the pictures for Pacioli's book. Pacioli is our leading witness to Leonardo's work at this time, particularly the Last Supper in the Refectory of the Monastery of Santa Maria delle Grazie during 1495 1497, and he may well have advised on the perspective of the painting. Certainly Pacioli stimulated Leonardo's interest in perspective and it is possible that Leonardo's famous drawing of the proportions of the human body was inspired by Pacioli's comment on classical architecture; "For in the human body they found the two main figures ..., namely the perfect circle and the square." Pacioli seems to have made models of the polyhedra illustrated in his book, though we don't know if Leonardo used these for his drawings. A set was probably given to Pacioli's earlier patron, the Duke of Urbino, in 1494. Another set was paid for by Florence in 1504. *VFR
The first known printing of the Rhombicubeoctahedron, an Archimedian Solid with 26 faces, was Leonardo da Vinci's drawing in Divina Proportione

In 1807, the first meteorite strike to be recorded in the U.S. fell at Weston (now called Easton), Conn., at 6:30 a.m., making a hole 5-ft long and 4.5-ft wide. This was the New World's first witnessed fall of a meteorite, with subsequent recovery of specimens, since the arrival of the European settlers. Yale Professor Benjamin Silliman's description of the fall and his chemical analysis of the stone meteorite, the first performed in the U.S., received much attention in the national and international press. A thirty-pound fragment of this Chondrite H4 became the nucleus of Yale University’s Peabody Museum. This meteorite collection, the oldest in the country, was begun by Silliman.*TIS 1844 Grassman had sent a copy of his book to Gauss who replied that a) I already did that fifty years ago, and b) I didn’t actually read it because I’m very busy and the terminology is difficult. Michael Cro. we described Grassmann’s book, “Grassmann’s Die lineale Ausdehnungslehre (Linear Extension Theory) demonstrated deep mathematical insights. It also in one sense contained much of the modern system of vector analysis. This, however, was embedded within a far broader system, which included n-dimensional spaces and as many as sixteen different products of his base entities (including his inner and outer products, which are respectively somewhat close to the our modern dot and cross products). Moreover, Grassmann justifies his system by philosophical discussions that may have put off many of his readers.” *A history of vector analysis: the evolution of the idea of a vectorial system, By Michael J. Crowe pg 78 1893 The American, Dorothea Klumpke defended her thesis on Saturn’s rings for a doctorate in mathematics at the Sorbonne, before an expectant gathering of professors and several hundred spectators. “Your thesis,” said one of the examining professors during the awards ceremony, “is the ﬁrst which a woman has presented and successfully sustained with our faculty to obtain this degree. You worthily open the way.” Indeed she did, for she became a distinguished astronomer. *Sky & Telescope, August 1986, pp. 109–110. Reprinted in AWM Newsletter, 17, no. 5, p. 12-13. In 1900, German physicist Max Planck made public his ideas on quantum physics at a meeting of the German Physics Society, revolutionizing scientists' understanding of physics. Planck demonstrated that in certain situations energy exhibits characteristics of physical matter, something unthinkable at the time. He suggested the explanation energy exists in discrete packets, which he called "quanta."*TIS 1911 “So we arrived and were able to plant our ﬂag at the geographical South Pole. God be thanked!” From the diary of the Norwegian explorer, Roald Amundsen, the ﬁrst person to reach the South Pole. He was accompanied by four companions and ﬁfty-two sled dogs. *VFR In 1933, Rutherford suggested the names diplogen for the newly discovered heavy hydrogen isotope and diplon for its nucleus. He presented these ideas in the Discussion on Heavy Hydrogen at the Royal Society. For ordinary hydrogen, the lightest of the atoms, having a nuclues of a sole proton, he coined a related name: haplogen. (Greek: haploos, single; diploos, double.) In 1931, Harold Urey had discovered small quantities of atoms of heavy hydrogen wherever ordinary hydrogen occurred. The mass of its nucleus was double that of ordinary hydrogen. This hydrogen-2 is now called deuterium, as named by Urey (Greek: deuteros, second). Its nucleus, named a deuteron, has a neutron in addition to a proton. *TIS 1946 Denmark issued a stamp commemorating the 400th anniversary of the birth of the mathematician and astronomer Tycho Brahe. [Scott #300]. (TOP)*VFR 1981 The New Yorker carried a long interview with Marvin Minsky, tracing his biography and the development of artiﬁcial intelligence. [Mathematics Magazine 55(1982), p. 245]. *VFR 1952 U.S. Navy Approaches MIT to create Whirlwind
U.S. Navy issues a formal Letter of Intent to MIT for development of the Airplane Stability and Control Analyzer (ASCA) program, the beginning of the project Whirlwind. Constructed under the leadership of Jay. W. Forrester, the Whirlwind was the first high-speed electronic digital computer that was able to operate in real time with the remarkable electronic reliability. By December 1954, the computer comprised 12,500 vacuum tubes and 23,800 crystal diodes, occupying a two-story building. It operated until 1959.
Whirlwind served as an experimental prototype for the IBM’s AN/FSQ-7 manufactured for the SAGE air defense system, and influenced the early IBM 700 series computers and computers developed by Digital Equipment Corporation. *CHM In 1967, the first synthesis of biologically active DNA in a test tube was announced at a press conference by Arthur Kornberg who had worked with Mehran Goulian at Stanford and Robert L. Sinsheimer of MIT. Kornberg chose to replicate the relatively simple DNA chain of the Phi X174 virus, which infects bacteria (a bacteriophage). It has a single strand of DNA only about 5500 nucleotide building blocks long, and with about 11 genes, it was easier to purify without breaking it up. Having isolated the Phi X174 DNA, they used the DNA from E. coli, a common bacterium in the human intestine that could copy a DNA template from any organism. The viral DNA template thus copied was found to be able to infect bacteria - it was error-free, active DNA. *TIS
2009 On 14 December 2009, the Orient Express ceased to operate and the route disappeared from European railway timetables, reportedly a "victim of high-speed trains and cut-rate airlines" *Wik

2014. The annual Geminids meteor shower will reach its peak late on Saturday night and into early sunday morning.
The meteors will appear to radiate from a point near the star Castor, in the constellation Gemini.
In the Northern hemisphere, that will be westward and nearly overhead in the early hours of Sunday. *BBC News

BIRTHS

1503 The astrologer Nostradamus is born. [Muller] *VFR 1546 Tycho Brahe (14 Dec 1546; 24 Oct 1601) Danish astronomer whose work in developing astronomical instruments and in measuring and fixing the positions of stars paved the way for future discoveries. He studied the nova of 1572 ("Tycho's star") showed that it was a fixed star. His report, De nova...stella (1573), was taken by many as proof of the inadequacy of the traditional Aristotelian cosmology. In 1577, he moved to his own observatory on Hven Island (financed by King Frederick II). Before the invention of the telescope, using his nine-foot armillary sphere and his fourteen-foot mural quadrant, he charted the positions of 777 stars with an unparallelled accuracy. In 1599 he moved to Prague, with Johannes Kepler as his assistant. *TIS 1760 The Very Reverend James Wood (14 December 1760 – 23 April 1839) was a mathematician, Dean of Ely and Master of St John's College, Cambridge.
Wood was born in Holcombe where his father ran an evening school and taught his son the elements of arithmetic and algebra. From Bury Grammar School he proceeded to St John's College, Cambridge in 1778, graduating as senior wrangler in 1782. On graduating he became a fellow of the college and in his long tenure there produced several successful academic textbooks for students of mathematics. (The Elements of Algebra (1795); The Principles of Mechanics (1796); The Elements of Optics (1798))
Wood remained for sixty years at St. John's, serving as both President (1802–1815) and Master (1815–1839); on his death in 1839 he was interred in the college chapel and bequeathed his extensive library to the college, comprising almost 4,500 printed books on classics, history, mathematics, theology and travel, dating from the 17th to the 19th centuries.[3]
Wood was also ordained as a priest in 1787 and served as Dean of Ely from 1820 until his death.{He was succeeded by another eminent mathematician, George Peacock)*Wik 1904 Nikolai Grigor'evich Chudakov (1904–1986) was a Russian and Soviet mathematician. He was born in Lysovsk, Novo-Burassk, Saratov, Russian Empire. His father worked as a medical assistant.
He first studied at the Faculty of Physics and Mathematics at Saratov State University, but then he transferred to Moscow University. He then graduated in 1927. In 1930, he was named head of higher mathematics at Saratov University. In 1936, he successfully defended his thesis and became a Doctor of Science. Among others, he considerably improved a result from Guido Hoheisel and Hans Heilbronn on an upper bound for prime gaps. *Wik 1914 Solomon Spiegelman (14 Dec 1914; 21 Jan 1983) American microbiologist and geneticist who discovered that only one of two strands of molecules that make up DNA, carried the genetic information to produce new substances. The carrier was called ribonucleic acid (RNA). In 1962, he developed a technique that allowed the detection of specific RNA and DNA molecules in cells. This technique, called nucleic acid hybridization, is credited for helping to lay the groundwork for current advances in recombinant DNA technology. Much earlier, his Ph.D. thesis (1944) was the first work to establish that genes are activated and deactivated by compounds that he called inducers, which thus radically affect the pattern of proteins that a cell fabricates without actually altering the genes themselves. *TIS 1922 Nikolay Gennadiyevich Basov (14 Dec 1922, )Soviet physicist, best known for the development of the maser, the precursor of the laser. In 1955, while working as a research student with Aleksandr Prokhorov (1916- ) at the Soviet Academy of Sciences, he devised a microwave amplifier based on ammonia molecules. The two scientists shared the 1964 Nobel Prize (with American Charles Townes (1915- ), who independently developed a maser), for basic research in quantum electronics that led to the development of both the maser and the laser. These devices produce monochromatic, parallel, coherent beams of microwaves and light, respectively. Basov went on to develop the laser principle, and introduced the idea of using semiconductors to achieve laser action (1958). *TIS 1936 Charles Terence Clegg ("Terry") Wall (born 14 December 1936 in Bristol, England) is a leading British mathematician, educated at Marlborough and Trinity College, Cambridge. He is an emeritus professor of the University of Liverpool, where he was first appointed Professor in 1965. From 1978 to 1980 he was the President of the London Mathematical Society.
His early work was in cobordism theory in algebraic topology; this includes his 1959 Cambridge Ph.D thesis entitled "Algebraic aspects of cobordism", written under the direction of Frank Adams and Christopher Zeeman. His research was then mainly in the area of manifolds, particularly geometric topology and related abstract algebra included in surgery theory, of which he was one of the founders. His 1970 research monograph "Surgery on Compact Manifolds" is a major reference work in geometric topology.
In 1971 he conjectured that every finitely generated group is accessible. This conjecture is known as "Wall's conjecture". It motivated much progress in the understanding of splittings of groups. In 1985 Martin J. Dunwoody proved the conjecture for the class of finitely presented groups. The resolution of the full conjecture took until 1991 when, surprising to most mathematicians at the time, Dunwoody found a finitely generated group that is not accessible and hence the conjecture turned out to be not correct in its general formulation.
C.T.C Wall's work since the mid-1970s has mostly been in singularity theory as developed by R. Thom, J. Milnor and V. Arnold, and especially concerns the classification of isolated singularities of differentiable maps and of algebraic varieties. He has written two research monographs on singularity theory, "The Geometry of Topological Stability" (1989) (containing a great deal of original work) with Andrew du Plessis, and "Singular Points of Plane Curves" (2004).*Wik

DEATHS

1710 Henry Aldrich (1647 – 14 December 1710) was an English theologian and philosopher.He had wide interests including mathematics, music, and architecture. He was well known as a humorist and Suttle describes him as".. a punner of the first value. "
In 1674 he published Elementa geometricae which led to him being described by his Christ Church colleagues as ".. a great mathematician of our house."
In 1691 he published Artis logicae compendium a treatise on logic which was to be the main text on the topic for 150 years in England. Even when Richard Whately published Elements of logic in 1826 it still took Aldrich's work as his starting point. *SAU 1897 Francesco Brioschi (22 December 1824 – 13 December 1897) was an Italian mathematician born in Milan in 1824. From 1850 he taught analytical mechanics in the University of Pavia. After the Italian unification in 1861, he was elected depute in the Parliament of Italy and then appointed twice secretary of the Education Minister. In 1863 he founded the Politecnico di Milano university, where he worked until death. In 1870 he became member of the National Academy of the Lincei and in 1884 he succeed Quintino Sella as president of the National Academy of the Lincei. He directed the Il Politecnico (English translation: The Polytechnic) review and, between 1867 and 1877, Annali di matematica pura e applicata (English translation: Annals of pure and applied mathematics). He died in Milan in 1897.
As mathematician, Brioschi publicized in Italy various algebraic theories and studied the problem of solving fifth and sixth grade equations using elliptic functions. Brioschi is also remembered as a distinguished teacher: among his students in the University of Pavia there were Eugenio Beltrami, Luigi Cremona and Felice Casorati.*Wik 1927 Yulian-Karl Vasilievich Sokhotsky (2 Feb 1842 in Warsaw, Poland - 14 Dec 1927 in Leningrad, USSR (now St Petersburg, Russia)) The magister's thesis of Sokhotskii was the first research paper on complex analysis published in Russian. It contains many important results which were later ascribed to other mathematicians. First of all, there is the famous theorem on the behaviour of an analytic function in a neighbourhood of an essential singularity. This theorem was published by Sokhotskii (in his magister's thesis) and by Casorati in 1868, whereas Weierstrass published it eight years later - in 1876. Furthermore, Sokhotskii was the first to apply the calculus of residues to Legendre polynomials. The credit for this procedure is usually given to Hermann Laurent. Finally, the so-called Plemelj formulas are also due to Sokhotskii, who published them in his doctor's thesis in 1873, that is to say 35 years before Plemelj. *SAU 1976 Donald H(oward) Menzel (11 Apr 1901, 14 Dec 1976) was an American astronomer best known for his arguments against the existance of extraterrestrial UFO's. Menzel was one of the first practitioners of theoretical astrophysics in the United States and pioneered the application of quantum mechanics to astronomical spectroscopy. An authority on the sun's chromosphere, he discovered with J. C. Boyce (1933) that the sun's corona contains oxygen. With W. W. Salisbury he made (1941) the first of the calculations that led to radio contact with the moon in 1946. He supervised the assignment of names to newly discovered lunar features. *TIS1989 Andrey Dmitriyevich Sakharov (21 May 1921, 14 Dec 1989) Soviet nuclear physicist, an outspoken advocate of human rights in the Soviet Union. At the end of World War II, Sakharov returned to pure science and the study of cosmic rays. Two years later, he began work with a secret research group on the development of the hydrogen bomb, and he is believed to have been principally responsible for the Soviets' success in exploding their first thermonuclear bomb (1954). With I.E. Tamm, he proposed controlled thermonuclear fusion by confining an extremely hot ionized plasma in a torus-shaped magnetic bottle, known as a tokamak device. He became politically more active in the 1960s, campaigned against nuclear proliferation, and from 1980 to 1986, he was banished and kept under police surveillance.*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

Wednesday, 13 December 2017

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.com1883 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

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. *Wik1759 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

Tuesday, 12 December 2017

The science of pure mathematics may claim to be the most original creation of the human spirit.
~A N Whitehead

The 346th day of the year; 346 is a Smith number. The sum of its digits equals the sum of the digits of its prime factors. 346 = 2 x 173 and 3+4+6 = 2+1+7+3. One more such number for a day this year. (Smith numbers were named by Albert Wilansky who noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith.) There is only one more year day that is a Smith Number.

346 is also the fourth Franel number, the sum of the cubes of the terms in the nth row of the arithmetic triangle. \( 346 = 1^3 + 4^3 + 6^3 + 4^3 + 1^3\) The numbers are named for Swiss Mathematician Jérôme Franel (1859–1939).

EVENTS

In 1871, spectroscopic observations of an eclipse in India made by French astronomer Jules Janssen led him to propose that the corona, normally only visible during a solar eclipse, is a physical part of the Sun and is composed of both hot gases and cooler particles.*TIS 1885 In the midst of his inaugural lecture at Oxford, Sylvester “refreshed” the audience with his sonnet “To a missing member of a family group of terms in an algebraical formula.” [Osiris, 1(1936), 109; Nature 33, 7 Jan 1886, p. 228; Collected Mathematical Papers, vol. 4, p. 293] *VFR In 1901, Guglielmo Marconi sent the first transatlantic radio signal from Poldhu in Cornwall, which was received by Percy Wright Page in St John's, Newfoundland. 1955 English engineer Christopher Cockerell filed the patent for his new invention, the hovercraft, a craft capable of traveling over land, water, mud or ice and other surfaces both at speed and when stationary. *Yovisto
The first mention in the historical record of the concepts behind surface-effect vehicles that used the term hovering was by Swedish scientist Emanuel Swedenborg in 1716. In the 1930-45 period several designs were implemented in different countries but classified. Even Cockerell's model was at first classified, but when declassified, he applied for a patent.

1980 Apple’s initial public offering was the largest IPO since the Ford Motor went public in 1956. Nonetheless, it sold out in minutes. Originally priced to sell at \($14\) a share, the stock opened at \($22\)and all 4.6 million shares were sold almost immediately. The stock rose almost 32% that day to close at \($29\), giving the company a market evaluation of \($1.778 \)billions. The three founders of Apple Computer, Steve Jobs, Steve Wozniak and Mike Markkula weren’t only ones who did well that day. More than 40 of Apple’s 1,000 employees became instant millionaires thanks to the stock options.*CHM 1980, Leonardo daVinci's 36-sheet manuscript Codex Leicester was auctioned at Christie's. It was bought by Armand Hammer for $4.5 million. At the time, it was the highest price paid for a complete manuscript. (It has subsequently been resold). The Codex Leicester, written 1506-10, embraces a wide variety of topics, from astronomy to hydrodynamics, and includes Leonardo's observations and theories related to rivers and seas; the properties of water; rocks and fossils; air; and celestial light. All of this is expressed in his signature mirror writing, as well as in more than 300 pen-and-ink sketches, drawings, and diagrams, many of them illustrating imagined or real experiments.*TIS

BIRTHS

1731 Erasmus Darwin (12 Dec 1731; 18 Apr 1802) Prominent English physician , poet , philosopher, botanist, naturalist and the grandfather of naturalist Charles Darwin and the biologist Francis Galton. Erasmus Darwin was one of the leading intellectuals of 18th century England. As a naturalist, he formulated one of the first formal theories on evolution in Zoonomia, or, The Laws of Organic Life (1794-1796). Although he did not come up with natural selection, he did discuss ideas that his grandson elaborated on sixty years later, such as how life evolved from a single common ancestor, forming "one living filament". Although some of his ideas on how evolution might occur are quite close to those of Lamarck, Erasmus Darwin also talked about how competition and sexual selection could cause changes in species. *TIS 1803 James Challis (12 Dec 1803; 3 Dec 1882) British clergyman and astronomer, famous in the history of astronomy for his failure to discover the planet Neptune. Astronomer and mathematician John Couch Adams had studied the known deviations in the orbit of the planet Uranus which indicated a planet even further out. In 1845, Adams gave Astronomer Royal George Airy a calculated orbital path for the unknown planet. But Airy was more interested in the primary job of navigation and timekeeping observations. Airy informed Challis, who did not begin until July 1846, and actually sighted the new planet four times without recognising it. On 23 Sep 1845, the new planet was instead discovered from Berlin Observatory. Challis admitted that Adam's prediction was within 2° of the planet's position. *TIS 1832 Peter Ludwig Mejdell Sylow (12 Dec 1832 in Christiania (now Oslo), Norway - 7 Sept 1918 in Christiania (now Oslo), Norway) In his paper Théorèmes sur les groupes de substitutions which Sylow published in Mathematische Annalen Volume 5 (pages 584 to 594) appear the three Sylow theorems. Cauchy had already proved that a group whose order is divisible by a prime p has an element of order p. Sylow proved what is perhaps the most profound result in the theory of finite groups.
If pn is the largest power of the prime p to divide the order of a group G then:
G has subgroups of order pn,
G has 1 + kp such subgroups,
any two such subgroups are conjugate.
Almost all work on finite groups uses Sylow's theorems.
Sylow became an editor of Acta Mathematica and, in 1894, he was awarded an honorary doctorate from the university of Copenhagen.
Lie had a special chair created for Sylow at Christiania University and Sylow taught at the university from 1898. *SAU 1866 Kazimierz Ajdukiewicz (12 Dec 1890; 12 Apr 1963) Polish logician and semanticist who was the chief contributor to the Warsaw school of philosophy and logic. He is credited with developing in 1920 the first deductive theory for the study of logic based on syntax. The dominant theme of Ajdukiewicz's thought was the problem of the dependence of our knowledge and conception of knowledge on language. His main contributions are in the field of logical syntax (with the theory of semantical categories) and in epistemology, with the so-called "radical conventionalism", a doctrine where he claimed that there exist conceptual apparatuses which are not intertranslatable and that scientific knowledge grows through the replacement of one such conceptual apparatus by another.*TIS 1927 Robert (Norton) Noyce (12 Dec 1927; Jun 1990) was a U.S. engineer and coinventor (1959), with Jack Kilby, of the integrated circuit, a system of interconnected transistors on a single silicon microchip. He held sixteen patents for semiconductor devices, methods, and structures. In 1968, he and colleague Gordon E. Moore cofounded N.M. Electronics, which later was renamed Intel Corporation. Noyce served as Intel's president and chairman (1968-75), then as vice chairman until 1979. *TIS 1939 Michael Gazzaniga (12 Dec 1939, )American cognitive neuroscientist and author who studies how the brain enables humans to perform those advanced mental functions that are generally associated with what we call the mind. In over four decades of split-brain research he has advanced understanding of how the brain works, by revealing the separate and highly specialized functions and abilities of each hemisphere. Gazzaniga has focused on how the brain facilitates such higher cognitive functions as remembering, speaking, interpreting, and making judgments. His most recent research uses three-dimensional magnetic resonance images of the brain's surface to compare normal brains with, for example, those having a mental disorders such as schizophrenia. *TIS

DEATHS

1685 John Pell (1 March 1611 in Southwick, Sussex, England - 12 Dec 1685 in Westminster, London, England) Malcolm wrote, "The mathematician John Pell is a significant figure in the intellectual history of 17th century England - significant, however, more because of his activities, contacts and correspondence than because of his published work. His few publications are, nevertheless, valuable sources of information about his intellectual biography.
Pell worked on algebra and number theory. He gave a table of factors of all integers up to 100000 in 1668. Pell's equation y2 = ax2 + 1, where a is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation. *SAU
He introduced the division sign (obelus, ÷) into England. The obelus was first used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra. Rahn's book was interpreted into English and published, with additions made by John Pell. According to some sources, John Pell was a key influence on Rahn and he may be responsible for the development of the symbol. The word obelus comes from a Greek word meaning a "roasting spit." The symbol wasn't new. It had been used to mark passages in writings that were considered dubious, corrupt or spurious.*TIS 1889 Viktor Bunyakovsky (16 Dec 1804 in Bar, Podolskaya gubernia (now Vinnitsa oblast), Ukraine - 12 Dec 1889 in St Petersburg, Russia) worked on Number Theory as well as geometry, mechanics and hydrostatics. He discovered the Cauchy-Schwarz inequality 25 years before Cauchy or Schwarz.*SAU 1919 Paul Gustav Samuel Stäckel (20 August 1862 — 12 December 1919) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime for the first time.*Wik 1921 Henrietta Swan Leavitt (4 Jul 1868, 12 Dec 1921) American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies. *TIS 1965 Tibor Radó (June 2, 1895 – December 12, 1965) was a Hungarian mathematician who moved to the USA after World War I. He was born in Budapest and between 1913 and 1915 attended the Polytechnic Institute. In World War I, he became a First Lieutenant in the Hungarian Army and was captured on the Russian Front. He escaped from a Siberian prisoner camp and, traveling thousands of miles across Arctic wasteland, managed to return to Hungary.
He received a doctorate from the University of Szeged in 1923. He taught briefly at the university and then became a research fellow in Germany for the Rockefeller Foundation. In 1929, he moved to the United States and lectured at Harvard University and the Rice Institute before obtaining a faculty position in the Department of Mathematics at Ohio State University in 1930. In 1935 he was granted American citizenship.
In the 1920s, he proved that surfaces have an essentially unique triangulation.
In 1933, Radó published "On the Problem of Plateau" in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions".
In World War II he was science consultant to the United States government, interrupting his academic career.
He became Chairman of the Department of Mathematics at Ohio State University in 1948.
His work focused on computer science in the last decade of his life and in May 1962 he published one of his most famous results in the Bell System Technical Journal: the Busy Beaver function and its non-computability ("On Non-Computable Functions").
In computability theory, a busy beaver (from the colloquial expression for an "industrious person") is a Turing machine that attains the maximum "operational busyness" (such as measured by the number of steps performed, or the number of nonblank symbols finally on the tape) among all the Turing machines in a certain class. The Turing machines in this class must meet certain design specifications and are required to eventually halt after being started with a blank tape. *Wik (another source gives his death as Dec 29th of the same year??)1977 Arthur Erdélyi (2 Oct 1908 in Budapest, Hungary - 12 Dec 1977 in Edinburgh, Scotland) studied in Brno and Prague and came to Scotland before the Second World War to avoid the Nazi invasion of Czechoslovakia. He became a lecturer at Edinburgh and after a period in the USA he returned to Edinburgh as a Professor. He was an expert on Special Functions. He became President of the EMS in 1971. *SAU 1994 Nicolaas Hendrik "Nico" Kuiper (Dutch pronunciation: [kœypəʁ]; 28 June 1920, Rotterdam - 12 December 1994, Utrecht) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.
Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.
He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985. *Wik 2014 Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics.
He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission for the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. In 2010, he was elected an Honorary Member of the Bertrand Russell Society.
He spent much of his career at Middlesex University. He was a fellow at the Institute for Advanced Study in Princeton, New Jersey, and is a member of the Académie Internationale d'Histoire des Sciences. *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

Monday, 11 December 2017

The 345th day of the year; 345 is the average number of squirts from a cow's udder needed to yield a US gallon of milk. *Archimedes-lab.org (I have not personally verified this, so the proof is left to the reader)

The numbers 345 and 184 form an unusual pair. Their sum is a square, the sum of their squares is a square, and the sum of their cubes is a square. \( 345+184=23^2, 345^2+184^2 = 391^2, 345^3+184^3 = 6877^2 \) There are an infinite number of such pairs, but all the others are quite large.

Jim Wilder@wilderlab pointed out that the digits of 345 show up in two interesting equations, \( 3^2 + 4^2 = 5^2\) and \(3^3 + 4^3 + 5^3 = 6^3\)

EVENTS

1610 Galileo composed the cipher “The mother of love emulates the ﬁgures of Cynthia” to “copyright” his claim that Venus had phases like the moon. This idea, which may have been cribbed from a student, provided the ﬁrst hard evidence that the earth revolved around the sun. *Science News, Nov. 26, 1983, p. 347. (The student in question was surely Benedetto Castelli, See Dec 5, 1610)
1719 The ﬁrst aurora borealis display recorded in America took place in New England: “This evening, about eight o’clock, there arose a bright and red light in the E.N.E. like the light which arises from a house on ﬁre (as I am told by several credible people who saw it, when it ﬁrst arose) which soon spread itself through the heavens from east to west, reaching about 43 or 44 degrees in height, and was equally broad.” *VFR
1860 Charles Dodgson and Alice Liddle met Queen Victoria. (at Christ Church Deanery, Oxford ) *VFR
1884 David Hilbert passed his Ph.D. orals at the University of Konigsberg, where he would teach for nearly ten years before moving to the University of Gottingen where he spent the rest of his illustrious career. *MathDL
1867 James Clerk Maxwell wrote to Peter Guthrie Tait with a thought experiment for violating the Second Law of Thermodynamics that came to be known as Maxwell's Demon. It was Lord Kelvin who would coin the term for the idea in 1874 *Wik
1902 The University of Texas ﬁred George Bruce Halsted. When asked why Halsted was ﬁred, an Austin lawyer responded: “Well, Halsted just had more intelligence than the remainder of the faculty, taken together, and they just couldn’t stand it.” See D. Reginald Traylor, Creative Teaching: Heritage of R. L. Moore (1972), pp. 34-37. *VFR
In 1911, at Stockholm, Sweden, Marie Curie became the first person to be awarded a second Nobel prize. She had isolated radium by electrolyzing molten radium chloride. At the negative electrode the radium formed an amalgam with mercury. Heating the amalgam in a silica tube filled with nitrogen at low pressure boiled away the mercury, leaving pure white deposits of radium. This second prize was for her individual achievements in Chemistry, whereas her first prize (1903) was a collaborative effort with her husband, Pierre, and Henri Becquerel in Physics for her contributions in the discovery of radium and polonium.*TIS
1946 Frederick Williams Receives Patent for Memory Device The patent is issued for a device for random-access memory. The Williams tube was a modified cathode-ray tube that painted dots and dashes of phosphorescent electrical charge on a screen representing binary ones and zeros. It became the primary memory for vacuum tube machines such as the IBM 701. Williams developed his device at Manchester University. *CHM
1969 Yuri Matiyasevich reads journal article by Julia Robinson that will lead him to proof of Hilbert's 10th problem. Having been frustrated by the problem, he had given up hope of solving it. Asked to review an article by Robinson, he was inspired by the novelty of her approach and went back to work on H10. By Jan 3, 1970 he had a proof. He would present the proof on January 29, 1970
In 1972, Apollo XVII astronauts Gene Cernan and Harrison Schmitt landed on the moon for a three-day exploration, which would be the final Apollo mission to the moon.
In 1998, scientists announced in the Dec 11 issue of the journal Science that they have deciphered the entire genetic blueprint of an animal - the tiny nematode worm, Caenorhabditis elegans. This is the first time genetic instructions have been spelt out for an animal that, like humans, has a nervous system, digests food, and has sex. The worm's genetic code is spelled out by 97 million genetic letters corresponding to 20,000 genes. This work is a milestone in global efforts to unravel the entire human genetic code - or genome - which is expected to be completed in 2003. The research grew into a collaboration between 1,500 scientists in 250 laboratories worldwide. The efforts were led by John Sulston, in England and Dr Bob Waterston in the U.S.*TIS

BIRTHS

1712 Francesco Algarotti (11 Dec 1712; 3 May 1764) Italian connoisseur of the arts and sciences, recognized for his wide knowledge and elegant presentation of advanced ideas. At age 21, he wrote Il Newtonianismo per le dame (1737; "Newtonianism for Ladies"), a popular exposition of Newtonian optics. He also wrote upon architecture, opera and painting. *TIS
1781 Sir David Brewster (11 Dec 1781; 10 Feb 1868) Scottish physicist noted for his experimental work in optics and polarized light (light in which all waves lie in the same plane.) He is known for Brewster's Law, which relates the refractive index of a material to its polarizing angle (which is the incident angle at which reflected light becomes completely polarized. He patented the kaleidoscope in 1817. Later, he used lenses to improve three-dimensional images viewed with a stereoscope. Brewster also recommended the use of the lightweight, flat Fresnel lens in lighthouses.*TIS A nice blog about Brewster is here.
1863 Annie Jump Cannon (11 Dec 1863; 13 Apr 1941) American, deaf astronomer who specialized in the classification of stellar spectra. In 1896 she was hired at the Harvard College Observatory, remaining there for her entire career. The Harvard spectral classification system had been first developed by Edward C. Pickering, Director of the Observatory, around the turn of the century using objective prism spectra taken on improved photographic plates. In conjunction with Pickering Cannon was to further develop, refine, and implement the Harvard system. She reorganized the classification of stars in terms of surface temperature in spectral classes O, B, A, F, G, K, M, and cataloged over 225,000 stars for the monumental Henry Draper Catalog of stellar spectra, (1918-24).*TIS
1840 Carl Johannes Thomae (11 December 1840, Laucha an der Unstrut – 1 April 1921, Jena) (sometimes called "Johannes Thomae", "Karl Johannes Thomae", or "Johannes Karl Thomae") was a German mathematician. Carl Johannes Thomae's research was concerned with function theory and with what German-speaking mathematicians often call "Epsilontik", the precise development of analysis, differential geometry, and topology using epsilon-neighborhoods in the style of Weierstrass. The Thomae function, the Thomae transformation formula (aka, Thomae's transformation and Thomae's theorem), the Thomae formula for hyperelliptic curves, and the Sears–Thomae transformation formula are named after him. He called himself Riemann's student, although he never attended a lecture by Riemann. *TIS
1845 Vaclav Jerabek (11 Dec 1845 in Kolodeje, Pardubice, Czech Republic - 20 Dec 1931 in Telc, Czech Republic) a member of the Royal Bohemian Society of Sciences, the Moravian Society of Natural Sciences, and a honorary member of the Union of Czech Mathematicians.

His main research interest was in constructive geometry. He is best remembered by mathematicians for the Jerabek hyperbola. Given a triangle, the isogonal-conjugate images of lines are conics passing through the vertices of the triangle. The Jerabek hyperbola is the isogonal-conjugate image of the Euler line. It is a rectangular hyperbola, passing through the orthocenter and the circumcenter and many other interesting points of the triangle. The center of the Jerabek hyperbola lies on the nine-point circle.

Jerabek wrote over 50 papers, published mostly in Casopis pro pestovani matematiky a fysiky, some of them in the Belgian journal Mathesis. He donated his extensive library to the University of Brno.*SAU
1870 George Lidstone (11 Dec 1870 in London, England - 12 May 1952 in Edinburgh, Scotland) was an actuary who worked for various Edinburgh insurance companies. He wrote papers on various numerical and statistical topics. *SAU
1882 Max Born (11 Dec 1882; 5 Jan 1970) German physicist who shared the Nobel Prize for Physics in 1954 (with Walther Bothe), for his statistical formulation of the behavior of subatomic particles. Born's studies of the wave function led to the replacement of the original quantum theory, which regarded electrons as particles, with a mathematical description. *TIS
1873 Josip Plemelj (December 11, 1873 – May 22, 1967) was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the application of integral equations to potential theory.*Wik
1884 Otto Szász (11 December 1884, Hungary – 19 December 1952, Cincinnati, Ohio) was a Hungarian mathematician who worked on real analysis, in particular on Fourier series. He proved the Müntz–Szász theorem and introduced the Szász–Mirakyan operator. The Hungarian Mathematical and Physical Society awarded him the Julius König prize in 1939. *Wik
1906 Samarendra Nath Roy or S. N. Roy (11 December 1906 – 23 July 1964) was an Indian-born American mathematician and an applied statistician. He was well known for his pioneering contribution to multivariate statistical analysis, mainly that of the Jacobians of complicated transformations for various exact distributions, rectangular coordinates and the Bartlett decomposition. *Wik

DEATHS

1748 E(wald) Georg von Kleist (c. 1700, 11 Dec 1748) German physicist, was dean of the Cathedral of Kamin. Kleist experimented to store electric charge efficiently, and discovered (1745) the Leyden jar, a fundamental electric circuit element for storing electricity, now usually referred to as a capacitor. The first Leyden jar was a stoppered glass jar partially filled with water with a wire or nail extending through the cork into the water. While holding the jar in one hand, the jar was charged by placing the end of the wire into contact with a static electricity producer, then removed. When Kleist touched the wire with his other hand, a discharge took place, giving himself a violent shock. The device was more thoroughly investigated by Pieter van Musschenbroek (1946).*TIS
1784 Anders Johan Lexell (24 Dec 1740 in Äbo, Sweden (now Turku, Finland) - 11 Dec 1784 in St Petersburg, Russia) Lexell's work in mathematics is mainly in the area of analysis and geometry. Lexell made a detailed investigation of exact equations differential equations. His work here extended a necessary condition which had been discovered earlier by Condorcet and Euler. He also gave a proof which was not based on using the calculus of variations. In addition Lexell developed a theory of integrating factors for differential equations at the same time as Euler but, although it has often been thought that he learned of the technique, some state that he independently discovered original methods to solve problems investigated by Euler.

Lexell did work in analysis on topics other than differential equations, for example he suggested a classification of elliptic integrals and he worked on the Lagrange series. He was also the first to develop a general system of polygonometry. This is a study of polygons similar to earlier work on triangles. It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles.

Lexell made major contributions to spherical geometry and trigonometry. In fact trigonometry was the main tool used by Lexell in his work on polygonometry. Spherical geometry was a major tool in his astronomical studies. *SAU
1796 Johann Daniel Titius (2 Jan 1729, 11 Dec 1796) Prussian astronomer, physicist, and biologist whose formula (1766) expressing the distances between the planets and the Sun was confirmed by J.E. Bode in 1772, when it was called Bode's Law. Titius suggested that the mean distances of the planets from the sun very nearly fit a simple relationship of A=4+(3x2n) giving the series 4, 7, 10, 16, 28*, 52, 100, corresponding to the relative distance of the six known planets, up to Saturn, and an unassigned value (*) between Mars and Jupiter. Olbers searched for a planetary object at this empty position, thus discovering the asteroid belt. However, since the discovery of Neptune, which did not fit the pattern, the "law" is regarded as a coincidence with no scientific significance.*TIS
1906 Victor Mayer Amédée Mannheim (17 July 1831 in Paris, France - 11 Dec 1906 in Paris, France) Amédée Mannheim entered the École Polytechnique in Paris in 1848 at the age of 17. Two years later he went to Metz where he attended the École d'Application. Although slide rules existed before Mannheim's time, invented by Oughtred and Gunter and others, it was Mannheim who standardised the modern version of the slide rule which was in common use until pocket calculators took over a few years ago. It was while he was a student at Metz that the ideas for this slide rule came to Mannheim.

Koppelman writes, "He was a dedicated and popular teacher, strongly devoted to the École Polytechnique, and was one of the founders of the Société Amicale des Anciens Elèves de l'École. "

Mannheim retired from his army post in 1890, having attained the rank of colonel in the engineering corps. He continued teaching at the École Polytechnique until he retired in 1901 at the age of 70.

He made numerous contributions to geometry and for his outstanding contributions to the subject he was awarded the Poncelet Prize of the Académie des Sciences in 1872. He studied the polar reciprocal transformation introduced by Chasles and applied his results to kinetic geometry. Mannheim's own definition of kinetic geometry considered it to be the study of motion of a figure without reference to any forces, time or other properties external to the figure.

He also studied surfaces, in particular Fresnel's wave surfaces. The paper [5] studies this topic of his work in detail. *SAU
1910 Jules Tannery (March 24, 1848 – December 11, 1910) was a French mathematician who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard.

He discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."

He notably influenced Paul Painlevé, Jules Drach, and Émile Borel to take up science.

His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.*Wik
1941 (Charles-) Émile Picard (24 Jul 1856, 11 Dec 1941) was a French mathematician whose theories did much to advance research into analysis, algebraic geometry, and mechanics. He made his most important contributions in the field of analysis and analytic geometry. He used methods of successive approximation to show the existence of solutions of ordinary differential equations. Picard also applied analysis to the study of elasticity, heat and electricity. *TIS
1945 Charles Fabry (11 Jun 1867, 11 Dec 1945) French physicist who specialized in optics, devising methods for the accurate measurement of interference effects. He worked with Alfred Pérot, during 1896-1906, on the design and uses of a device known as the Fabry-Pérot interferometer, specifically for high-resolution spectroscopy, composed of two thinly silvered glass plates placed in parallel, producing interference due to multiple reflections. In 1913, Fabry demonstrated that ozone is plentiful in the upper atmosphere and is responsible for filtering out ultraviolet radiation from the Sun, protecting life on the surface of Earth from most of its harmful effects. *TIS
1950 Hantaro Nagaoka (Born 15 Aug 1865; died 11 Dec 1950)Japanese physicist who was influential in advancing physics in Japan in the early twentieth century. In 1904, he published his Saturnian model of the atom, inspired by the rings around the planet Saturn. He placed discrete, negatively charged electrons of the same tiny mass, spaced in a ring revolving around a central huge positive spherical mass at its centre. Considering the electrostatic forces, hee made a mathematical analogy to Maxwell's model of the stability of the motion of Saturn's rings in a huge central gravitational field. However, Nagaoka's theory failed in other ways, and he sidelined it in 1908. *TIS
1950 Astronomer Leslie John Comrie, died (Born Aug 15 1893) …“showed how to ‘program’ commercial machines for scientiﬁc computation; developed impeccable interpolation techniques; produced mathematical tables of the highest standards of accuracy and presentation; and, in eﬀect, created computational science.” For this work he was elected F. R. S. a few months before his death on this date. *VFR He was a New Zealand astronomer and pioneer in the application of punched-card machinery to astronomical calculations. He joined HM Nautical Almanac Office (1926-36), where he replaced the use of logarithm tables with desk calculators and punched card machines for the production of astronomical and mathematical tables. This made scientific use of these machines, made originally for only business uses. In 1938, he founded the Scientific Computing Service Ltd., the first commercial calculating service in Great Britain, to further his ideas of mechanical computation for the preparation of mathematical tables. His use of card processing systems prepared the way for electronic computers.*TIS
1984 Krafft Arnold Ehricke (24 Mar 1917, 11 Dec 1984) German-born American physicist; rocketry engineer and space-travel theorist. During WW II, he was a key member of the famed Peenemunde Rocket Development team, specializing in the propulsion system for the German V-2 rocket (1942-45). He moved to the U.S. with Wernher Von Braun's rocket team in 1945. Entering the U.S. private industry in 1953, he helping develop the Atlas missile at General Dynamics. Subsequently, he invented the first liquid hydrogen propelled upper stage launch vehicle, the Centaur which enabled the U.S. to explore the solar system by launching planetary probes. A vial of his cremated remains accompany those of Star Trek creator Gene Roddenberry and others in space orbit, launched 20 Apr 1997. *TIS
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I'm a retired math teacher, calc-stats-the regular stuff... Interested in Math, math history, and assorted other curiosities.Married and in love with a gorgeous woman. I have a math page on the etymology of math terms, and another, On This Day in Math, which covers historical events related to the current date.