## Tuesday, 4 October 2016

### On This Day in Math - October 4

“What the mathematician predicts today has a habit of becoming what the physicists ﬁnd tomorrow.”
From the London Times

The 278th day of the year; 278 = 2x2x2x2x2x2x2x2+22

1789 - 278= 1511 is prime (278th prime minus 278).Derek's Daily Math  for more

278 is the fifth smallest number n such that nn starts with the digits of n, $278^278 = 2.78... × 10^679$

EVENTS

1479 University of Copenhagen founded. The University of Copenhagen was founded in 1479 and is the oldest university in Denmark. Between the closing of the Studium Generale in Lund in 1536 and the establishment of the University of Aarhus in the late 1920s, it was the only university in Denmark. The university became a centre of Roman Catholic theological learning, but also had faculties for the study of law, medicine, and philosophy.
The university was re-established in 1537 after the Lutheran Reformation and transformed into an evangelical-Lutheran seminary. Between 1675 and 1788, the university introduced the concept of degree examinations. An examination for theology was added in 1675, followed by law in 1736. By 1788, all faculties required an examination before they would issue a degree. *Wik

1621 The Duke of Württemberg declared Katharina Kepler free of a witchcraft charge for which she had barely avoided execution … with the help of her son, the astronomer Johannes Kepler.
The famous scientist was very well along his career, and his mother a "too-old-for-this-crap" 69, when authorities in her native town of Leonberg initiated proceedings in 1615.
She was an eccentric, cantankerous old dame, just the sort liable to face a gossip campaign that would promote her into partnership with the Evil One. She was only one of a number of people targeted in the town’s witch-spasm, noticeably occurring as the Catholic-Protestant conflict was stoking that crucible of modernity, the Thirty Years’ War. *http://www.executedtoday.com

In 1675, Christian Huygens patented a pocket watch. Huygens was a Dutch astronomer an physicist who establishing the wave theory of light and making astronomical discoveries. He also patented the first pendulum clock in 1656, which he has developed to meet his need for exact time measurement while observing the heavens. In 1673, he studied the relation of the length of a pendulum to its period of oscillation.*TIS (Some accounts suggest that Robert Hooke had developed a watch with the coiled spring almost ten years earlier..others question whether Hooke had a coiled spring.)

1582 St Theresa of Avila died overnight on the night between the 4th and the 15th of October. On that day the Gregorian calendar went into effect in Spain and the day after the 4th, was the 15th in order to catch up for the misalignment of the Julian Calendar. *VFR

1864 A Fife church minister, Rev William Leitch, who first imagined space flight - beating Jules Verne by about four years, died on this day. By a wonderful coincidence, this is the day that Sputnik was launched (see 1957 below). An expert in the history of space exploration has discovered that Rev William Leitch, a Presbyterian minister from Monimail near Cupar, was the first to develop the idea that not only could rockets fly in space but could do so more quickly and smoothly outside Earth’s atmosphere.
Because it seems he wrote the paper, Gods Glory in the Heavens, on his way to Canada to assume a university position there, the Canadians are claiming him for their own. Retired astronaut Chris Hadfield – the first Canadian to walk in space – has been quick to claim Leitch, tweeting : “Just learned that a Canadian invented space travel … cool!” *Scotland Blog, Guardian.com

1934 Enrico Fermi measured the speed of a neutron.*TIS

1938 Paul Erdos arrives at the Institute for Advanced Study at Princeton. Alarmed by Hitler's demands to annex the Sudatenland, Erdos hurriedly left Budapest and made his way through Italy and France to London. He would pass through Ellis Island on his way to a position at Princeton's Institute for Advanced Study on October 4. He would not see his homeland again for ten years. * Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdos

1957 Sputnik I, the ﬁrst artificial earth satellite was placed in orbit by the Soviets—the Dawn of the Space Age. It traveled at a speed of 18,000 mph and circled the earth about every 95 minutes. The impact that Sputnik had on mathematics was unbelievable. The U. S. Government was convinced that the Russians were ahead of us in mathematics and science, so they poured money into the schools and into teacher retraining. *VFR (Like many of my generation, I stood on the lawn and watched in the evening to see it go by, listening to its broadcast beeps on my transister radio.)

In 1971, the mole - the amount of substance (matter) - was adopted as a chemical measurement added to the six base quantities of the SI (International System of scientific units). The decision was made by the Conférence Général des Poids et Mesures (CGPM), the principal executive organization under the Treaty of the Meter. IUPAC's participation was led by M.L. McGlashan. The mole is the amount of substance of a system which contains as many elementary entities as there are carbon atoms in 0.012 kg of carbon 12. The elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The agreed symbol for the unit is mol, and the symbol for amount of substance is n. *TIS

2000 Mathematics Magazine publishes "A proof that the Halting Problem is undecidable" in poetic form (in the fashion of Dr Seuss) by Geoffrey K. Pullum who was then at Stevenson College, Univ of Calif, Santa Cruz. The first few lines are :
No program can say what another will do.
Now, I won’t just assert that, I’ll prove it to you:
I will prove that although you might work till you drop,
you cannot tell if computation will stop.
It appears that the professor is now at the School of Philosophy, Psychology and Language Sciences, University of Edinburgh, and where he posted a slightly altered version. It seems he has decided the first two lines should be slightly altered.  *@JohnDCook,Twitter The original can be found here.

2011  The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2011 with one half to Saul Perlmutter, of the Supernova Cosmology Project at Lawrence Berkeley National Laboratory and the University of California, Berkeley; and the other half jointly to Brian P. Schmidt, of the High-z Supernova Search Team at Australian National University, Weston Creek, Australia, and Adam G. Riess, of the High-z Supernova Search Team at Johns Hopkins University and the Space Telescope Science Institute, Baltimore for the discovery of the accelerating expansion of the Universe through observations of distant supernovae. *ScienceDaily (Oct. 4, 2011)

BIRTHS

1562 Christian Longomontanus (4 Oct 1562; 8 Oct 1647) Byname of Christian Severin, a Danish astronomer and astrologer who is best known for his association with, and published support for, Tycho Brahe. He became the first professor of astronomy at the University of Copenhagen, and in 1610 he received funds for instruments and he probably constructed a small observatory at his home. Longomontanus used Tycho's data to compile the Astronomia danica (1622), an exposition of the Tychonic system, which holds that the Sun revolves around the Earth and the other planets revolve around the Sun. He began the construction of the Copenhagen Observatory in 1632, but died before its completion.*TIS

1716 James Lind FRSE FRCPE (4 October 1716 – 13 July 1794) was a Scottish physician. He was a pioneer of naval hygiene in the Royal Navy. He is of matheamtical interest because he conducted the first modern clinical trial. He developed the theory that citrus fruits cured scurvy. He argued for the health benefits of better ventilation aboard naval ships, the improved cleanliness of sailors' bodies, clothing and bedding, and below-deck fumigation with sulphur and arsenic. He also proposed that fresh water could be obtained by distilling sea water. His work advanced the practice of preventive medicine and improved nutrition.
The concepts behind clinical trials are ancient. The Book of Daniel chapter 1, verses 12 through 15, for instance, describes a planned experiment with both baseline and follow-up observations of two groups who either partook of, or did not partake of, "the King's meat" over a trial period of ten days. Persian physician Avicenna, in The Canon of Medicine (1025) gave similar advice for determining the efficacy of medical drugs and substances. In spite of this history, there seems to have been no clinical trials actually practiced in Western Europe. He blocked a group of twelve men suffering form the effects of scurvy after two months at sea into six different treatment groups of two each. He applied six different treatments, one group getting an issue of cider, one getting citrus, and four other possible alternatives. (The word placebo would not be used until 1772.) Both men in the citrus group showed considerable improvement, and one of the Cider subjects showed mild improvement after the study was stopped in six days. *Wik

1759 Louis François Antoine Arbogast (4 Oct 1759, 18 April 1803) Arbogast was interested in the history of mathematics and classified Mersenne's papers and collected manuscript copies of memoirs and letters of Fermat, Descartes, Johann Bernoulli, Varignon, de L'Hôpital and others. This is an extremely important collection, part of which is now in Paris and part in Florence.
He was friendly with François Français and together they worked on the calculus of derivations and the operational calculus. After Arbogast died in 1803, François Français inherited his collection of manuscripts, and also his mathematical papers. He continued Arbogast's work on the operational calculus and presented a memoir on this topic, in particular applying the methods to study projectiles in a resistant medium, to the Académie des Sciences in 1804. This memoir was very highly praised by Biot in a report of 22 April 1805, but the work was not published.
The historical manuscripts which went to François Français on Arbogast's death were bought by Libri (See Deaths, Sep 28 1869) from a bookseller in Metz in 1839.
We should mention one other important contribution made by Arbogast. He was responsible for the law introducing the decimal metric system in the whole of the French Republic.
Arbogast was elected to the Académie des Sciences in 1792 and the mathematics section of the Institut National in 1796. *SAU

1794 Félix Savary, (Oct 4, 1797, July 15, 1841)was a French astronomer who studied at the École Polytechnique, where he was later a professor of astronomy. He was a librarian at the Bureau des Longitudes between 1823 and 1829, and was elected to the French Academy of Sciences on December 24, 1832.
In his works Mémoire sur les orbites des étoiles doubles and Sur la détermination des orbites que décrivent autour de leur centre de gravité deux étoiles très rapprochées l'une de l'autre, published in 1827, he was the first to use observations of a visual binary star to calculate the orbit of one star about the other. He applied his method to the star ξ Ursae Majoris.
He worked with Ampère, publishing in 1823 the work Mémoire sur l'application du calcul aux phénomènes électro-dynamiques. *Wik

1804 Wilhelm Eduard Weber (4 Oct 1804, 23 June 1891) Weber developed sensitive magnetometers, worked on the ratio between the electrodynamic and electrostatic units of charge, worked in electrodynamics and the electrical structure of matter. He collaborated with Gauss.*SAU

1841 Thomas Corwin Mendenhall (4 Oct 1841; 23 Mar 1924) American physicist and meteorologist, the first to propose the use of a ring pendulum for measuring absolute gravity. From 1889 to 1894 he served both as Director of the U.S. Coast and Geodetic Survey and also Superintendent of the U.S. Standard Weights and Measures where he oversaw the shift in the fundamental standards of the U.S. from the English yard and pound to the International Meter and Kilogram. Mendenhall devised a quarter second's pendulum for gravity measurements and instituted improvements in the measurement of base lines with wire tapes, in the construction of instruments for precise leveling and in the methods used in triangulation and gravity work, and developed a comprehensive plan for the study of terrestrial magnetism. *TIS

1873 Gheorghe Ţiţeica (October 4, 1873–February 5, 1939) publishing as George or Georges Tzitzeica) was a Romanian mathematician with important contributions in geometry. He is recognized as the founder of the Romanian school of differential geometry.*Wik

1903 John Atanasoff born. Together with Cliﬀord Berry he designed the ﬁrst electronic digital computer. who was belatedly credited (1973) with developing the first electronic digital computer. Built in 1937-42 at Iowa State University by Atanasoff and a graduate student, Clifford Berry, it introduced the ideas of binary arithmetic, regenerative memory, and logic circuits. These ideas were communicated from Atanasoff to John Mauchly, who used them in the design of the better-known ENIAC built and patented several years later. On 19 Oct 1973, a US Federal Judge signed his decision following a lengthy court trial which declared the ENIAC patent invalid and named Atanasoff the original inventor of the electronic digital computer, the Atanasoff- Berry Computer or the ABC.*TIS  (Thony Christie suggests that there may have been a better choice for the first to develop an electronic digital computer.)

1906 Sister Mary Celine Fasenmyer, R.S.M., (October 4, 1906, Crown, Pennsylvania – December 27, 1996, Erie, Pennsylvania) was a mathematician. She is most noted for her work on hypergeometric functions and linear algebra.*Wik

1916 Vitaly Lazarevich Ginzburg, ( October 4, 1916 – November 8, 2009) was a Soviet and Russian theoretical physicist, astrophysicist, Nobel laureate, a member of the Soviet and Russian Academies of Sciences and one of the fathers of Soviet hydrogen bomb.[2][3] He was the successor to Igor Tamm as head of the Department of Theoretical Physics of the Academy's physics institute *Wik & *TIS

1918 Kenichi Fukui (4 Oct 1918; 9 Jan 1998) Japanese chemist who shared the 1981 Nobel Prize for Chemistry with Roald Hoffmann for investigation of the mechanisms of chemical reactions. In 1952, at Kyoto University, Fukui introduced his "frontier orbital theory of reactions." He proposed that the course of a reaction is determined by geometry and relative energies of molecular orbitals of reactants. The theory explains electrophilic attack, for example, occurs at the carbon atom having the greatest density of frontier (highest energy) electrons. In the mid-1960s, Fukui and Hoffmann discovered - almost simultaneously and independently of each other - that symmetry properties of frontier orbitals could explain certain reaction courses that had previously been difficult to understand. *TIS

1925 Professor Renfrey Burnard (Ren) Potts AO, (1925–2005), BSc(Hons) (Adel), D Phil (Oxon), DSc (Oxon), FAA, FTSE, FACS, FAustMS, was an Australian mathematician and is notable for the Potts model and his achievements in: operations research, especially networks; transportation science, car-following and road traffic; Ising-type models in mathematical physics; difference equations; and robotics. He was interested in computing from the early days of the computing revolution and oversaw the first computer purchases at the University of Adelaide.*Wik

1935 Hitoshi Kumano-Go (4 Oct 1935, 24 Aug 1982) published a series of papers which studied the local and global uniqueness of the solutions of the Cauchy problem for partial differential equations. This work used ideas from earlier contributions to the topic by Calderon and Zygmund. In two papers Kumano-Go also studied non-uniqueness of solutions of the Cauchy problem.
Kumano-Go spent the two academic years 1967-69 visiting the Courant Institute of Mathematical Sciences at New York University. These were years of great benefit to Kumano-Go who was able to develop many ideas in conversations with Kurt Friedrichs, Peter Lax, Louis Nirenberg and others. He became involved in founding the theory of pseudo-differential operators and after his return to Osaka he continued to publish important contributions to this topic.
An important monograph written by Kumano-Go was Partial differential equations which was again written in Japanese and was published in 1978. This is a textbook which in addition to studying partial differential equations provides an introduction to pseudo-differential operators. In addition to his work on pseudo-differential operators, Kumano-Go published a series of papers on the product of Fourier integral operators. This collaborative work with his colleagues led to results which were applied to the construction of the fundamental solution of a first order hyperbolic system and the study of the wave front sets of solutions.
Kumano-Go suffered ill health and was admitted to Osaka Hospital in May 1981. The doctors discovered that he was suffering from a brain tumour from which no cure was possible. At the height of his mathematical contributions at the age of 46, Kumano-Go sadly died. *SAU

DEATHS

1821 John Rennie (7 Jun 1761, 4 Oct 1821) Scottish engineer and architect who designed London Bridge. After working as a millwright with Andrew Meikle he studied at Edinburgh University (1780-83). He was employed by Boulton & Watt for five years In 1791, he moved to London and started his own engineering company. Over the next few years he became famous as a bridge-builder, including Leeds Bridge, Southwark Bridge and Waterloo Bridge. He was also designed and built docks at Hull, Liverpool, Greenock and Leith and improving the harbours and dockyards at Portsmouth, Chatham and Plymouth. His last project was London Bridge, though he died in 1821 before it was finished. The bridge was completed by his son, Sir John Rennie.*TIS

1885 Heinrich Scherk was a mathematician born in what is now Poland who discovered an important example of a minimal surface. Scherk discovered the third non-trivial examples of a minimal surface which appeared in his paper Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen published in Crelle's Journal. The first two examples, the catenoid and the helicoid (also called the screw surface), had been found by the Frenchman Jean Baptiste Marie Meusnier in 1776. The catenoid arises from rotating the catenary curve about a horizontal line. Scherk's result was certainly seen as a major breakthough and brought him considerable fame; two surfaces, Scherk's First Surface and Scherk's Second Surface, as they are named today, are studied in the paper. Scherk's doubly periodic surface is the first example of a complete, embedded, doubly periodic minimal surface. His minimal surfaces have recently been the basis of sculptures by the American artist Brent Collins who has based many of his works on Scherk's second minimal surface. *SAU

1918 Matteo Bottasso was an Italian mathematician who used the vector calculus in studying problems in geometry, mechanics and physics. *SAU

1947 Max (Karl Ernst Ludwig) Planck (23 Apr 1858, 4 Oct 1947) was a German theoretical physicist. He studied at Munich and Berlin, where he studied under Helmholz, Clausius and Kirchoff and subsequently joined the faculty.he became professor of theoretical physics (1889-1926). His work on the law of thermodynamics and the distribution of radiation from a black body led him to abandon classical Newtonian principles and introduce the quantum theory (1900), for which he was awarded the Nobel Prize for Physics in 1918. This assumes that energy is not infinitely subdivisible, but ultimately exists as discrete amounts he called quanta (Latin, "how much"). Further, the energy carried by a quantum depends in direct proportion to the frequency of its source radiation.*TIS

1954 Georg Karl Wilhelm Hamel(12 Sept 1877, 4 Oct 1954) worked in function theory, mechanics and the foundations of mathematics. He is perhaps best known for the Hamel basis, published in 1905, when he made an early and explicit use of the Axiom of Choice to construct a basis for the real numbers as a vector space over the rational numbers. He wrote a number of papers on an axiomatic theory of mechanics, the first two in 1909. His first textbook on mechanics was Elementare Mechanik which was published in 1912. *SAU

1969 Léon Nicolas Brillouin (August 7, 1889;Sèvres, near Paris, France – October 4, 1969; New York, USA) was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory. *Wik

1973 Hermann Kober was a Polish-born mathematician who spent much of his life as a school teacher in England but published many papers on analysis. *SAU

1974 Robert Lee Moore (14 November 1882 – 4 October 1974) was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics. Moore entered the University of Texas at the unusually low age of 16, in 1898, already knowing calculus thanks to self-study. He completed the B.Sc. in three years instead of the usual four; his teachers included G. B. Halsted and L. E. Dickson. After a year as a teaching fellow at Texas, he taught high school for a year in Marshall, Texas.
An assignment of Halsted's led Moore to prove that one of Hilbert's axioms for geometry was redundant. When E. H. Moore (no relation), who headed the Department of Mathematics at the University of Chicago, and whose research interests were on the foundations of geometry, heard of Robert's feat, he arranged for a scholarship that would allow Robert to study for a doctorate at Chicago. Oswald Veblen supervised Moore's 1905 thesis, titled Sets of Metrical Hypotheses for Geometry.
Moore then taught one year at the University of Tennessee, two years at Princeton University, and three years at Northwestern University. In 1910, he married Margaret MacLelland Key of Brenham, Texas; they had no children. In 1911, he took up a position at the University of Pennsylvania.
In 1920, Moore happily returned to the University of Texas at Austin​ as an associate professor, and was promoted to full professor three years later. In 1951, he went on half pay, but continued to teach his habitual five classes a year, including a section of freshman calculus, until the University authorities forced his definitive retirement in 1969, his 87th year. In 1973, the University of Texas honored him by giving the name Moore Hall to a new building housing the physics, mathematics, and astronomy departments.*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