Thursday 14 September 2023

On This Day in Math - September 14


Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
~Leonhard Euler

The 257th day of the year; 257 is a prime number of the form 223+1 and therefore a Fermat prime. It is currently the second largest known Fermat prime.

257 is the third consecutive number (255,256,257) for which the regular n-gon is constructible with straightedge and compass. The 255th day of the year; 255= 28-1 is the product of three distinct Fermat Primes, 3*5*17, 256=28 is a power of two, and 257 is a Fermat Prime *HT to Don S. McDonald ‏@McDONewt  (Goldbach used the fact that all Fermat Numbers are 2 + product of all smaller Fermat Primes to prove that no two Fermat Numbers share a common prime divisor)

257 = 44 + 1 It is the largest known prime of the form nn + 1. *Prime Curios

More than 90% of all positive integers are composite numbers that have a lowest prime factor of 257 or less.

2257 - 1 is the largest number in Mersenne's list of primes in the preface to his Cogitata Physica-Mathematica (1644), it later turned out to be Composite. * Dan Garbowitz ‏@DGoneseventh

Ones and zeros, 257 written in different bases, 1000000012, 100014   10116


1752 The first day of the Gregorian calendar in Britain and its colonies. The dates 3 to 13 September did not exist in England in 1752 due to the conversion to the Gregorian calendar. Poor Richard’s Almanac for 1752 carried the catchy heading, “September hath XIX days.” Benjamin Franklin wrote Much of Europe made the change in 1582, and since 1600 was a leap year under the Gregorian but not the Julian calendar, England had to omit eleven days, not ten. *VFR England and the American Colonies dropped the Roman era Julian Calendar, which had become 10 days out of synchrony with the solar cycle, and adopted the Gregorian Calendar. People rioted in the streets thinking the government stole 11 days of their lives. The Act also rectified other dating anomalies, such as changing the start of the legal year from 25 March to 1 January (except in Scotland where they had changed the New Year to Jan 1 in 1600.)  

Benjamin Franklin, who was then 46, didn't think about losing 10 days. He looked on the bright side, and advised his readers to do the same. He gave the following advice to readers of his newspaper, Poor Richard's Almanac: Do not to look upon the loss of 10 days with wonder or scorn. Do not regret the removal of 10 days from the calendar. All those who love sleep can console themselves by thinking about how wonderful it will be to go to bed on the second of the month and to sleep until the morning of the 14th.
Instituted by Pope Gregory XIII in 1582, the calendar has 365 days with an extra day every four years (the leap year) except in years divisible by 100 but not divisible by 400. Thus, the calendar year has an average length of 365.2422 days. It moved the day's date up from September 3rd to September 14th. Some other countries, including Russia, did not change until the twentieth century.*TIS
In 1755 William Hogarth’s satirical print, “An Election Entertainment,” was published. It contains a Tory sign bearing the inscription “Give us our eleven days.” (out the window).  Despite thousands of tales of ignorant peasants protests and riots, there seems to be no true records of such an event. Historian Robert Poole  has written, "the riots, like the Snarks, are universally known, but defy detection."

In a letter from Bernardino Ferrari to Sebastiano Canterzani describes the interest created by Galvani's "Frog" experiment. Writing from Milan he said "Now here the experiments are also repeated in ladies’ salons, and they furnish a good spectacle to all. " *Walter Bernardi, The Controversy on Animal Electricity (web post)

1814 Francis Scott Key wrote “The Star-Spangled Banner.” Actually he wrote a poem called "Defence of Fort McHenry" . The Poem was written by the 35-year-old lawyer and amateur poet after witnessing the bombardment of Fort McHenry by the British Royal Navy ships in Chesapeake Bay during the Battle of Fort McHenry in the War of 1812. The tune was actually a popular British tune written for a mens social club in London which had become popular in the US too. It became the official National Anthem on March 3, 1931 when President Hoover signed a Congressional resolution to that effect. Mathematics??? umm, OK, the song has a range of 1 1/2 octaves, so the highest note has a frequency that is the square root of eight times the lowest note. *wik (by the way all you patriotic types, sing the second verse)

 The Donati Comet was first seen and named after its discoverer, Giovanni Battista Donati, at Florence earlier in the year. It was the second-brightest comet of the nineteenth century It reached perihelion on 30 Sep 1858.  On Sep 14th, the night before his third debate with Stephen Douglas, Abraham Lincoln sat on the porch of the Jonesboro, Illinois hotel and viewed the comet with a friend.  On Sept. 27,  It became the first comet to be photographed.

1959 Bank of America accepts the ERMA (Electronic Recording Method of Accounting) system. This revolutionary system digitized checking for the Bank of America by creating a computer-readable font. A special scanner read account numbers preprinted on checks in magnetic ink. The system was developed at the Stanford Research Institute in Menlo Park, California.*CHM

1959 Life Magazine cover story is picture of the first seven Nasa Astronauts.

2015 Einstein was right, when large Gravitational events happen in space, they produce a gravitational wave pulsing through the universe at the speed of light. The Laser Interferometer Gravitational-Wave Observatories (LIGO) recorded the first evidence on this date of a gravitational wave which had resulted from a merging of a pair of black holes each of about 30 sloar masses which had merged about 1.3 billion light years ago. As of December of 2018, LIGO has recorded eleven gravitational wave events, ten from megers of black holes, and one from a collision of two neutron stars. *Wik, *The Perfectionists, Simon Winchester.

1648 Caspar (or Kaspar) Neumann (14 September 1648 – 27 January 1715) was a German professor and clergyman from Breslau with a special interest in mortality rates. His collection and publication of the births and deaths in Breslaw were the foundation of E. Halley's, An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities upon Lives presented to the Royal Society. Halley noted that no similar records existed of sufficient quantity in an area where the population was stable.
He first did an apprenticeship as a pharmacist. He finished his higher school education at Breslau's Maria-Magdalen grammar school. In 1667 he became a student of theology at the university of Jena, and on Nov. 30, 1673 was ordained as a priest, having been requested as a traveling chaplain for Prince Christian, the son of Ernest I, Duke of Saxe-Gotha. On his return home, following a two-year journey through west­ern Ger­ma­ny, Switz­er­land, north­ern It­a­ly, and south­ern France, he became a court-chaplain at Altenburg, and married the daughter of J. J. Rabe, physician in ordinary to the prince of Saxe-Friedenstein. In 1678 he was made the deacon of St. Maria-Magdalen in Breslau and became pastor in 1689. *Wik He was a student of Erhard Weigel

1713 Johann Kies (September 14, 1713—July 29, 1781) a German astronomer and mathematician. Born in Tübingen, Kies worked in Berlin in 1751 alongside Jérôme Lalande in order to make observations on the lunar parallax in concert with those of Nicolas Louis de Lacaille at the Cape of Good Hope.
From 1742 to 1754, at the recommendation of the mathematician Leonhard Euler, he was made professor of mathematics at Berlin's Academy of Sciences and astronomer at its observatory.
He subsequently taught also at the Collegium of Tübingen. From 1754 to 1755, Kies served as director of the Astronomisches Rechen-Institut in Heidelberg.
Kies was one of the first to propagate Newton's discoveries in Germany, and dedicated two of his works to the Englishman: De viribus centralibus (Tübingen, 1758) and De lege gravitatis (Tübingen, 1773). Kies is also the author of a work on lunar influences: De influxu lunae in partes terrae mobiles (Tübingen, 1769). He wrote many other works, both in French and in Latin, on astronomy.
Kies corresponded with Euler from 1747 to 1767. Their correspondence consists of 8 letters, all of which were written by Kies.
The crater Kies on the Moon is named in his honor. *TIA

1769 (Baron) Friedrich Wilhelm Heinrich Alexander von Humboldt (14 Sep 1769; 6 May 1859) was a German natural scientist, archeologist, explorer and geographer, who made two major expeditions to Latin America (1799-1804) and to Asia (1829). During the first, equipped with the best scientific instruments, he surveyed and collected geological, zoological, botanical, and ethnographic specimens, including over 60,000 rare or new tropical plants. He charted and made observations on a cold ocean current along the Peruvian coast, now named, the Humboldt Current. In geology, he made pioneering observations of stratigraphy, structure and geomorphology; he understood the connections between volcanism and earthquakes. Humboldt named the Jurassic System. *TIS
Basalt prisms at Santa María Regla, Mexico by Alexander von Humboldt, *Wik 

1837 Nicolai Vasilievich Bugaev (14 Sept 1837 , 11 June 1903) His research was mainly on analysis and number theory. Bugaev gave proofs of theorems stated without proof by Liouville. He wrote on algebraic integrals of certain differential equations. His work in Moscow was to lead to the creation of the Moscow school of the theory of functions of a real variable in 1911, eight years after his death by Egorov, one of his students. Sonin was another of Bugaev's pupils who went on to make a major contribution to mathematics.
Bugaev's most important work in number theory was based on an analogy between some operations in number theory and the operations such as differentiation and integration in analysis. Bugaev built a systematic theory of discontinuous functions which he called arithmology. *SAU

1858 Henry Burchard Fine (September 14, 1858 – December 22, 1928) born in Chambersburg, Pennsylvania. After earning his Ph.D. in Germany he joined the Princeton faculty. He is responsible for building that department into a world class mathematics department. The mathematics building at Princeton is named in his honor.*VFR (Fine Hall is the tallest building on the campus)

1887 Karl Taylor Compton (14 Sep 1887; 22 Jun 1954) American educator and physicist who directed development of radar during WW II. His research included the passage of photoelectrons through metals, ionization and the motion of electrons in gases, fluorescence, the theory of the electric arc, and collisions of electrons and atoms. In 1933, President Roosevelt asked him to chair the new Scientific Advisory Board. When the National Defense Research Committee was formed in 1940, he was chief of Division D (detection: radar, fire control, etc.) In 1941, he was in charge of those divisions concerned with radar within the new Office of Scientific Research and Development (OSRD). Afterwards he was cited for personally shortening the duration of the war. (Brother of Arthur H. Compton, American Physicist and Nobel Laureate.)*TIS In the famous photo of physicists in the Solvay Converence, Compton is one of only two Americans Present.

1891 Ivan Matveevich Vinogradov (14 Sept 1891 , 20 March 1983) Vinogradov used trigonometric series to attack deep problems in analytic number theory.*SAU

1906 Franz Rellich (September 14, 1906–September 25, 1955) was an Austrian-Italian mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differential equations.*Wik

1914 Robert Sinclair Dietz (14 Sep 1914; 19 May 1995) was an American geophysicist and oceanographer who set forth a theory (1961) of seafloor spreading (a term he coined), in which new crustal material continually upwells from the Earth's depths along the mid-ocean ridges and spreads outward at a rate of several inches per year. While a student Dietz identified the Kentland structure in Indiana as a meteoric impact site. His professors steered him toward marine geology. He became the founder and director of the Sea Floor Studies Section at the Naval Electronics Laboratory (1946-1963). He also achieved prominence by studying meteorite craters, both on Earth and on the moon and arguing that these impact craters were common. He died of a heart attack.*TIS
 While at the Scripps Institution of Oceanography he observed the nature of the Emperor chain of seamounts that extended from the northwest end of the Hawaiian Island–Midway chain and speculated over lunch with Robert Fisher in 1953 that something must be carrying these old volcanic mountains northward like a conveyor belt.  

1920 Alberto Pedro Calderón (September 14, 1920- April 16, 1998) was one of the leading mathematicians of the 20th century. He was born in Mendoza, Argentina. His name is associated with the University of Buenos Aires, but first and foremost with the University of Chicago, where Calderón and his mentor, the distinguished analyst Antoni Zygmund, started one of the longest (more than 30 years) and most productive collaborations in mathematical history. Together they developed the ground-breaking theory of singular integral operators, thus creating the "Chicago School of (hard) Analysis" (sometimes simply known as the "Calderón-Zygmund School"); this has been one of the most influential movements in pure mathematics, but with remarkable applications to science and engineering as well. Calderón’s work, characterized by great originality, elegance and power reshaped the landscape of mathematical analysis and ranged over a wide variety of topics: from singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón’s work has also had a powerful impact on practical applications including signal processing, geophysics, and tomography. *Wik

1926 Hans-Joachim Bremermann​ (26 October, 1934 in Berlin - ) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe.*Wik


1638 Pierre Vernier (19 Aug 1584, 14 Sep 1638) French mathematician who developed the vernier scale, which enabled instruments to make more accurate linear or angular measurements. He first described it in a work entitled La construction, l'usage et les propriétés du cadran nouveau (1631)*. It consists of a small graduated scale or arc made to slide along a larger fixed scale or arc to enable determining the increment between two graduations of the larger scale. The ten divisions of the smaller, vernier scale are equal to nine of the fixed scale. For example, calipers with a larger scale graduated in tenths of inches can be read by use of the vernier scale to within one-hundredths of an inch. Vernier scales are also used on sextants and mercury
column barometers.*TIS
The vernier scale was invented in its modern form in 1631 by Vernier), but its use was described in detail in English in Navigatio Britannica (1750) by John Barrow, the mathematician and historian. In some languages, this device is called a nonius. It was also commonly called a nonius in English until the end of the 18th century. Nonius is the Latin name of the Portuguese astronomer and mathematician Pedro Nunes (1502–1578) who in 1542 invented a related but different system for taking fine measurements on the astrolabe (nonius) that was a precursor to the vernier. The French astronomer Jérôme Lalande (1732-1807) popularized the name of the instrument as a "vernier" in his book on astronomy (1764) *Wik

1712 Giovanni Domenico Cassini (8 Jun 1625, 14 Sep 1712) Italian-French astronomer who discovered (1675) the dark gap subdividing Saturn's rings into two parts, now known as Cassini's Division. He stated that Saturn's ring, believed by Huygens to be a single body, was actually composed of small particles. Cassini also discovered four of Saturn's moons: Iapetus (Sep 1671), Rhea (1672) and on 21 Mar 1684,* Tethys and Dione. He compiled new tables (1662) on the annual motion of the Sun. He observed shadows of four Galilean satellites on Jupiter (1664), and measured its rotation period by studying the bands and spots on its surface. He determined the period of rotation of Mars (1666), and attempted the same for Venus. His son Jacques was also an astronomer.*TIS (There were four consecutive Cassini generations to hold the post at the French Observatory. After Giovanni came Giovanni's son Jacques, then his grandson César-François Cassini de Thury, and finally his great grandson Jean-Dominique Cassini, Conte de Cassini.)
The Cassini spaceprobe, launched in 1997, was named after him and became the fourth to visit Saturn and the first to orbit the planet. It met it's end falling into the atmosphere of Saturn on the 15 September, 2017.

1835 The Rt. Rev. John Mortimer Brinkley D.D. (ca. 1763 (Baptized 31 Jan,1763, Woodbridge, Suffolk – 14 September 1835, Dublin) was the first Royal Astronomer of Ireland and later Bishop of Cloyne.
He graduated B.A. in 1788 as senior wrangler and Smith's Prizeman, was elected a fellow of the college and was awarded M.A. in 1791. He was ordained at Lincoln Cathedral in the same year, and in 1792 became the second Andrews Professor of Astronomy in the University of Dublin, which carried the new title of Royal Astronomer of Ireland. Together with John Law, Bishop of Elphin, he drafted the chapter on "Astronomy" in William Paley's Natural Theology. His main work concerned stellar astronomy and he published his Elements of Plane Astronomy in 1808. In 1822 he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. He was awarded the Copley Medal by the Royal Society in 1824. Brinkley's observations that several stars shifted their apparent place in the sky in the course of a year were disproved at Greenwich by his contemporary John Pond, the Astronomer Royal. In 1826, he was appointed Bishop of Cloyne in County Cork, a position he held for the remaining nine years of his life. Brinkley was elected President of the Royal Astronomical Society in 1831, serving in that position for two years.
He died in 1835 at Leeson Street, Dublin and was buried in Trinity College chapel. He was succeeded at Dunsink Observatory by Sir William Rowan Hamilton. *Wik

1882 Georges Leclanché ( 1839, 14 Sep 1882) French engineer who invented the wet cell Leclanché battery (1866), ancestor of the familiar carbon-zinc dry cell batteries used to power portable electric lights and electronic devices. His wet cell, provided an e.m.f. of about 1.5 volts. A porous pot containing manganese dioxide and a carbon rod as current collector was immersed in an electrolyte of ammonium chloride solution with a negative terminal of zinc metal. From 1867, Leclanché gave full-time attention to his invention, which was adopted the following year by the Belgian telegraph service. He opened a factory to manufacture the battery. In 1881, J.A. Thiebaut had the idea of packing the chemicals in a zinc cup. Carl Gassner made the first commercially successful "dry" cell.*TIS

1912 Georg Landsberg (30 Jan 1865 , 14 Sept 1912) studied the theory of functions of two variables and also the theory of higher dimensional curves. In particular he studied the role of these curves in the calculus of variations and in mechanics.
He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums. His most important work, however was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen (Leipzig, 1902) which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years. *SAU

1916 Pierre-Maurice-Marie Duhem (10 Jun 1861, 14 Sep 1916) was a French physicist, philosopher of science and mathematician who emphasized a history of modern science based on evolutionary metaphysical concepts. He had a wide variety of mathematical interests from mechanics and physics to philosophy and the history of mathematics. Duhem studied magnetism following the work of Gibbs and Helmholtz and also worked on thermodynamics and hydrodynamics producing over 400 papers. He maintained that the role of theory in science is to systematize relationships rather than to interpret new phenomena.*TIS

1925 Charles Tweedie (27 June 1868 , 14 Sept 1925) studied at Edinburgh, Göttingen and Berlin. He returned to Edinburgh as assistant to Chrystal. He served as a Schools Inspector and published works on the History of Mathematics. He became President of the EMS in 1903 and an honorary member in 1915. *SAU

1926 Johan Ludvig Emil Dreyer (13 Feb 1852, 14 Sep 1926) Danish astronomer who compiled the New General Catalog of Nebulae and Clusters of Stars, (NGC) in 1888. When he became Director of the Armagh Observatory in 1882, financially it was destitute, with no prospect of replacing its aging instruments. Though Dreyer obtained a new 10-inch refractor by Grubb, the lack of funding for an assistant, precluded him from a continuation of traditional positional astronomy. Instead he concentrated on the compilation of observations made earlier. The NGC he listed 7840 objects and in its supplements (1895, 1908) he added a further 5386 objects. It still remains one of the standard reference catalogs.*TIS

1932 Ernest Julius Wilczynski (13 Nov 1876 , 14 Sept 1932) began his research career as a mathematical astronomer. This interest lasted until he was appointed to Berkeley. By that time he had published over a dozen papers in astronomy, but his interests moved towards differential equations which arose in his study of the dynamics of astronomical objects. From there his interests became pure mathematical interests in differential equations. However, Wilczynski's main work was in projective differential geometry and ruler surfaces. He extended Halphen's work, devised new methods and extended the theory of curves to surfaces.*SAU

1973 Eleanor Pairman (8 June 1896, 14 Sept 1973) graduated from Edinburgh. She went to London where she worked with Karl Pearson and then went to the USA where she gained a doctorate from Radcliffe College. *SAU

2011 Rudolf Ludwig Mössbauer (31 Jan 1929 - 14 September 2011) German physicist and co-winner (with American Robert Hofstadter) of the Nobel Prize for Physics in 1961 for his researches concerning the resonance absorption of gamma-rays and his discovery in this connection of the Mössbauer effect. The Mössbauer effect occurs when gamma rays emitted from nuclei of radioactive isotopes have an unvarying wavelength and frequency. This occurs if the emitting nuclei are tightly held in a crystal. Normally, the energy of the gamma rays would be changed because of the recoil of the radiating nucleus. Mössbauer's discoveries helped to prove Einstein's general theory of relativity. His discoveries are also used to measure the magnetic field of atomic nuclei and to study other properties of solid materials. *TIS
Rudolf Mössbauer was an excellent teacher. He gave highly specialized lectures on numerous courses, including Neutrino Physics, Neutrino Oscillations, The Unification of the Electromagnetic and Weak Interactions and The Interaction of Photons and Neutrons With Matter. In 1984, he gave undergraduate lectures to 350 people taking the physics course. He told his students: “Explain it! The most important thing is, that you are able to explain it! You will have exams, there you have to explain it. Eventually, you pass them, you get your diploma and you think, that's it! – No, the whole life is an exam, you'll have to write applications, you'll have to discuss with peers... So learn to explain it! You can train this by explaining to another student, a colleague. If they are not available, explain it to your mother – or to your cat!” *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

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