Tuesday, 24 October 2017

On This Day in Math - October 24

Gauss-Weber Monument in Gotttingen

Now it is quite clear to me that there are no solid spheres in the heavens, and those that have been devised by authors to save the appearances, exist only in their imagination, for the purpose of permitting the mind to conceive the motion which the heavenly bodies trace in their courses.
~Tycho Brahe

The 297th day of the year; 2972 = 88209 and 88+209 = 297. (Numbers that have this property are a type of Kaprekar number; there are only three such numbers of three digits, now you know one of them.)

And this one from * Jim Wilder @wilderlab 2973=26,198,073 and 26+198+073=297


1676 Newton summarized the stage of development of his method in the “Epistola posterior,” which he sent to Oldenburg to transmit to Leibniz. *VFR (see Oct 26, 1676) This may be the first time Newton used irrational exponents in communication to others. It is one of the earlier uses by anyone. In the letter to Oldenburg, Newton remarks that Leibniz had developed a number of methods, one of which was new to him.

1729 Euler mentioned the gamma function in a letter to Goldbach. In 1826 Legendre gave the function its symbol and name. * F. Cajori, History of Mathematical Notations, vol. 2, p. 271 (the Oct 13 date is for the Julian Calendar still used in Russia when Euler wrote from there. It was the 24th in most of the rest of the world using the Gregorian Calendar.)

1826 Abel wrote Holmboe his impressions of continental mathematics and mathematicians.
Upon reaching Paris from Berlin, he worked on what would be called the Paris Treatise that he submitted to the Academy in October 1826. In this memoir, Abel obtained among other things, an important addition theorem for algebraic integrals. It is also in this treatise that we see the first occurrence of the concept of the genus of an algebraic function. Cauchy and Legendre were appointed referees of this memoir. In Paris, Abel was disappointed to find little interest in his work, which he had saved for the Academy. He wrote to Holmboe, “I showed the treatise to Mr. Cauchy, but he scarcely deigned to glance at it."
*Krishnaswami Alladi, NEILS HENRIK ABEL, Norwegian mathematical genius (paper on UFL website)

1844 Michael Faraday in a letter (his first?) to Ada Lovelace declines an invitation to be her tutor, and in response to her questions about his religion, he describes himself as, "of a small and despised sect of Christians, known, if they are known at all, as Sandemanian." Michael Brooks, in his book Free Radicals, describes the sect as resposible for Faraday's lack of much interest in the applications of his scientific discoveries; "It was his calling, as he saw it, to study nature, which was 'written by the finger of God', and make clear the eternal power and divine nature of the creator."

In 1851, William Lassell discovered Ariel and Umbriel, satellites of Uranus. All of Uranus's moons are named after characters from the works of William Shakespeare or Alexander Pope's The Rape of the Lock. The names of all four satellites of Uranus then known were suggested by John Herschel in 1852 at the request of Lassell. Ariel has an approx. diameter of 1160-km, an orbital period of 2.52 days, and orbital radius of 191,240-km from Uranus. The name Umbriel comes from Alexander Pope's The Rape of the Lock. Umbriel has a diameter of 1170-km, an orbital period of about 4 days and orbit radius of 266,000-km. Lassell, a British astronomer, had previously also discovered Neptune's largest satellite, Triton and (with Bond) discovered Saturn's moon Hyperion. He was a successful brewer before turning to astronomy.*TIS *Wik

1902 In Science, George Bruce Halsted wrote that his student R. L. Moore, who had proved that one of Hilbert’s betweenness axioms was redundant, “was displaced in favor of a local schoolmarm,” Miss Mary E. Decherd. *VFR Halstead was contentious in many ways, and Moore's rejection may have been a response to the fact that Halstead had suggested him. Halstead would be fired himself on December 11 of the same year. *D. Reginald Traylor , Creative Teaching: The Heritage of R. L. Moore, pg 35-37

1904 Emmy Noether matriculated at the University of Erlangen. *VFR The University was only yards from her house. Images of both are at this site from The Renaissance Mathematicus.

1927 From the 24th to 29th October 1927 in Brussels, the fifth Solvay Conference took place, Perhaps the most famous science conference in history. 17 of the 29 attendees were or became Nobel Prize winners. It is also famously remembered for it was at this conference that Einstein, who liked to invent catchy phrases, uttered his, "God does not play dice" . Bohr replied, "Einstein, stop telling God what to do".
A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. de Donder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin; P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr;
I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch.-E. Guye, C.T.R. Wilson, O.W. Richardson

1989 “Welcome to the White House on this glorious fall day. I’m sorry if I’m just a little bit late. I was sitting in there trying to solve a few quadratic equations. [Laughter] Somewhat more difficult than balancing the budget, I might say. And then I thought it might be appropriate to have a moment of silence in memory of those substitute teachers back home. [Laughter].” Remarks by President George Bush (the elder) at the Presentation Ceremony for the Presidential Awards for Excellence in Science and Math Teaching.

1994 Lynchburg College Professor Thomas Nicely, Reports a flaw in the Pentium chip by Intel that he discovered while he was trying to calculate Brun's constant,(The sum of the reciprocals of all the twin primes, 1/3+1/5+1/5+1/7+1/11+1/13.... which converges to about 1.902).
The Pentium chip occasionally gave wrong answers to a floating-point (decimal) division calculations due to errors in five entries in a lookup table on the chip. Intel spent millions of dollars replacing the faulty chips.
Nicely first noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors until October 19, 1994. On October 24, 1994 he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro. *Wik


1632 Antonie van Leeuwenhoek (24 Oct 1632; 26 Aug 1723.) Dutch microscopist who was the first to observe bacteria and protozoa. His researches on lower animals refuted the doctrine of spontaneous generation, and his observations helped lay the foundations for the sciences of bacteriology and protozoology.*TIS "The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite. "

1804 Wilhelm Eduard Weber (24 Oct 1804; 23 Jun 1891) German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

1821 Philipp Ludwig von Seidel (23 October 1821, Zweibrücken, Germany – 13 August 1896, Munich)  formulated the notion of uniform convergence.*VFR 
 Lakatos credits von Seidel with discovering, in 1847, the crucial analytic concept of uniform convergence, while analyzing an incorrect proof of Cauchy's. In 1857, von Seidel decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.   The Gauss–Seidel method is a useful numerical iterative method for solving linear systems. *Wik

1853 Heinrich Maschke (24 October 1853 in Breslau, Germany (now Wrocław, Poland) – 1 March 1908 Chicago, Illinois, USA) was a German mathematician who proved Maschke's theorem.*Wik

1873 Sir Edmund Taylor Whittaker (24 Oct 1873; 24 Mar 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS

1898 Lillian Rose Vorhaus Kruskal Oppenheimer (October 24, 1898 in New York City – July 24, 1992) was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis.  Lillian taught origami to Persi Diaconis when he was working as a magician;
She was the mother of three sons William Kruskal(developed the Kruskal-Wallis one-way analysis of variance), Martin David Kruskal(co-inventor of solitons and of surreal numbers), and Joseph Kruskal ( Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph) who all went on to be prominent mathematicians. Her grandson Clyde P. Kruskal (son of Martin) is an American computer scientist,working on parallel computing architectures, models, and algorithms. *Wik

1906 Aleksandr Osipovich Gelfond (24 Oct 1906; 7 Nov 1968) Russian mathematician who originated basic techniques in the study of transcendental numbers (numbers that cannot be expressed as the root or solution of an algebraic equation with rational coefficients). He profoundly advanced transcendental-number theory, and the theory of interpolation and approximation of complex-variable functions. He established the transcendental character of any number of the form ab, where a is an algebraic number different from 0 or 1 and b is any irrational algebraic number, which is now known as Gelfond's theorem. This statement solved the seventh of 23 famous problems that had been posed by the German mathematician David Hilbert in 1900. *TIS

1908 John Tuzo Wilson, CC, OBE, FRS, FRSC, FRSE (October 24, 1908 – April 15, 1993) the world-renowned Canadian geophysicist, served as Director General of the Ontario Science Centre from 1974 to 1985. He was instrumental in developing the theory of Plate Tetonics in the 1960s. This theory describes the formation, motion and destruction of the Earth's crust, the origin of volcanic eruptions and earthquakes, and the growth of mountains. Dr. Wilson's signficant contributions to this theory revolutionized Earth Sciences. He proposed the existence of transform faults to explain the numerous narrow fracture zones and earthquakes along oceanic ridges. He also showed that rising magma plumes beneath the Earth's crust could create stationary hot spots, leading to the formation of mid-plate volcanic chains like the Hawaiian Islands.
The first graduate of geophysics from the University of Toronto in 1930, Dr. Wilson went on to study at Cambridge and Princeton, earning his doctorate in 1936. After spending two years with the Geological Survey of Canada and almost a decade with the Canadian Military Engineers, he accepted the position of Professor of Geophysics at the University of Toronto in 1946. Internationally recognized for his major contributions as a research scientist, educator and visionary, Dr. Wilson received many prestigious
awards, including the Vetlesen Prize, the Earth Sciences equivalent of the Nobel Prize.*THE HISTORICAL

1922 Werner Buchholz​  (October 24, 1922 in Detmold, Germany - ). He was a member of the teams that designed the IBM 701​ and Stretch models. Buchholz used term byte to describe eight bits—although in the 1950s, when the term first was used, equipment used six-bit chunks of information, and a byte equaled six bits. Buchholz described a byte as a group of bits to encode a character, or the numbers of bits transmitted in parallel to and from input-output. *CHM

1932 Pierre-Gilles de Gennes (24 Oct 1932; 18 May 2007) French physicist who was awarded the 1991 Nobel Prize for Physics for "discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers." He described mathematically how, for example, magnetic dipoles, long molecules or molecule chains can under certain conditions form ordered states, and what happens when they pass from an ordered to a disordered state. Such changes of order occur when, for example, a heated magnet changes from a state in which all the small atomic magnets are lined up in parallel to a disordered state in which the magnets are randomly oriented. Recently, he has been concerned with the physical chemistry of adhesion. *TIS


1601 Tycho Brahe (14 December 1546 – 24 October 1601) Kepler inherited his vast accurate collection of astronomical data. He used this to derive his laws of planetary motion. *VFR In 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point. He always carried a small box of glue in his pocket for use when the new nose became wobbly. Tycho Brahe was famous for the most accurate and precise observations achieved by any astronomer before the invention of the telescope. Born to an aristocratic family in Denmark in 1546, he was one of twin boys – the other twin was still-born – and while still a baby Tycho was stolen from his parents by a rich, childless uncle, who paid for his education and sent him to Leipzig University to study law. His imagination had been fired, however, by a total eclipse of the sun in 1560 and he was determined to be an astronomer. He found that the existing tables recording the positions of planets and stars were wildly inaccurate and dedicated himself to correcting them. *History Today Was Tycho Murdered? Read an excellent blog on "The crazy life and crazier death of Tycho Brahe, history’s strangest astronomer".

1635 Wilhelm Shickard (22 April 1592 – 24 October 1635) He invented and built a working model of the first modern mechanical calculator. *VFR
Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables.
In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize the designs or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed the calculator based upon Schickard's original plans; it is still on display there today. 
He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.

1655 Pierre Gassendi (22 Jan 1592, 24 Oct 1655) French scientist, mathematician, and philosopher who revived Epicureanism as a substitute for Aristotelianism, attempting in the process to reconcile Atomism's mechanistic explanation of nature with Christian belief in immortality, free will, an infinite God, and creation. Johannes Kepler had predicted a transit of Mercury would occur in 1631. Gassendi used a Galilean telescope to observed the transit, by projecting the sun's image on a screen of paper. He wrote on astronomy, his own astronomical observations and on falling bodies. *TIS

1870 Charles Joseph Minard (27 Mar 1781; 24 Oct 1870 at age 89) French civil engineer who made significant contributions to the graphical representations of data. His best-known work, Carte figurative des pertes successives en hommes de l'Armee Français dans la campagne de Russe 1812-1813, dramatically displays the number of Napoleon's soldiers by the width of an ever-reducing band drawn across a map from France to Moscow. At its origin, a wide band shows 442,000 soldiers left France, narrowing across several hundred miles to 100,000 men reaching Moscow. With a parallel temperature graph displaying deadly frigid Russian winter temperatures along the way, the band shrinks during the retreat to a pathetic thin trickle of 10,000 survivors returning to their homeland. *TIS Minard advocated the graphing idea that the ratio of information to ink should be as high as possible.

1930 Paul Emile Appell (27 Sept 1855 in Strasbourg, France - 24 Oct 1930) Appell's first paper in 1876 was based on projective geometry continuing work of Chasles. He then wrote on algebraic functions, differential equations and complex analysis. In 1878 he noted the physical significance of the imaginary period of elliptic functions in the solution of the pendulum which had been though to be purely a mathematical curiosity. He showed that the double periodicity follows from physical considerations. *SAU

1940 Pierre-Ernest Weiss (25 Mar 1865, 24 Oct 1940) French physicist who investigated magnetism and determined the Weiss magneton unit of magnetic moment. Weiss's chief work was on ferromagnetism. Hypothesizing a molecular magnetic field acting on individual atomic magnetic moments, he was able to construct mathematical descriptions of ferromagnetic behaviour, including an explanation of such magnetocaloric phenomena as the Curie point. His theory succeeded also in predicting a discontinuity in the specific heat of a ferromagnetic substance at the Curie point and suggested that spontaneous magnetization could occur in such materials; the latter phenomenon was later found to occur in very small regions known as Weiss domains. His major published work was Le magnetisme ( 1926).*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

Monday, 23 October 2017

On This Day in Math - October 23

God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved.
~Hermann Klaus Hugo Weyl

Remember, 1023 is the exponent for a mole, so about 6:02 (am or pm) you can set down to a Mole of molecules of your favorite brew.  Happy Mole Day.

The 296th day of the year; 296 is the number of partitions of 30 with distinct parts. (Even very young students can enjoy exploring the number of partitions of integers, and the difference in the number when the parts must be distinct. The idea can be explored for very young students with number rods, etc)

A cube with an 8x8 checker board on each fact has a total of 296 lattice points (where the squares meet)

The somewhat famous "look and say" sequence in math, 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, (the second term is 11 because the previous term has One, one; etc) has 296 digits in the 18th term.


4004 B.C. The date of the creation of the world according to the computation of Archbishop James Usher (1581–1656), who had a curious fascination for the integration of numerology, astronomy, and scripture. It was highly regarded for several centuries primarily because in 1701 it was inserted into the margin of the King James version of the Bible. *Sky and Telescope, vol. 62, Nov. 81, 404–405.

526 Boethius executed.Boethius translated Nicomachus's treatise on arithmetic (De institutione arithmetica libri duo) as well as Euclid and Iamblichus.
There is a long tradition, going back at least to the eighth century, regarding Boethius as having been executed for maintaining the Catholic faith against the Arian Theodoric. While Theodoric was probably paranoid about spies representing the Catholic eastern emperor-in-waiting Justinian (who would, in fact, later “reconquer” the Italian peninsula), and Boethius claims in the Consolation that he was hated for being smarter than everyone else, the truth is probably that he was caught up in the usual machinations of an imperial court.
A member of the Senate was accused of treasonably conspiring with Justinian’s predecessor Justin I against Theodoric. Boethius defended the accused (apparently the only person to do so, although the charges were surely trumped up), and in the Consolation, Boethius says he was only defending the Senate (implying that the accusations were meant to undermine the authority of the Senate by challenging its loyalty to the king).
In any event, the sources we have say that Boethius was condemned by the Senate (who appear to have thrown him under the bus) without being able to speak in his own defense. After an indeterminate time of imprisonment, he was executed.
It was while he awaited death that he wrote his most famous and arguably most influential work, The Consolation of Philosophy.” From “Executed Today” web site

1613 Kepler, in a letter to an unknown recipient goes into great detail concerning his attempts over the preceding two years to find a wife. *A Christmas Trilogy RMAT

1676 Hooke's diary records that he had “Mercator's Music” copied on 23 October . This is "Mercator's earliest thinking on music, has major sections on the consonances and on the arithmetic of proportions using ratios or using logarithms.  Descartes, Newton, and Nicolaus Mercator all worked on the problem of musical timing ( To divide the octave into tones) using logs in the mid-17th century. *Benjamin Wardhaugh, Historia Mathematica, Volume 35, Issue 1, February 2008, Pages 19–36 A longer, clearer essay on the problem, with lots of interesting notes about Mercator, and historical thought on ratios by Wardhaugh is at the Convergence web site of the MAA

In 1803, John Dalton presented an essay on the absorption of gases by water, at the conclusion of which he gave a series of atomic weights for 21 simple and compound elements. He read his paper at a meeting of the Manchester Literary and Philosophical Society. *TIS

1852 August DeMorgan reported the conjecture of his student, Francis Guthrie: Four colors suffice to color planar maps so that adjacent regions have different color. It was solved by Kenneth Appel and Wolfgang Haken in 1976. In a letter to W.R. Hamilton he recalls, “A student of mine asked me today to give him a reason for a fact which I did not know was a fact – and do not yet. He says that if a figure be anyhow divided, and the compartments differently colored so that figures with any portion of common boundary line are differently colored --- four colors may be wanted, but not more…” *Dave Richeson, Euler’s Gem, pg 132)

1892  The Duck-Rabbit double illusion was first published in Fliegende Blätter, a German humor magazine (Oct. 23, 1892, p. 147). The ambiguous figure in which the brain switches between seeing a rabbit and a duck was "originally noted" by American psychologist Joseph Jastrow (Jastrow 1899, p. 312; 1900; see also Brugger and Brugger 1993). Jastrow used the figure, together with such figures as the Necker cube and Schröder stairs, to point out that perception is not just a product of the stimulus, but also of mental activity (Kihlstrom 2002). Jastrow's cartoon was based on one originally published in Harper's Weekly (Nov. 19, 1892, p. 1114) which, in turn, was based on the earlier illustration in Fliegende Blätter,*Mathworld.Wolfram.com

1906, Santos-Dumont won the Archdeacon prize by flying his Hargrave box kite inspired aircraft at Bagatelle in Paris. He was hailed by many in Europe as the first to fly, despite the fact that the Wright Brothers had achieved such a feat three years earlier in the United Sates. But Orville and Wilbur Wright kept their invention under wraps, avoiding any public exhibitions while they sought a patent. Most aeronauts in Europe considered them to be bluffing.
Earlier, on October 19, 1901, Santos-Dumont won the French Aero Club’s Deutsch Prize, rounding the Eiffel Tower and landing at Parc Saint Cloud in twenty-nine minutes and thirty seconds in his dirigible. *theappendix.net

2017 Today is Mole Day. Celebrated annually on October 23 from 6:02 a.m. to 6:02 p.m., Mole Day commemorates Avogadro's Number (6.02 x 10^23) (Which I recently learned from John D. Cook was approximately 24 factorial or 24!) , which is a basic measuring unit in chemistry. Mole Day was created as a way to foster interest in chemistry. Schools throughout the United States and around the world celebrate Mole Day with various activities related to chemistry and/or moles. Founded by the National Mole Day Foundation on 15th May 1991.
For a given molecule, one mole is a mass (in grams) whose number is equal to the atomic mass of the molecule. For example, the water molecule has an atomic mass of 18, therefore one mole of water weighs 18 grams. An atom of neon has an atomic mass of 20, therefore one mole of neon weighs 20 grams. In general, one mole of any substance contains Avogadro's Number of molecules or atoms of that substance. This relationship was first discovered by Amadeo Avogadro (1776-1858) and he received credit for this after his death. *Mole Day Org web page


1865 Piers Bohl (23 Oct 1865 in Walka, Livonia (now Valka, Latvia) - 25 Dec 1921 in Riga, Latvia) Among Bohl's achievements was, rather remarkably, to prove Brouwer's fixed-point theorem for a continuous mapping of a sphere into itself. Clearly the world was not ready for this result since it provoked little interest.
Bohl also studied questions regarding whether the fractional parts of certain functions give a uniform distribution. His work in this area was carried forward independently by Weyl and Sierpinski. There are many seemingly simple questions in this area which still seem to be open. For example it is still unknown whether the fractional parts of (3/2)n form a uniform distribution on (0,1) or even if there is some finite subinterval of (0,1) which is avoided by the sequence. *SAU

1875 Gilbert Newton Lewis (23 Oct 1875, 23 Mar 1946 at age 70) American chemist who collaborated with Irving Langmuir in developing an atomic theory. He developed a theory of valency, which introduced the covalent bond (c. 1916), whereby a chemical combination is made between two atoms by the sharing of a pair of electrons, one contributed from each atom. This was part of his more general octet theory, published in Valence and the Structure of Atoms and Molecules (1923). Lewis visualized the electrons in an atom as being arranged in concentric cubes. The sharing of these electrons he illustrated in the Lewis dot diagrams familiar to chemistry students. He generalized the concept of acids and bases now known as Lewis acids and Lewis bases. *TIS

1893 Ernest Julius Öpik (23 Oct 1893; 10 Sep 1985) Estonian astronomer best known for his studies of meteors and meteorites, and whose life work was devoted to understanding the structure and evolution of the cosmos. When Soviet occupation of Estonia was imminent, he moved to Hamburg, then to Armagh Observatory, Northern Ireland (1948-81). Among his many pioneering discoveries were: (1) the first computation of the density of a degenerate body, namely the white dwarf 40 Eri B, in 1915; (2) the first accurate determination of the distance of an extragalactic object (Andromeda Nebula) in 1922; (3) the prediction of the existence of a cloud of cometary bodies encircling the Solar System (1932), later known as the ``Oort Cloud''; (4) the first composite theoretical models of dwarf stars like the Sun which showed how they evolve into giants (1938); (5) a new theory of the origin of the Ice Ages (1952). *TIS

1905 Felix Bloch (23 Oct 1905; 10 Sep 1983) Swiss-born American physicist who shared (with independent discoverer, E.M. Purcell) the Nobel Prize for Physics in 1952 for developing the nuclear magnetic resonance (NMR) method of measuring the magnetic field of atomic nuclei. He obtained his PhD under Werner Heisenberg in 1928, then taught briefly in Germany, but as a Jew, when Hitler came to power, he left Europe for the USA. Bloch's concept of magnetic neutron polarization (1934) enabled him, in conjunction with L. Alvarez, to measure the neutron's magnetic moment. During WW II he worked on the atomic bomb. Thereafter, Bloch and co-workers developed NMR, now widely used technique in chemistry, biochemistry, and medicine. In 1954 he became the first director of CERN.*TIS

1908 Ilya Mikhaylovich Frank (23 Oct 1908; 22 June 1990) Russian physicist who, with Igor Y. Tamm, theoretically explained the mechanism of Cherenkov radiation. In 1934, Cherenkov discovered that a peculiar blue light is emitted by charged particles traveling at very high speeds through water. Frank and Tamm provided the theoretical explanation of this effect, which occurs when the particles travel through an optically transparent medium at speeds greater than the speed of light in that medium. This discovery resulted in the development of new methods for detecting and measuring the velocity of high-speed particles and became of great importance for research in nuclear physics. For this, Frank received the Nobel Prize for Physics in 1958 (jointly with Pavel A. Cherenkov and Igor Y. Tamm). *TIS

1920 Tetsuya Theodore Fujita (23 Oct 1920; 19 Nov 1998) was a Japanese-American meteorologist who increased the knowledge of severe storms. In 1953, he began research in the U.S. Shortly afterwards, he immigrated and established the Severe Local Storms Project. He was known as "Mr. Tornado" as a result of the Fujita scale (F-scale, Feb 1971), which he and his wife, Sumiko, developed for measuring tornadoes on the basis of their damage. Following the crash of Eastern flight 66 on 24 Jun 1975, he reviewed weather-related aircraft disasters and verified the downburst and the microburst (small downburst) phenomena, enabling airplane pilots to be trained on how to react to them. Late in his career, he turned to the study of storm tracks and El Nino. *TIS


1581 Michael Neander (April 3, 1529 – October 23, 1581) German mathematician and astronomer was born in Joachimsthal, Bohemia, and was educated at the University of Wittenberg, receiving his B.A. in 1549 and M.A. in 1550.
From 1551 until 1561 he taught mathematics and astronomy in Jena, Germany. He became a professor in 1558 when the school where he taught became a university. From 1560 until his death he was a professor of medicine at the University of Jena. He died in Jena, Germany. The crater Neander on the Moon is named after him. *Wik

1944 Charles Glover Barkla (7 Jun 1877, 23 Oct 1944) was a British physicist who was awarded the Nobel Prize for Physics in 1917 for his work on X-ray scattering. This technique is applied to the investigation of atomic structures, by studying how X-rays passing through a material and are deflected by the atomic electrons. In 1903, he showed that the scattering of x-rays by gases depends on the molecular weight of the gas. His experiments on the polarization of x-rays (1904) and the direction of scattering of a beam of x-rays (1907) showed X-rays to be electromagnetic radiation like light (whereas, at the time, William Henry Bragg who held that X-rays were particles.) Barkla further discovered that each element has its own characteristic x-ray spectrum. *TIS

1985 John Semple studied at Queen's University Belfast and Cambridge. He held a post in Edinburgh for a year before becoming Professor of Pure Mathematics at Queen's College Belfast. He moved to King's College London where he spent the rest of his career. His most important work was in Algebraic geometry, in particular work on Cremona transformations and work extending results of Severi . He wrote two famous texts Algebraic projective geometry (1952) and Algebraic curves (1959) jointly with G T Kneebone. *SAU

2007 David George Kendall FRS (15 January 1918 – 23 October 2007)[2] was an English statistician, who spent much of his academic life in the University of Oxford and the University of Cambridge. He worked with M. S. Bartlett during the war, and visited Princeton University after the war. He was appointed the first Professor of Mathematical Statistics in the Statistical Laboratory, University of Cambridge in 1962, in which post he remained until his retirement in 1985. He was elected to a professorial fellowship at Churchill College, and he was a founding trustee of the Rollo Davidson Trust.
Kendall was a world expert in probability and data analysis, and pioneered statistical shape analysis including the study of ley lines. He defined Kendall's notation for queueing theory.
The Royal Statistical Society awarded him the Guy Medal in Silver in 1955, followed in 1981 by the Guy Medal in Gold. In 1980 the London Mathematical Society awarded Kendall their Senior Whitehead Prize, and in 1989 their De Morgan Medal. He was elected a fellow of the Royal Society in 1964. *Wik

2011 John McCarthy (September 4, 1927 – October 23, 2011) was an American computer scientist and cognitive scientist who received the Turing Award in 1971 for his major contributions to the field of Artificial Intelligence (AI). He was responsible for the coining of the term "Artificial Intelligence" in his 1955 proposal for the 1956 Dartmouth Conference and was the inventor of the LISP programming language.*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

Sunday, 22 October 2017

On This Day in Math - October 22

One of the most baneful delusions by which the minds, not only of students, but even of many teachers of mathematics in our classical colleges, have been afflicted with is, that mathematics can be mastered by the favored few, but lies beyond the grasp and power of the ordinary mind.
~Florian Cajori, The Teaching and History of Mathematics in the United States

The 295th day of the year; 295 may be interesting only because it seems to be the least interesting day number of the year. (Willing to be contradicted, send your comments)
[Here are several of the best I received from David Brooks:
295 can be partitioned in 6486674127079088 ways.
295 is a 31-gonal number.

And Derek Orr pointed out that "295 is the second proposed Lychrel number." A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called the 196-algorithm, after the most famous number associated with the process. In base ten, no Lychrel numbers have been yet proved to exist, but many, including 196, are suspected on heuristic and statistical grounds. The name "Lychrel" was coined by Wade Van Landingham as a rough anagram of Cheryl, his girlfriend's first name.

1668 Leibniz writes to the German emperor to request permission to publish a "Nucleus Libareaus". This was the beginnings of the foundation of Acta Eruditorium, the first German scientific journal.

1685 Abraham De Moivre was a student of physics at the University, Collège d'Harcourt, in the 1680s. After the Revocation of the Edict of Nantes, (October 22, 1685 ) he went into seclusion in the priory of St. Martin (possibly that which became the Conservatoire National des Arts et Métiers ??) and then emigrated to England, having no contact with France until he was elected a Foreign Associate of the Academy of Sciences just before his death.*VFR

1922 M. C. ESCHER visited here(Alhambra) on 18 - 24 Oct 1922 and was impressed by the patterns, but he didn't really use them in his art until after his second visit on 22-26 May 1936 *VFR

1746 Princeton chartered as the College of New Jersey -- the name by which it was known for 150 years -- Princeton University was British North America's fourth college. Located in Elizabeth for one year and then in Newark for nine, the College of New Jersey moved to Princeton in 1756. It was housed in Nassau Hall, which was newly built on land donated by Nathaniel FitzRandolph. Nassau Hall contained the entire College for nearly half a century. *Princeton Univ web page

In 1797, the first parachute jump was made by André-Jacques Garnerin, released from a balloon 2,230-ft above the Parc Monceau, Paris. He rode in a gondola fixed to the lines of a 23-ft diameter parachute, which was supported by a wooden pole and had its 32 white canvas gores folded like a closed umbrella. Lacking any vent in the top of the parachute, Garnerin descended with violent oscillations, and suffered the first case of airsickness. For his next jump, he added a hole in the top of the parachute. He made his fifth jump on 21 Sep 1802 over London, from a height of 3,000-ft. This was the first parachute descent made in England. He landed near St. Pancras Church. Having eliminated the center vent for this jump, he again suffered a fit of vomiting. *TIS See A larger TIS article here.

1850 Fechner’s law introduced. [Springer’s 1985 Statistics Calendar] A pioneering though in many situations incorrect formulation of the relationship between the physical strength of a stimulus and its strength as perceived by humans, proposed by G. T. Fechner in 1860. Fechner postulated that sensation increases as the log of the stimulus. For example, by Fechner's law, if light A was twice as bright as light B (measured by an instrument), it would appear to the human eye to be log 2 (times a constant to allow for such factors as the units used) brighter than light B. Later experiments have shown conclusively that the Fechner's law doesn't generally apply.

1908 First meeting of the Spanish Association for the Advancement of Science was held October 22–29. Sixteen papers were read in the section of mathematics.*VFR

1938 In the back of a beauty shop in the Astoria section of Queens New York, Chester A. Carlson and his assistant Otto Kornei, conducted the first successful experiment in electrophotography. The message, “10.-22.-38 ASTORIA,” was even less inspiring than Alexander Graham Bell’s first phone conversation, but the effect was just as great. In 1949 Haloid Corporation marketed the Xerox Model A, a crude machine that required fourteen manual operations. Today five million copiers churn out 2,000 copies each year for every American citizen. *VFR


1511 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibus and made a favorable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read.[5] In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik

1587 Joachim Jungius (22 Oct 1587 in Lübeck, Germany - 23 Sept 1657 in Hamburg) a German mathematician who was one of the first to use exponents to represent powers and who used mathematics as a model for the natural sciences. Jungius proved that the catenary is not a parabola (Galileo assumed it was). *SAU (I can not find the first use by Jungius anywhere, but Cajori gives Descartes 1637 use in Geometrie as the first example of the common form today. A year earlier, James Hume produced a copy of Viete's Algebra in which he used exponents as powers of numbers, but his exponents were Roman Numerals.)

1659 Georg Ernst Stahl (22 October 1659 – 24 May 1734) was a German chemist, physician and philosopher. He was a supporter of vitalism, and until the late 18th century his works on phlogiston were accepted as an explanation for chemical processes
Stahl used the works of Johann Joachim Becher to help him come up with explanations of chemical phenomena. The main theory that Stahl got from J. J. Becher was the theory of phlogiston. This theory did not have any experimental basis before Stahl. He was able to make the theory applicable to chemistry.[4] Becher's theories attempted in explaining chemistry as comprehensively as seemingly possible through classifying different earths according to specific reactions. Terra pinguis was a substance that escaped during combustion reactions, according to Becher.[10] Stahl, influenced by Becher's work, developed his theory of phlogiston.People who dismiss Phlogiston theory as early ignorance should read The Renaissance Mathematicus blog, The Phlogiston Theory – Wonderfully wrong but fantastically fruitful.

1792 Guillaume-Joseph-Hyacinthe-Jean-Baptiste Le Gentil de la Galaziere  (12 Sep 1725; 22 Oct 1792) was a French astronomer who attempted to observe the transit of Venus across the sun by travelling to India in 1761. He failed to arrive in time due to an outbreak of war. He stayed in India to see the next transit which came eight years later. This time, he was denied a view because of cloudy weather, and so returned to France. There, he found his heirs had assumed he was dead and taken his property.*TIS A more detailed blog about his life is at Renaissance Mathematicus

1843 John S Mackay graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU

1881 Clinton Joseph Davisson (22 Oct 1881; 1 Feb 1958) American experimental physicist who shared the Nobel Prize for Physics in 1937 with George P. Thomson of England for discovering that electrons can be diffracted like light waves. Davisson studied the effect of electron bombardment on surfaces, and observed (1925) the angle of reflection could depend on crystal orientation. Following Louis de Broglie's theory of the wave nature of particles, he realized that his results could be due to diffraction of electrons by the pattern of atoms on the crystal surface. Davisson worked with Lester Germer in an experiment in which electrons bouncing off a nickel surface produced wave patterns similar to those formed by light reflected from a diffraction grating, and supporting de Broglie's electron wavelength = (h/p). *TIS

1895 Rolf Herman Nevanlinna​ (22 October 1895 – 28 May 1980) was one of the most famous Finnish mathematicians. He was particularly appreciated for his work in complex analysis.Rolf Nevanlinna's most important mathematical achievement is the value distribution theory of meromorphic functions. The roots of the theory go back to the result of Émile Picard in 1879, showing that a complex-valued function which is analytic in the entire complex plane assumes all complex values save at most one.*Wik

1905 Karl Guthe Jansky (22 Oct 1905; 14 Feb 1950) was an American electrical engineer who discovered cosmic radio emissions in 1932. At Bell Laboratories in NJ, Jansky was tracking down the crackling static noises that plagued overseas telephone reception. He found certain radio waves came from a specific region on the sky every 23 hours and 56 minutes, from the direction of Sagittarius toward the center of the Milky Way. In the publication of his results, he suggested that the radio emission was somehow connected to the Milky Way and that it originated not from stars but from ionized interstellar gas. At the age of 26, Jansky had made a historic discovery - that celestial bodies could emit radio waves as well as light waves. *TIS Image: Karl Jansky makes adjustments to his antenna *Wik

1907 Sarvadaman D. S. Chowla (22 October 1907, London–10 December 1995, Laramie, Wyoming) was a prominent Indian mathematician, specializing in number theory. Among his contributions are a number of results which bear his name. These include the Bruck–Chowla–Ryser theorem, the Ankeny–Artin–Chowla congruence, the Chowla–Mordell theorem, and the Chowla–Selberg formula, and the Mian–Chowla sequence.*Wik

1916 Nathan Jacob Fine (22 October 1916 in Philadelphia, USA - 18 Nov 1994 in Deerfield Beach, Florida, USA) He published on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis. He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society. The material which he presented in the Earle Raymond Hedrick Lectures twenty years earlier form the basis for the material in this text.*SAU

1927 Alexander Ivanovich Skopin (22 Oct 1927 in Leningrad (now St Petersburg), Russia - 15 Sept 2003 in St Petersburg, Russia) He was a Russian mathematician known for his contributions to abstract algebra. Skopin's student work was in abstract algebra, and concerned upper central series of groups and extensions of fields. In the 1970s, Skopin received a second doctorate concerning the application of computer algebra systems to group theory. From that point onward he used computational methods extensively in his research, which focused on lower central series of Burnside groups. He related this problem to problems in other areas of mathematics including linear algebra and topological sorting of graphs. *Wik

1941 Stanley Mazor was born in Chicago on October 22, 1941. He studied mathematics and programming at San Francisco State University. He joined Fairchild Semiconductor in 1964 as a programmer and then a computer designer in the Digital Research Department where he shares patents on the Symbol computer. In 1969, he joined Intel. In 1977, he began his teaching career in Intel's Technical Training group, and later taught classes at Stanford, University of Santa Clara, KTH in Stockholm and Stellenbosch, S.A. In 1984 he was at Silicon Compiler Systems. He co-authored a book on chip design language while at Synopsys 1988-1994. He was invited to present The History of the Microcomputer at the 1995 IEEE Proceedings. He is currently the Training Director at BEA Systems. *CHM


1950 Ada Isabel Maddison (13 April 1869 in Cumberland, England - 22 Oct 1950 in Martin's Dam, Wayne, Pennsylvania, USA) A British mathematician best known for her work on differential equations. Although Maddison passed an honors exam for the University of Cambridge, she was not given a degree there. Instead, she went to Bryn Mawr in Pennsylvania. In 1893, the University of London awarded her a bachelor's degree in mathematics with honors. After further study at the University of Göttingen, Maddison went back to Bryn Mawr, where she taught as well as doing time consuming administrative work. Her will endowed a pension fund for Bryn Mawr's administrative staff.*Wik

1977 Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry. Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School, although he also appreciated the greater rigor of modern algebraic geometry. Another contribution of his was the introduction of finite and non-continuous structures into geometry. In his best known paper he proved the following theorem: In a Desarguesian plane of odd order, the ovals are exactly the irreducible conics. Some critics felt that his work was no longer geometry, but today it is recognized as a separate sub-discipline: combinatorial geometry.
In 1938 he lost his professorship as a result of the anti-Jewish laws enacted under Benito Mussolini's government; he spent the next 8 years in Great Britain (mostly at the University of Manchester), then returned to Italy to resume his academic career *Wik

1979 Reinhold Baer (22 July 1902 in Berlin, Germany - 22 Oct 1979 in Zurich, Switzerland) Baer's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups. *SAU

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

Saturday, 21 October 2017

On This Day in Math - October 21

“Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.”~Ron Graham on Martin Gardner

The 294th day of the year; 294 is a practical number because all numbers strictly less than 294 can be formed with sums of distinct divisors of 294. There are only 84 such numbers in the year.

294 is the number of planar 2-connected graphs with seven vertices.

Found this oddity in my notes: 111152- 2942 = 123,456,789

2(294)+9(294)+4(294) - 1 is 4409, a prime

1621 Kepler's Mother, Katherine, during her trial for witchcraft was shown the "instruments of torture."
"The whole case was now passed on the law faculty of the University of Tübingen, Kepler’s Alma Mater, who decided that Katharine should be taken to the hangman and shown the instruments of torture and ordered to confess. On 21st October 1621 this was duly carried out but the stubborn old lady refused to bend she said,"
“Do with me what you want. Even if you were to pull one vein after another out of my body, I would have nothing to admit.” Then she fell to her knees and said a Pater Noster. God would she said, bring the truth to light and after her death disclose that wrong and violence had been done to her. He would not take the Holy Ghost from her and would stand by her.
For more about this unusual woman, read Thony Christie's blog at *The Renaissance Mathematicus

1743 In the United States, on October 21, 1743, Benjamin Franklin tracked a hurricane for the first time. It was the first recorded instance in which the progressive movement of a storm system was recognized.

1796 The date of a still uninterpreted cryptic entry "Vicimus GEGAN"" in Gauss’s scientific diary. There is a another insertion that also remains uninterpreted. He wrote "REV. GALEN" in the diary on April 8, 1799 *VFR
*Genial Gauss Gottingen

1803 John Dalton's Atomic Theory was first presented on 21st October 1803 to the Manchester Literary and Philosophical Society of which he was President 1816-1844. *Open Plaques

1805 British Admiral Nelson defeated the combined French and Spanish fleets in the Battle of Trafalgar by adopting the tactic of breaking the enemy line in two and concentrating his firepower on a few ships (orthodox tactics had the opponents facing each other in roughly parallel lines—the “line-ahead” formation). For an analysis of why this works see David H. Nash, “Differential equations and the Battle of Trafalgar”, The College Mathematics Journal, 16(1985), 98–102. *VFR

1845 After two unsuccessful attempts to present his work in person to the Royal Astronomer Sir George Biddell Airy, John Couch Adams left a copy of his calculation regarding a hypothetical planet at the Royal Observatory. Airy criticized the work and didn’t search for the planet until later. Consequently he didn’t discover Neptune. See 23 September 1846.

1854 Florence Nightingale embarked for the Crimea on 21 October with thirty-eight nurses: ten Roman Catholic Sisters, eight Anglican Sisters of Mercy, six nurses from St. John's Institute, and fourteen from various hospitals. *Victorian Web Org

1965 Greece issued a postage stamp picturing Hipparchus and an astrolabe to commemorate the opening of the Evghenides Planetarium in Athens. [Scott #835]. *VFR

1976, the United States made a clean sweep of the Nobel Prizes, winning or sharing awards in chemistry, physics, medicine, economics, and literature. (No peace prize was awarded.)

1988 Science (pp. 374-375) reported that the 100-digit number 11104 + 1 was factored by using computers working in parallel using a quadratic sieve method. [Mathematics Magazine 62 (1989), p 70].*VFR

2011 Several people were awarded with the Ignobel Prize for mathematics for predictions about the end of the earth. Among the winners was the inappropriately named Elizabeth Clare Prophet who predicted the demise of the Earth in 1990, which most scholars on the existence of the earth dispute. *improbable.com

2015 Marty McFly and Doctor Emmet Brown "return" to this date in the future in the 1989 Sci-fi-sequel, Back to the Future II. The "future" included rocket powered skateboards... Do Razors count?


1687 Nicolaus(I) Bernoulli (21 Oct 1687 in Basel, Switzerland - 29 Nov 1759 in Basel) Nicolaus Bernoulli was one of the famous Swiss family of mathematicians. He is most important for his correspondence with other mathematicians including Euler and Leibniz. *SAU (Can't tell your Bernoulli's without a scorecard? Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1823 Birthdate of Enrico Betti. In algebra, he penetrated the ideas of Galois by relating them to the work of Ruffini and Abel. In analysis, his work on elliptic functions was further developed by Weierstrass. In “Analysis situs”, his research inspired Poincar´e, who coined the term “Betti numbers” to characterize the connectivity of surfaces. *VFR He was the first to give a proof that the Galois group is closed under multiplication. Betti also wrote a pioneering memoir on topology, the study of surfaces and space. Betti did important work in theoretical physics, in particular in potential theory and elasticity.*TIS

1833 Alfred Bernhard Nobel (21 Oct 1833; 10 Dec 1896) a Swedish chemist and inventor of dynamite and other, more powerful explosives, was born in Stockholm. An explosives expert like his father, in 1866 he invented a safe and manageable form of nitroglycerin he called dynamite, and later, smokeless gunpowder and (1875) gelignite. He helped to create an industrial empire manufacturing many of his other inventions. Nobel amassed a huge fortune, much of which he left in a fund to endow the annual prizes that bear his name. First awarded in 1901, these prizes were for achievements in the areas of physics, chemistry, physiology or medicine, literature, and peace. The sixth prize, for economics, was instituted in his honour in 1969. *TIS (The well-known anecdote that there is no Nobel prize in mathematics as he thought Mittag-Leffler might win it seems to have no basis in fact

1855 Giovanni Battista Guccia (21 Oct 1855 in Palermo, Italy - 29 Oct 1914 in Palermo, Italy) Guccia's work was on geometry, in particular Cremona transformations, classification of curves and projective properties of curves. His results published in volume one of the Rendiconti del Circolo Matematico di Palermo were extended by Corrado Segre in 1888 and Castelnuovo in 1897. *SAU

1882 Harry Schultz Vandiver (21 Oct 1882 in Philadelphia, Pennsylvania, USA - 9 Jan 1973 in Austin, Texas, USA) Harry developed an antagonism towards public education and left Central High School at an early age to work as a customshouse broker for his father's firm. D H Lehmer writes:
He was self-taught in his youth and must have had little patience with secondary education since he never graduated from high school. This impatience, especially with mathematical education, was to last the rest of his life.
When he was eighteen years old he began to solve many of the number theory problems which were posed in the American Mathematical Monthly, regularly submitting solutions. In addition to solving problems, he began to pose problems himself. By 1902 he was contributing papers to the Monthly. For example he published two short papers in 1902 A Problem Connected with Mersenne's Numbers and Applications of a Theorem Regarding Circulants.
In 1904 he collaborated with Birkhoff on a paper on the prime factors of a^n - b^n published in the Annals of Mathematics. In fact the result they proved was not new, although they were not aware of the earlier work which had been published by A S Bang in 1886. Also in the year 1904, Vandiver published On Some Special Arithmetic Congruences in the American Mathematical Monthly and, although still working as an agent for his father's firm, he did attend some graduate lectures at the University of Pennsylvania. He also began reading papers on algebraic number theory and embarked on a study of the work of Kummer, in particular his contributions to solving Fermat's Last Theorem. Over the next few years he published papers such as Theory of finite algebras (1912), Note on Fermat's last theorem (1914), and Symmetric functions formed by systems of elements of a finite algebra and their connection with Fermat's quotient and Bernoulli's numbers (1917).
The outbreak of World War I in 1914 did not directly affect the United States since the Democratic president Woodrow Wilson made a declaration of neutrality. This policy was controversial but popular enough to see him re-elected in 1916. However US shipping was being disrupted (and sunk) by German submarines and, under pressure from Republicans, Wilson declared war on Germany on 6 April 1917. Vandiver joined the United States Naval Reserve and continued to serve until 1919 when the war had ended. After leaving the Naval Reserve, Birkhoff persuaded Vandiver to become a professional mathematician and to accept a post at Cornell University in 1919. Despite having no formal qualifications, his excellent publication record clearly showed his high quality and he was appointed as an instructor. He also worked during the summer with Dickson at Chicago on his classic treatise History of the Theory of Numbers. In 1924 he moved to the University of Texas where he was appointed as an Associate Professor. He spent the rest of his career at the University of Texas, being promoted to full professor in 1925, then named as distinguished professor of applied mathematics and astronomy in 1947. He continued in this role until he retired in 1966 at the age of 84. *SAU

1893 Bill Ferrar graduated from Oxford after an undergraduate career interrupted by World War I. He lectured at Bangor and Edinburgh before moving back to Oxford. He worked in college administration and eventually became Principal of Hertford College. He worked on the convergence of series. *SAU

1914 Martin Gardner born in Tulsa, Oklahoma. From 1957 to 1980 he wrote the “Mathematical Games” column in Scientific American. Many of these columns have been collected together into the numerous books that he has written. If you want to know more about the person who has done more to popularize mathematics than any other, see the interview with Gardner in Mathematical People. Proiles and Interviews (1985), edited by Donald J. Albers and G. L. Alexanderson, pp. 94–107. *VFR (My favorite tribute to Martin was this one from Ron Graham, “Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.”)

1872 Jacques Babinet (5 March 1794 – 21 October 1872) was a French physicist, mathematician, and astronomer who is best known for his contributions to optics. A graduate of the École Polytechnique, which he left in 1812 for the Military School at Metz, he was later a professor at the Sorbonne and at the Collège de France. In 1840, he was elected as a member of the Académie Royale des Sciences. He was also an astronomer of the Bureau des Longitudes.
Among Babinet's accomplishments are the 1827 standardization of the Ångström unit for measuring light using the red Cadmium line's wavelength, and the principle (Babinet's principle) that similar diffraction patterns are produced by two complementary screens. He was the first to suggest using wavelengths of light to standardize measurements. His idea was first used between 1960 and 1983, when a meter was defined as a wavelength of light from krypton gas.
In addition to his brilliant lectures on meteorology and optics research, Babinet was also a great promoter of science, an amusing and clever lecturer, and a brilliant, entertaining and prolific author of popular scientific articles. Unlike the majority of his contemporaries, Babinet was beloved by many for his kindly and charitable nature. He is known for the invention of polariscope and an optical goniometer. *Wik

1881 Heinrich Eduard Heine (16 March 1821 in Berlin, Germany - 21 Oct 1881 in Halle, Germany) Heine is best remembered for the Heine-Borel theorem. He was responsible for the introduction of the idea of uniform continuity.*SAU

1967 Ejnar Hertzsprung (8 Oct 1873, 21 Oct 1967) Danish astronomer who classified types of stars by relating their surface temperature (or color) to their absolute brightness. A few years later Russell illustrated this relationship graphically in what is now known as the Hertzsprung-Russell diagram, which has become fundamental to the study of stellar evolution. In 1913 he established the luminosity scale of Cepheid variable stars.*TIS

1969 WacLlaw Sierpinski (14 March 1882 in Warsaw, - 21 Oct 1969 in Warsaw) His grave carries—according to his wish—the inscription: Investigator of infinity. [Kuratowski, A Half Century of Polish Mathematics, p. 173; Works, p. 14] *VFR Sierpinski's most important work is in the area of set theory, point set topology and number theory. In set theory he made important contributions to the axiom of choice and to the continuum hypothesis. *SAU

2000 Dirk Jan Struik (30 Sept 1894 , 21 Oct 2000) Dirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician and Marxian theoretician who spent most of his life in the United States.
In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time.
Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994), Mathematics, and Marxism.
It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics.
Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.
In 1950 Stuik published his Lectures on Classical Differential Geometry.
Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.
Struik died October 21, 2000, 21 days after celebrating his 106th birthday. *Wik

2002 Bernhard Hermann Neumann (15 Oct 1909 in Berlin, Germany - 21 Oct 2002 in Canberra, Australia) Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them. *SAU

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

Friday, 20 October 2017

On This Day in Math - October 20

The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.
~Paul Dirac

The 293rd day of the year; 293 is a Sophie Germain Prime. (A prime number p such that 2p + 1 is also prime.) Sophie Germain used them in her investigations of Fermat's Last Theorem. It is an unproven conjecture that there are infinitely many Sophie Germain primes.

293 is also the sum of five cubes, \(293 = 2^3 + 2^3 + 3^3 + 5^3 + 5^3\)

and from Jim Wilder @Wilderlab : 293202 begins with the digits 202 and 202293 begins with the digits 293.


1698 Halley began a scientific voyage on HMS Paramore & set out to measure magnetic variation & search for Terra Incognita. His log entry from the 20th says "Wind WSW a Small Gale I sailed from Deptford about Noon " *Kate Morant‏@KateMorant (Deptford is a small area near Greenwich, east of London along the Thames)

1735 Benjamin Franklin’s paper “On the Usefulness of Mathematics,” appeared in the Pennsylvania Gazette. [NCTM yearbook # 32(1970), p. 20]*VFR
I have also seen the date given as October 30. Some historians also question whether or not this was actually written by Franklin.

1744 In Euler's missing letter of October 20, 1744, Euler announced that he had just discovered a simple curve that exhibited something called a cusp of the second kind or a ramphoid from the Greek for a bird’s beak. L'H^opital (1661-1704) is responsible for defining these two types of cusps. In 1740, Jean-Paul de Gua de Malves (1713- 1785) published a proof that no algebraic curve could have a cusp of the second kind in [Gua de Malves 1740]. Euler was familiar with Gua de Malves' work and had initially accepted his result, but in 1744 he discovered that there was a subtle flaw in the supposed proof. In this letter, he wrote to Cramer that even in the fourth order there is a curved line of this kind, whose equation is, y4- 2xy2 + x2 = x3+ 4yx, which simplifies to y = x(1/2) +/- x(3/4)

*Ed Sandifer, How Euler Did It, MAA

1881 In a letter to Newcomb dated Oct. 20, 1881, Sylvester writes to Charles S. Pierce, "Who is to be the new superintendent of the Coast Survey?
Why should you not allow it to be known that you would accept the appointment supposing you would be willing to do so!" Sylvester was the eminent British mathematician who served as the first chairman of the Department of Mathematics at the Johns Hopkins University (1876-1883). He returned to England in 1884 to occupy the chair of Savilian Professor of Geometry at Oxford. *THE CHARLES S. PElRCE-SIMON NEWCOMB CORRESPONDENCE

1958 Italy issued a stamp to celebrate the 350th anniversary of the birth of Evangelista Torricelli, mathematician and physicist. [Scott #754]. *VFR

1975 The Public Record office in London released information on the Colossus, one of the first programmable electronic digital computers. It was built in 1943 for work on cryptography. The Colossus machines were electronic computing devices used by British codebreakers to help read encrypted German messages during World War II. They used vacuum tubes (thermionic valves) to perform the calculations.
Colossus was designed by engineer Tommy Flowers with input from Harry Fensom, Allen Coombs, Sidney Broadhurst and William Chandler at the Post Office Research Station, Dollis Hill to solve a problem posed by mathematician Max Newman at Bletchley Park. The prototype, Colossus Mark 1, was shown to be working in December 1943 and was operational at Bletchley Park by February 1944. An improved Colossus Mark 2 first worked on 1 June 1944, just in time for the Normandy Landings. Ten Colossi were in use by the end of the war. No information about the computer was released until this date. *Wik

1980, Carl Sagan appeared on the cover of TIME

1983, the length of the meter was redefined by the international body Conférence Générale des Poids et Mesures (GCPM) by a method to give greater accuracy. Originally based on one ten-millionth of the distance from the North Pole to the equator, the meter was re-established as the distance that light travels in a vacuum in 1/299,792,458 of a second *TIS

2004 The First Ubuntu Linux Distribution Released. Ubuntu is a free computer operating system based on Debian GNU​/Linux. Its name loosely translated from the Zulu means "humanity," or "a person is a person only through other people." Ubuntu is intended to provide an up-to-date, stable operating system for the average user, with a strong focus on usability and ease of installation. Ubuntu has been rated the most popular Linux distribution for the desktop, claiming approximately 30 percent of desktop Linux installations, according to the 2007 Desktop Linux Market survey. Ubuntu is open source and free. It is sponsored by Canonical Ltd, which is owned by South African entrepreneur Mark Shuttleworth​.*CHM

1616 Thomas Bartholin (20 Oct 1616; 4 Dec 1680) Danish anatomist and mathematician who was first to describe fully the entire human lymphatic system (1652). He was one of the earliest defenders of Harvey's discovery of the circulation of blood. He was a member of the mathematical faculty of the University of Copenhagen, 1647-49, and anatomy professor there, 1649-61. He published many works on anatomy, physiology and medicine, (1645-74) and in 1658 a general work on pharmacology. In 1654, along with the rest of the medical faculty at the university, Bartholin published advice to the people on how to take care of themselves during the plague. King Christian V named Bartholin as his personal physician, with an annual salary, although Bartolin rarely had to treat the king. *TIS

1632 Sir Christopher Wren (20 Oct 1632; 25 Feb 1723) Architect, astronomer, and geometrician who was the greatest English architect of his time whose famous masterpiece is St. Paul's Cathedral, among many other buildings after London's Great Fire of 1666. Wren learned scientific skills as an assistant to an eminent anatomist. Through astronomy, he developed skills in working models, diagrams and charting that proved useful when he entered architecture. He inventing a "weather clock" similar to a modern barometer, new engraving methods, and helped develop a blood transfusion technique. He was president of the Royal Society 1680-82. His scientific work was highly regarded by Sir Isaac Newton as stated in the Principia. *TIS (I love the message on his tomb in the Crypt of St. Pauls: Si monumentum requiris circumspice ...."Reader, if you seek his monument, look about you."

1863 William Henry Young (20 Oct 1863 in London, England - 7 July 1942 in Lausanne, Switzerland) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.

1865 Aleksandr Petrovich Kotelnikov (20 Oct 1865 in Kazan, Russia - 6 March 1944 in Moscow, USSR) In 1927 he published one of his most important works, The Principle of Relativity and Lobachevsky's Geometry. He also worked on quaternions and applied them to mechanics and geometry. Among his other major pieces of work was to edit the Complete Works of two mathematicians, Lobachevsky and Zhukovsky. He received many honours for his work, being named Honoured Scientist in 1934, then one year before he died he was awarded the State Prize of the USSR. *SAU

1891 Sir James Chadwick (20 Oct 1891; 24 Jul 1974) English physicist who received the Nobel Prize for Physics (1935) for his discovery of the neutron. He studied at Cambridge, and in Berlin under Geiger, then worked at the Cavendish Laboratory with Rutherford, where he investigated the structure of the atom. He worked on the scattering of alpha particles and on nuclear disintegration. By bombarding beryllium with alpha particles, Chadwick discovered the neutron - a neutral particle in the atom's nucleus - for which he received the Nobel Prize for Physics in 1935. In 1932, Chadwick coined the name "neutron," which he described in an article in the journal Nature. He led the UK's work on the atomic bomb in WW II, and was knighted in 1945. *TIS

1904 Hans Lewy (October 20, 1904 – August 23, 1988) was an American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables.*Wik

1914 R. H. Bing (October 20, 1914, Oakwood, Texas – April 28, 1986, Austin, Texas) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His first two names were just single letters that do not stand for anything. Bing's mathematical research was almost exclusively in 3-manifold theory and in particular, the geometric topology of R3. The term Bing-type topology was coined to describe the style of methods used by Bing.
Bing established his reputation early on in 1946, soon after completing his Ph.D. dissertation, by solving the Kline sphere characterization problem. In 1948 he proved that the pseudo-arc is homogeneous, contradicting a published but erroneous 'proof' to the contrary. In 1951 he proved results regarding the metrizability of topological spaces, including what would later be called the Bing-Nagata-Smirnov metrization theorem.*Wik

1631 Michael Maestlin (30 September 1550, Göppingen – 20 October 1631, Tübingen) was a German astronomer and mathematician, known for being the mentor of Johannes Kepler.
Maestlin studied theology, mathematics, and astronomy/astrology at the Tübinger Stift in Tübingen, a town in Württemberg. He graduated as Magister in 1571 and became in 1576 a Lutheran deacon in Backnang, continuing his studies there.
In 1580 he became a Professor of mathematics, first at the University of Heidelberg, then at the University of Tübingen where he taught for 47 years from 1583. In 1582 Maestlin wrote a popular introduction to astronomy.
Among his students was Johannes Kepler (1571-1630). Although he primarily taught the traditional geocentric Ptolemaic view of the solar system, Maestlin was also one of the first to accept and teach the heliocentric Copernican view. Maestlin corresponded with Kepler frequently and played a sizable part in his adoption of the Copernican system. Galileo Galilei's adoption of heliocentrism was also attributed to Maestlin.
The first known calculation [3] of the reciprocal of the golden ratio as a decimal of "about 0.6180340" was written in 1597 by Maestlin in a letter to Kepler.
He is also remembered for :
Catalogued the Pleiades cluster on 24 December 1579. Eleven stars in the cluster were recorded by Maestlin, and possibly as many as fourteen were observed.
Occultation of Mars by Venus on 13 October 1590, seen by Maestlin at Heidelberg. *Wik

1896 François-Félix Tisserand (13 Jan 1845, 20 Oct 1896) French astronomer whose 4-volume textbook Traité de mécanique céleste (1889-96; "Treatise on Celestial Mechanics") updated Pierre-Simon Laplace's work. At age 28, he was named Director at Toulouse Observatory (1873-78). He went to Japan to observe the 1874 transit of Venus. The 83-cm telescope he installed at the Toulouse Observatory in 1875 had a wooden base insufficiently stable for photographic work, but he was able to use it for observation of the satellites of Jupiter and of Saturn. From 1892 until his death he was director of the Paris Observatory, where he completed the major work, Catalogue photographique de la carte du ciel, and arranged for its publication.*TIS

1972 Harlow Shapley (2 Nov 1885, 20 Oct 1972) Astronomer, known as "The Modern Copernicus," who discovered the Sun's position in the galaxy. From 1914 to 1921 he was at Mt. Wilson Observatory, where he calibrated Henrietta S. Leavitt's period vs. luminosity relation for Cepheid variable stars and used it to determine the distances of globular clusters. He boldly and correctly proclaimed that the globulars outline the Galaxy, and that the Galaxy is far larger than was generally believed and centered thousands of light years away in the direction of Sagittarius. In the early 1920's, Shapley entered a "Great Debate" with Heber D. Curtis. They truly argued over the "Scale of the Universe."*TIS

1974 Harold Ruse graduated from Oxford and held a position at Edinburgh University. he later became a professor at Southampton and Leeds. He worked on Harmonic Spaces. He became Secretary of the EMS in 1930 and President in 1935. *SAU

1984 Paul A.M. Dirac (8 Aug 1902, 20 Oct 1984) English physicist and mathematician who originated quantum mechanics and the spinning electron theory. In 1933 he shared the Nobel Prize for Physics with the Austrian physicist Erwin Schrödinger.*TIS

1987 Andrey Nikolayevich Kolmogorov (25 Apr 1903, 20 Oct 1987) Russian mathematician whose basic postulates for probability theory that have continued to be an integral part of analysis. This work had diverse applications such as his study of the motion of planets (1954), or the turbulent air flow from a jet engine (1941). In topology, he investigated cohomology groups. He made a major contribution to answering the probability part of Hilbert's Sixth Problem, and completely resolved (1957) Hilbert's Thirteenth Problem. Kolmogorov was active in a project to provide special education for gifted children, not only by writing textbooks and in teaching them, but in expanding their interests to be not necessarily in mathematics, but with literature, music, and healthy activity such as on hikes and expeditions. *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

Thursday, 19 October 2017

On This Day in Math - October 19

I am a great believer in the simplicity of things and as you probably know I am inclined to hang on to broad & simple ideas like grim death until evidence is too strong for my tenacity.
~Sir Ernest Rutherford

The 292nd day of the year; The continued fraction representation of pi  is [3; 7, 15, 1, 292, 1, 1, 1, 2...]; the convergent obtained by  truncating before the surprisingly large term 292 yields the excellent  rational approximation \( \frac{355}{113} \) for pi. 
The approximation was found by Chinese mathematician and astronomer Zu Chongzhi(429–500 AD), using Liu Hui's algorithm which is based on the areas of regular polygons approximating a circle*Wik

292 is the number of ways to make change for 1 dollar (or for 1 Euro), using only 1, 5 and 25 cent coins (base five coins).

292! + 291! ± 1 are 595-digit twin primes. (are there smaller sums of consecutive factorials like this that are twin primes?)


1698 Halley began a scientific voyage on HMS Paramore & set out to measure magnetic variation & search for Terra Incognita *Kate Morant‏@KateMorant
This was the first time a sea voyage had been planned for the sole purpose of scientific discovery. 

1752 Franklin described his kite experiment in a letter written in Philadelphia and addressed to Peter Collinson, who had earlier provided Franklin with some simple apparatus for performing electrical experiments. A copy of the original letter is at present in the archives of the Royal Society in London. *Julian Rubin web site

1759 Gauss writes,in a letter to his former teacher, E. A. W. von Zimmermann, when he showed up at the Göttingen University library, "I cannot deny, that I found it very unpleasant that most of my beautiful discoveries in indefinite analysis were not original. What consoles me is this. All of Euler's discoveries that I have so far found, I have made also, and still more so. I have found a more general, and, I think, more natural viewpoint; yet I still see an immeasurable field before me..." *Animating Creativity, The LaRouche Youth Movement web page.

1892: The first long-distance telephone line opened between the cities of New York and Chicago, although it could only handle one call at a time.
Seated at a telephone in the American Telephone and Telegraph Company’s office in Quincy street, Chicago Mayor Washburne conducted Chicago’s end of the above conversation. At the. other end of the wire was Mayor Grant of New York. With this simple ceremony the long-distance telephone between Chicago and New York was formally placed in service.

Sixty persons were present to see it done. They were telephone men, merchants, and newspaper men. There were 150 people around Mayor Grant at the company’s office in Cortland street. New York, and the company so managed matters that everybody got a chance to test the workings of the line. They invited all to stand beneath two funnels fastened to the gas fixture and keep perfectly still. They did so and heard the “Star Spangled Banner” played by a cornetist in New York. Then the New York crowd gathered around similar funnels while Cornetist Cobb of Johnny Hand’s orchestra played the national anthem for them. *chicagology.com

This was not the first long distance call in the US, that had happened fifteen years earlier in California. The world's first long-distance telephone line, established in 1877, connected French Corral with Bowman Lake (previously known as French Lake) at the headwaters of the Yuba River. It was strung across trees and poles for a distance of 60 mi (97 km) in Nevada County, California, passing through Birchville, Sweetland, North San Juan, Cherokee, North Columbia, Lake City, North Bloomfield, Moores Flat, Graniteville, and Milton.
The line was operated by the Ridge Telephone Company for the service of Milton Mining and Water Company, as well as other water companies. The line was an improvement over the system used in nearby Downieville, California The site is now a California Historical Landmark. *Wik Unfortunately, it seems no one made note of the first conversation.

1901 Alberto Santos-Dumont won the French Aero Club’s Deutsch Prize, rounding the Eiffel Tower and landing at Parc Saint Cloud in twenty-nine minutes and thirty seconds in his dirigible. Later it became common that a crowd would gather to see the aviator driving his Baladeuse (The Wanderer), a personal sized dirigible, over the streets as if it were a carriage or automobile.
A few years later, on October 23, 1906, Santos-Dumont won the Archdeacon prize by flying his Hargrave box kite inspired aircraft at Bagatelle in Paris. He was hailed by many in Europe as the first to fly, despite the fact that the Wright Brothers had achieved such a feat three years earlier in the United Sates. But Orville and Wilbur Wright kept their invention under wraps, avoiding any public exhibitions while they sought a patent. Most aeronauts in Europe considered them to be bluffing., *theappendix.net

1948 The National Bureau of Standards authorized construction of its Standards Western Automatic Computer. The machine, which would be built at the Institute for Numerical Analysis in Los Angeles, had an objective to compute using already-developed technology. This was in contrast to the machine’s cousin, the Standards Eastern Automatic Computer, which tested components and systems for computer *CHM

1965 The London Times reported that an archaeologist has located what he believes to be the tomb of Archimedes.*VFR

In 1973, a US Federal Judge signed his decision following a lengthy court trial which declared the ENIAC patent invalid and belatedly credited physicist John Atanasoff with developing the first electronic digital computer, the Atanasoff- Berry Computer or the ABC. Built in 1937-42 at Iowa State University by Atanadoff 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.*TIS

1994 The Pentium FDIV bug error was isolated to the Pentium Pro chip by Professor Thomas R. Nicely at Lynchburg College, Virginia, USA while working on Brun's constant (the sum of the reciprocals of the odd twin primes).   Nicely had noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors (such as programming errors, motherboard chipsets, etc.) until October 19, 1994. On October 24, 1994 he reported the issue to Intel.   The bug was rarely encountered by average users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results) *Wik

2014 Small chance that Comet C/2013 A1 (Siding Spring), discovered in the beginning of 2013, might collide with Mars. At the moment, based on the observation arc of 74 days, the nominal close approach distance between the red planet and the comet might be as little as 0.00073 AU, that is approximately 109,200 km! Distance to Mars’ natural satellite Deimos will be smaller by 6000 km, making it 103,000 km. On the 19th October 2014, the comet might reach apparent magnitude of -8…-8.5, as seen from Mars! *Spaceobs.org


1795 Arthur Jules Morin​ (19 October 1795 – 7 February 1880) was a French physicist. He conducted experiments in mechanics and invented the Morin dynamometer.
In 1850, he was elected a foreign member of the Royal Swedish Academy of Sciences. His name is one of the 72 names inscribed on the Eiffel Tower.*Wik (He was also the director of my favorite Paris Museum, Musee des Arts et Métiers.) In the issue of Nature which appeared on 5 February 1880 the following report appears:-
We regret to state that General Morin, the well-known director of the Conservatoire des Arts et Métiers, is lying in a very precarious state in consequence of a severe cold. Great anxiety is felt for him at the Institute, of which he is one of the most respected and popular members. The General is aged 85 years. In the following issue of Nature, his death in Paris on 7 February was reported. *SAU

1871 John Miller (19 Oct 1871 in Glasgow, Scotland - 14 July 1956 in Victoria Infirmary, Glasgow, Scotland) studied at Glasgow and Göttingen. He returned to Glasgow to the Royal College of Science and Technology (the precursor to Strathclyde University). He became President of the EMS in 1913. *SAU

1903 Jean Frédéric Auguste Delsarte (October 19, 1903, Fourmies – November 28, 1968, Nancy) was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalised shift operators. He was one of the founders of the Bourbaki group.*Wik

1910 Subrahmanyan Chandrasekhar (19 Oct 1910; 21 Aug 1995) Indian-born American astrophysicist who (with William A.Fowler) won the 1983 Nobel Prize for Physics for formulating the currently accepted theory on the later evolutionary stages of massive stars. He was one of the first scientists to combine the disciplines of physics and astronomy. Early in his career he demonstrated that there is an upper limit, now called the Chandrasekhar limit, to the mass of a white dwarf star. A white dwarf is the last stage in the evolution of a star such as the Sun. When the nuclear energy source in the center of a star such as the Sun is exhausted, it collapses to form a white dwarf. Further, it shows that stars much more massive than the Sun must either explode or form black holes. *TIS


1586 Egnatio Danti was an Italian Dominican who made contributions to architecture, geography and astronomy.Finally, among Danti's publications, we mention Trattato del radio latino (1586) which is Danti's work describing his surveying instrument. This book appeared in the year in which Danti died. The other task he undertook just before his death was to travel to Rome, at the request of Pope Sixtus, to assist the architect Domenico Fontana, who had become architect to the papacy when Sixtus was elected, in moving the Egyptian obelisk from its place in the circus of the Vatican. The obelisk had been brought to Rome in the 1st century AD and Danti and Fontana erected it in 1586 where it now stands in the centre of St Peter's Square in the Vatican. After his return from this trip to Rome, Danti contracted pneumonia from which he died. *SAU

1875 Sir Charles Wheatstone (6 Feb 1802, 19 Oct 1875) English physicist who popularized the Wheatstone bridge, a device that accurately measured electrical resistance and became widely used in laboratories. He didn't actually invent the "Wheatstone Bridge". His contemporary, Samuel Hunter Christie, came up with the idea of the bridge circuit, but Wheatstone set the precedent for using it in the way in which it has been most commonly used. Over time, the device became associated with him and took on his name. He did, however, invent the concertina (1829), the stereoscope (1838), and an early form of the telegraph. He also  developed a chronoscope (1842) to determine the velocity of projectiles at an English gunnery.*TIS (For students of discrete math, or interested in codes, Wheatstone was also the creator of the Playfair Cipher.) A story is told that among friends he was "the life of the party" however he was afraid to speak in public. It was not unlike Wheatstone to set up a speaking engagement and cancel at the very last minute due to an awful case of stage fright. As a result of this condition Michael Faraday commentated much of Whetstone's work to the Royal Society through Faraday's famous Friday night lectures. On one such occasion Wheatstone was scheduled to speak at the Royal society and of course literally ran out the back door of the conference hall at the last minute. Faraday stepped onto the stage and delivered one of his most famous lectures, which was on the discovery of the Electro-magnetic field.

1878 Irénée-Jules Bienaymé (28 August 1796 - 19 October 1878) was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.*Wik

1890 Émile Léonard Mathieu (15 May 1835 in Metz, France - 19 Oct 1890 in Nancy, France) is remembered especially for his discovery (in 1860 and 1873) of five sporadic simple groups named after him. These were studied in his thesis on transitive functions.*SAU

1937 Sir Ernest Rutherford (30 Aug 1871, 19 Oct 1937) (baron) New Zealand-born British physicist who laid the groundwork for the development of nuclear physics. He worked under Sir J. J. Thomson at Cambridge University (1895-98). Then he collaborated with Frederick Soddy in studying radioactivity. In 1899 he discovered alpha particles and beta particles, followed by the discovery of gamma radiation the following year. In 1905, with Soddy, he announced that radioactive decay involves a series of transformations. In 1907, with Hans Geiger and Ernest Marsden, he devised the alpha-particle scattering experiment that led in 1911 to the discovery of the atomic nucleus. In 1919 he achieved the artificial splitting of light atoms. In 1908 he was awarded the Nobel Prize for Chemistry. *TIS

1944 Denes König (21 Sept 1884 in Budapest, Hungary - 19 Oct 1944 in Budapest, Hungary) At Göttingen, König had been influenced by Minkowski's lectures on the four color problem. These lectures contributed to his growing interest in graph theory, on which he lectured in Budapest from 1911. His book, Theorie der endlichen und unendlichen Graphen, was published in 1936, and was a major factor in the growth of interest in graph theory worldwide. It was eventually translated into English under the title Theory of finite and infinite graphs (translated by R McCoart), Birkhauser, 1990; this also contains a biographical sketch by Tibor Gallai​.  König's work on the factorization of bipartite graphs relates closely to the marriage problem of Philip Hall. König's use of graphs to give a simpler proof of a determinant result of Frobenius seems to have led to some hostility between the two men.
After the Nazi occupation of Hungary, König worked to help persecuted mathematicians. This led to his death a few days after the Hungarian National Socialist Party took over the country. *SAU

1979 Marjorie Lee Browne (September 9, 1914 – October 19, 1979) was a notable mathematics educator, the second African-American woman to receive a doctoral degree in the U.S., and one of the first black women to receive a doctorate in mathematics in the U.S.*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