Sunday 3 February 2013

On This Day in Math - February 3


Euclid might be an extra course for learned men, like Homer.
But Euclid for children is barbarous.
~Oliver Heaviside

The 34th day of the year; 34 is the smallest integer such that it and both its neighbors are the product of the same number of primes.

1692 De la Pryme records in his diary that Newton had a fire in his study that destroyed the manuscript of his Optics. “Every one thought he would have run mad; he was so troubled ... *VFR C. Huygens diary has an entry mentioning that he had been told "Newton had become deranged in his mind..." over the fire by Colin. He later related the same to Leibniz.*R. Smith, The Friend, 1829; pg 410
The historical story is that Newton's dog, Diamond, had overturned a candle and set the documents afire.

1673(1672 os) Leibniz writes to Oldenburg describing his “accidental” meeting with the mathematician John Pell at the house of Robert Boyle. They discussed infinite series and after Leibniz described his work on the topic, Pell informed him that Nicholas Mercator had already written extensively on the topic. *Gerhart, The Early Mathematical Manuscripts of Leibniz, pg 162 On his return to France, Leibniz acquired Mercator's Book.

1806 Lagrange presented an attempt to prove Euclid’s parallel postulate to the mathematical and physical classe of the Institute National (as the Acad´emie des Sciences was known during the French Revolutionary Period). Here is how Biot, who, incidentally, died on this date in 1862 (see below), recalled the embarrasing incident in 1837: “Then one day Lagrange took out of his pocket a paper which he read at the Acad´emie [sic], and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognized it as such during his lecture. For, when he had finished, he put the paper in his pocket, and spoke no more of it. A moment of universial silence followed, and one passed immediately to other concerns. [Grattan-Guiness, 1990, p. 263] *VFR In his "A Budget of Paradoxes, De Morgan described the event thus:"Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed: he muttered Il faut que j'y songe encore,("I shall have to think it over again.") and put the paper in his pocket. *Augustus De Morgan. A Budget of Paradoxes, Volume I .

1851 In the Meridian Hall at the Paris Observatory, invited scientist of Paris watched the Earth rotate on its axis as indicated by Foucault’s 11 meter long pendulum centered on the meridian line. You may see the same pendulum swinging today in the Musee de Arts et Metiers on the rue Saint-Martin in Paris. Foucault also presented his “sine law” for the period it takes the pendulum to sweep a full circle at any given latitude. *Amir D Aczel, Pendulum, pg 90-103

In 1862, as a boy almost 15 yrs old, Thomas Edison (1847-1931), became the first publisher of a newspaper produced and sold on a moving train. He had set up a small press in the baggage car of the Grand Trunk Railroad train from Port Huron to Detroit, Mich. Already obsessed with telegraphy, he worked out the logistics of getting advance news. His weekly Grand Trunk Herald, a single sheet measuring 7-in. x 8-in., included local news and advertisements for his fathers store. He had been selling candy and newspapers on commission on that train run since age 12. Now, promoting his own newspaper he earned more. Edison became renowned as a pioneering boy journalist. At its peak, he sold about 200 copies a day to train riders. *TIS

1961 Historian Gerald Holton echoed the words of Newton (5 February 1675/76) in opening a session of a meeting where three of the four speakers were Nobel laureates in Physics when he said “How good it is to be able to sit at the feet of giants on whose shoulders we stand.” *The Physics Teacher, 26 (1988), p 264

1774 Karl Brandan Mollweide (3 Feb 1774 in Wolfenbüttel, Brunswick, now Germany - 10 March 1825 in Leipzig, Germany) He is remembered for his invention of the Mollweide projection of the sphere, a map projection which he produced to correct the distortions in the Mercator projection, first used by Gerardus Mercator in 1569. Mollweide announced his projection in 1805. While the Mercator projection is well adapted for sea charts, its very great exaggeration of land areas in high latitudes makes it unsuitable for most other purposes. In the Mercator projection the angles of intersection between the parallels and meridians, and the general configuration of the land, are preserved but as a consequence areas and distances are increasingly exaggerated as one moves away from the equator. To correct these defects, Mollweide drew his elliptical projection; but in preserving the correct relation between the areas he was compelled to sacrifice configuration and angular measurement.
The second piece of work to which Mollweide's name is attached today is the Mollweide equations which are sometimes called Mollweide's formulas. These trigonometric identities ares

sin(½(A - B)) / cos(½C) = (a - b) / c, and

cos(½(A - B)) / sin(½C) = (a + b) / c,

where A, B, C are the three angles of a triangle opposite to sides a, b, c, respectively. These trigonometric identities appear in Mollweide's paper Zusätze zur ebenen und sphärischen Trigonometrie (1808). *SAU

1862 William Jackson Humphreys (3 Feb 1862; 10 Nov 1949) American atmospheric physicist who applied basic physical laws to explain the optical, electrical, acoustical, and thermal properties and phenomena of the atmosphere. His book, Physics of the Air (1920), covers most of classical physical meteorology.*TIS

1893 Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.*Wik A report of his bravery during WWI during which he lost his nose:
January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.
When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU

1898 Pavel Samuilovich Urysohn, Pavel Uryson (February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer) is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology. His name is also commemorated in the term Menger-Urysohn dimension and in the term Urysohn integral equation. The modern definition of compactness was given by him and Pavel Alexandrov in 1923.*Wik

1905 Arne Carl-August Beurling (February 3, 1905 – November 20, 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey.
Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany in World War II for sending ciphered messages.[1] The T52 was one of the so-called "Fish cyphers", that using, transposition, created nearly one quintillion (893 622 318 929 520 960) different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Not wanting to reveal how this knowledge was attained the Swedish warning was not treated as credible by Soviets. *Wik

1951 Steven George Krantz (3 February 1951 San Francisco, California - ) is an American scholar, mathematician, and writer at Washington University in St. Louis. He has also taught at UCLA, Princeton, and Penn State. He is Editor-in-Chief of the Notices of the American Mathematical Society for the period (2010–2015). Krantz is also Editor-in-Chief of the Journal of Mathematical Analysis and Applications and Managing Editor and founder of the Journal of Geometric Analysis. He also edits for The American Mathematical Monthly, Complex Variables and Elliptic Equations, and The Bulletin of the American Mathematical Society.
Professor Krantz is author of many textbooks and popular books. His books Mathematical Apocrypha and Mathematical Apocrypha Redux are collections of anecdotes about famous mathematicians. Krantz's book An Episodic History of Mathematics: Mathematical Culture through Problem Solving is a blend of history and problem solving. A Mathematician's Survival Guide and The Survival of a Mathematician are about how to get into the mathematics profession and how to survive in the mathematics profession. Krantz's new book with Harold R. Parks entitled Mathematics: From Fascination to Insight is an entree to mathematics for the layman. *Wik

1737 Thommaso Ceva (20 Dec 1648; 3 Feb 1737) Italian mathematician, poet, and brother of the mathematician Giovanni Ceva. At the age of fifteen he entered the Society of Jesus. His education was entirely within the Jesuit Order and he obtained a degree in theology. His first scientific work, De natura gravium (1669), dealt with physical subjects, such as gravity and free fall, in a philosophical way. Tommaso Ceva's mathematical work is summed up in Opuscula Mathematica (1699) which examines geometry (geometric-harmonic means, the cycloid, and conic sections), gravity and arithmetic. He also designed an instrument to divide a right angle into a given number of equal parts. He gave the greater part of his time to writing Latin prose. His poem Jesus Puer was translated into many languages. *TIS

1862 Jean-Baptiste Biot (21 Apr 1774, 3 Feb 1862) French mathematician and physicist who co-developed the Biot-Savart law, that the intensity of the magnetic field produced by current flow through a wire varies inversely with the distance from the wire. He did work in astronomy, elasticity, heat, optics, electricity and magnetism. In pure mathematics, he contibuted to geometry. In 1804 he made a 13,000-feet (5-km) high hot-air balloon ascent with Joseph Gay-Lussac to investigate the atmosphere. In 1806, he accompanied Arago to Spain to complete earlier work there to measure of the arc of the meridian. Biot discovered optical activity in 1815, the ability of a substance to rotate the plane of polarization of light, which laid the basis for saccharimetry, a useful technique of analyzing sugar solutions.*TIS

1919 Edward Charles Pickering, (19 Jul 1846, 3 Feb 1919) U.S. physicist and astronomer. After graduating from Harvard, he taught physics for ten years at MIT where he built the first instructional physics laboratory in the United States. At age 30, he directed the Harvard College Observatory for 42 years. His observations were assisted by a staff of women, including Annie Jump Cannon. He introduced the use of the meridian photometer to measure the magnitude of stars, and established the Harvard Photometry (1884), the first great photometric catalog. By establishing a station in Peru (1891) to make the southern photographs, he published the first all-sky photographic map (1903).*TIS

1923 Adam Wilhelm Siegmund Günther (6 Feb 1848 in Nuremberg, Germany - 3 Feb 1923 in Munich, Germany) Günther's contributions to mathematics include a treatise on the theory of determinants (1875), hyperbolic functions (1881), and the parabolic logarithm and parabolic trigonometry (1882). He also wrote numerous books and journal articles [which] encompass both pure mathematics and its history and physics physics, geophysics, meteorology, geography, and astronomy. The individual works on the history of science, worth reading even today, bear witness to a thorough study, a remarkable knowledge of the relevant secondary literature, and a superior descriptive ability. *SAU

1925 Oliver Heaviside (18 May 1850, 3 Feb 1925) English physicist who predicted the existence of the ionosphere. In 1870, he became a telegrapher, but increasing deafness forced him to retire in 1874. He then devoted himself to investigations of electricity. In 1902, Heaviside and Kennelly predicted that there should be an ionised layer in the upper atmosphere that would reflect radio waves. They pointed out that it would be useful for long distance communication, allowing radio signals to travel to distant parts of the earth by bouncing off the underside of this layer. The existence of the layer, now known as the Heaviside layer or the ionosphere, was demonstrated in the 1920s, when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received. *TIS He adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations (later found to be equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of mathematics and science for years to come. Among many others, he coined the terms for admittance , conductance , impedance , permeability , and inductance. *Wik

1929 Agner Krarup Erlang (January 1, 1878 – February 3, 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory.*Wik

1956 (Félix-Édouard-Justin-) Émile Borel (7 Jan 1871; 3 Feb 1956) was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory. In one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library). This is now popularly known as the infinite monkey theorem. He was first to develop (1899) a systematic theory for a divergent series. He also published (1921-27) a number of research papers on game theory and became the first to define games of strategy. *TIS . “In Paris as a scholarship student preparing for the university, he entered the family circle of G. Darboux through friendship with his son, saw the “good life” of a leading mathematician, and set his heart on it.” *VFR [It began with Jonathon Swift and Gulliver's Travels, 1872, according to Professor Barrow. In the tale "a mythical professor of the Grand Academy of Lagado who aims to generate a catalogue of all scientific knowledge by having his students continuously generate random strings of letters..." (I think, see emphasis in the excerpt below, that it was random strings of words).. Anyway, according to the good Professor Barrow, the story was embellished in different forms until French Mathematician Emile Borel{there is a street and a square named for him in the 17th District in Paris} suggested that random typing monkeys could duplicate the French national library.] *Pballew, Typing Monkeys

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

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