Thursday, 4 August 2011

On This Day in Math - Aug 4


Accurate reckoning: the entrance into knowledge of all existing things and all obscure secrets.
Ahmes the Scribe, Quoted in A B Chase, Rhind Mathematical Papyrus (Reston Va. 1967)

The 216th day of the year; Since 216 = 33 + 43 + 53 = 63, it is the smallest cube that's also the sum of three cubes (Plato was among the first to notice this, and mentioned it in Book VIII of Republic). (Quick, what is the next cube that is the sum of three cubes?... and how can you be sure there will never be a day that is a cube that is the sum of two cubes?) It is also the sum of a twin prime (107 + 109).

EVENTS
In 1181, supernova seen in Cassiopia. First observed between August 4 and August 6, 1181, Chinese and Japanese astronomers recorded the supernova now known as SN 1181 in eight separate texts. One of only eight supernovae in the Milky Way observable with the naked eye in recorded history, it appeared in the constellation Cassiopeia and was visible in the night sky for about 185 days.*Wik

In 1693, champagne was invented by Dom Perignon.*(I'll drink to that.)

1597 Galileo wrote Kepler thanking him for the copy of Kepler’s Mysterium cosmographicum, which openly advocated the Copernican theory. Galileo admits he is also a Copernican. See 13 October 1597. *VFR  Thanks to The Renaissance Mathematicus, for pointing out that when he received this letter, Kepler had never heard of Galileo.  See more detail of this interesting story here.

1753 Euler, in a letter to Christian Goldbach, claimed that he had a proof of Fermat’s Last Theorem for the case n = 3. He gave no proof in that letter and none was published until 1770 when he published his Elements of Algebra in Russian.*VFR Euler's proof was wrong, but other methods that Euler developed can be used to provide a correct proof. You can see Euler's incorrect proof, with an explanation by Graeme McRae.

1810 Gauss married his second wife, Minna Waldeck, who bore him two sons and a daughter. *VFR Sons Chales and Eugene both emigrated to America and died in Missouri. Therese died in Dresden. An interesting story about Eugene and his relations with his father and history in America is told here which I believe is the work of a Kevin Brown.

1922 In 1922, every telephone in North America was silent for one minute at sunset marking the time funeral services were taking place for Alexander Graham Bell. He was laid to rest in a tomb blasted in the solid rock at the peak of Beinn Bhreagh Mountain on his estate in Nova Scotia, Canada. A watch tower had been built there years earlier by the inventor. His coffin was made in the inventor's own workshop by his laboratory staff. In a memory of the famous inventor, all the switchboards and switching stations of AT&T and the Bell System in the U.S. and Canada suspended service to the 13 million telephones then installed. Bell had died two days earlier on 2 Aug 1922. *TIS

BIRTHS
1755 Nicolas-Jacques Conté French inventor who devised a method of manufacturing pencil leads by mixing a finely powdered graphite with finely ground clay particles, baked, and used encased in wood. His innovation was prompted when imported plumbago supplies were disrupted by war. He was the first to use graphite - and that is still used as the basis for making pencil leads today. Using different ratios of clay to graphite varies the hardness of the pencil lead. He was commissioned by Napoleon as chief of the balloon corps in Egypt, where he invented ways to improvise tools and machines necessary to provide bread, cloth, munitions, surgical instruments and engineers' tools. As a youth, he had worked as a portrait painter. He lost his left eye in a chemistry laboratory accident*TIS

1795 Gouverneur Emerson American physician, statistician and agriculturalist who prepared a series of tables of deaths and causes in Philadelphia, during thirty years from 1807. These showed, for example, the excessive mortality of males during childhood. He began practice in Philadelphia on 4 Aug 1820, where yellow fever broke out a few weeks later, with 73 deaths by that fall. Emerson recorded cases, dates, locations, and outcomes. He concluded no current medical treatments was especially effective. When smallpox reappeared there, with 325 deaths in 1824, Emerson drafted a bill for control measures. There were only 6 cases of smallpox in the city in 1825, and 3 in 1826. In retirement, he turned to peach culture, and studied phosphate and guano fertilizers.*TIS

1805 Sir William Rowan Hamilton (Many think the correct birthdate is August 3 but his gravestone has Aug 4. The confusion arises from the fact he was born very near midnight.) Irish mathematician in the fields of optics, geometrics, and classical mechanics. By age 12, Hamilton had already learned fourteen languages when he met the American, Zerah Colburn, who could perform amazing mental arithmetical feats, and they joined in competitions. It appears that losing to Colburn sparked Hamilton's interest in mathematics. At 15, he began studied the works of LaPlace and Newton so by age 17 had become the greatest living mathematician. He contributed to the development of optics, dynamics, and algebra. His invention of the calculus of quaternions enabled a three-dimensional algebra or geometry which provided a basis for the later development of quantum mechanics. *TIS
Hamilton describes his memory of the discovery of the Quaternions to his son,
          "Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, `Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: `No, I can only add and subtract them.  But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on `Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.''  *from Hamilton By Sir Robert Stawell Ball.

1834 John Venn born in Hull, England. He is best known for the diagrams that he presented in his Symbolic Logic (1881). Leibniz was the first to systematically use geometric diagrams to represent syllogisms, and Euler developed the ideas, but Venn gets the credit for his book popularized them. *VFR He was a fellow of Gonville and Caius and there is a stained glass window memorial there in the dining hall, which I had the pleasure of visiting with Professor Anthony Edwards.

1837 Birthdate of E. L. W. Maximilian Curtze, expert on medieval mathematical texts. His work was aided by his excellent knowledge of the current mathematical literature, unusual talent for languages, and skill in deciphering hard-to-read handwriting. *VFR

1893 Francis Dominic Murnaghan (1873–1976) was an Irish mathematician, former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics (Murnaghan and Birch–Murnaghan equations of state).*SAU

1909 Saunders MacLane, American algebraist, born. *VFR Saunders Mac Lane was an American mathematician who worked in cohomology and category theory, but who is best known for the algebra book he wrote with Garrett Birkhoff.*SAU

1912 Aleksandr Danilovic Aleksandrov "approached the differential geometry of surfaces [by extending the notion of objects studied], extending the class of regular convex surface with the class of all convex surface .... To solve concrete problems Aleksandrov had to replace the Gaussian geometry of regular surfaces with a more general theory. In the first place the intrinsic properties (ie, the properties appear as a result of measurements carried out surface) of an arbitrary convex surface has been studied, and methods to be found for verification of theorems on the connection between the real and external properties of convex surfaces. Aleksandrov constructed a theory of intrinsic geometry on the convex basis. Due to the depth of this theory, the importance of its applications and the breadth of his statement, Aleksandrov comes second only to Gauss in the history of the development of the theory of surfaces." *from Math.info

DEATHS
1812 Georg Klügel was a German mathematician who wrote a Dictionary of Mathematics.*SAU

1874 Ludwig Otto Hesse worked on the development of the theory algebraic functions and the theory of invariants. He is remembered particularly for introducing the Hessian determinant.*SAU

1900 (Jean-Joseph-) Étienne Lenoir was a Belgian inventor who devised the world's first commercially successful internal-combustion engine. He moved to Paris where his work with electro-plating led him to other electrical inventions, among them a railway telegraph. Lenoir patented his first engine in 1860. Looking much like a double-acting steam engine, it fired an uncompressed charge of air and illuminating gas with an ignition system of his own design. One of these engines powered a road vehicle in 1863; another ran a boat. Because of improved designs by Nikolaus Otto and other inventors, the Lenoir engine became obsolete and only about 500 Lenoir engines were built. The Lenoir engine wasn't efficient enough, and the inventor died poor. *TIS

1906 Joseph Tilly was a Belgian soldier who published works on non-Euclidean geometry.*SAU

1920 Karl Friedrich Wilhelm Rohn In 1884 Rohn was promoted to extraordinary professor at Leipzig, then in 1887 he became a full professor at Technische Hochschule in Dresden where he held the chair of descriptive geometry. Felix Klein lectured during his visit to the United States in Evanston between 28 August and 9 September 1893. During these lectures he spoke about various models of the Kummer surface. He said that Rohn's work on this topic was the most significant. One of Rohn's models for the Kummer surface uses the generating lines on a hyperboloid of one sheet. He then took four lines from each of the two sets of generators, shaded the alternate regions, and then glued a copy of the shaded regions to the original along the boundary. In this way he produced a closed surface without boundary having sixteen real nodal points. He published this construction in 1881 and gave more details in an 1887 paper. Burau writes : In these early writings he demonstrated his ability to work out connections between geometric and algebraic- analytic relations. In the following years, Rohn further developed these capacities and became an acknowledged master in all questions concerning the algebraic geometry of the real P2 and P3, where it is possible to overlook the different figures. This concerns forms of algebraic curves and surfaces up to degree four, linear and quadratic congruences, and complexes of lines in P3. Gifted with a strong spatial intuition, Rohn possessed outstanding ability to select geometric facts from algebraic relations.
His love of geometry is also illustrated by his beautiful thread models which were especially produced to excite the curiosity of the uninitiated. Rohn constructed models of surfaces and space curves that he was studying, particularly in the early part of his career. In 1884 the Jablonowski Society proposed as prize problem asking for essays on the general surface of order 4, extending the work of Schläfli, Klein and Zeuthen on cubic surfaces; they awarded the prize to Rohn for his essay in 1886. He made important contributions to the theory of quartic surfaces, in particular of ruled quartics and quartics with a triple point. He also showed that the maximum number of separated ovals possible for a quartic surface is ten. He published Die Flächen vierter Ordnung hinsichtlich ihrer Knotenpunkte und ihrer Gestaltung: Gekrönte Preisschrift (1886). Rohn was made rector of the Technical University of Dresden during 1900-01. As rector he gave a speech on 23 April 1900 to celebrate the birthday of His Majesty the King. His speech was entitled Die Entwickelung der Raumanschauung im Unterricht and it was published by the Technical University of Dresden in 1900. In Dresden, Rohn gave the course 'Darstellende Geometrie' in the summer of 1904. It was the last session that he lectured at Dresden for in the following year he was appointed to the University of Leipzig. From 1 April 1905 until his death, Rohn held the chair of mathematics at the University of Leipzig. *SAU

1945 Gerhard Gentzen invented a 'natural deduction' which provided a logic closer to mathematical reasoning than the systems proposed by Frege, Russell and Hilbert.*SAU

2009 Professor James "Jim" Wiegold (15 April 1934 – 4 August 2009) was a Welsh mathematician. He earned a PhD at the University of Manchester in 1958, studying under Bernhard Neumann, and is most notable for his contributions to group theory.*Wik

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
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