**The science of pure mathematics may claim to be the most original creation of the human spirit.**

~A N Whitehead

The 346th day of the year; 346 is a Smith number. The sum of its digits equals the sum of the digits of its prime factors. 346 = 2 x 173 and 3+4+6 = 2+1+7+3. One more such number for a day this year. (Smith numbers were named by Albert Wilansky who noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith.) There is only one more year day that is a Smith Number.

346 is also the fourth Franel number, the sum of the cubes of the terms in the nth row of the arithmetic triangle. \( 346 = 1^3 + 4^3 + 6^3 + 4^3 + 1^3\) The numbers are named for Swiss Mathematician Jérôme Franel (1859–1939).

**EVENTS**

**1859 ** "Karl Weierstrass (1815-1897) used | | in an 1841 essay "Zur Theorie der Potenzreihen," in which the symbol appears on page 67. He also used the symbol in 1859 in "Neuer Beweis des Fundamentalsatzes der Algebra," in which the symbol appears on page 252. This latter essay was submitted to the Berlin Academy of Sciences on December 12, 1859." *Jeff Miller, Earliest Uses of Function Symbols

**1871**, spectroscopic observations of an eclipse in India made by French astronomer Jules Janssen led him to propose that the corona, normally only visible during a solar eclipse, is a physical part of the Sun and is composed of both hot gases and cooler particles.*TIS

His December 19 letter to Lassell describing his observation is here

**1885** In the midst of his inaugural lecture at Oxford, Sylvester “refreshed” the audience with his sonnet “To a missing member of a family group of terms in an algebraical formula.” [Osiris, 1(1936), 109; Nature 33, 7 Jan 1886, p. 228; Collected Mathematical Papers, vol. 4, p. 293] *VFR

**In 1901,** At Signal Hill, Newfoundland, Guglielmo Marconi and his assistant, George Kemp, confirmed the reception of the first transatlantic radio signals. With a telephone receiver and a wire antenna kept aloft by a kite, they heard Morse code for the letter "S" transmitted from Poldhu, Cornwall. Their experiments showed that radio signals extended far beyond the horizon, giving radio a new global dimension for communication in the twentieth century. *ethw.org

**1955** English engineer Christopher Cockerell filed the patent for his new invention, the hovercraft, a craft capable of traveling over land, water, mud or ice and other surfaces both at speed and when stationary. *Yovisto

The first mention in the historical record of the concepts behind surface-effect vehicles that used the term hovering was by Swedish scientist Emanuel Swedenborg in 1716. In the 1930-45 period several designs were implemented in different countries but classified. Even Cockerell's model was at first classified, but when declassified, he applied for a patent.

**1980** Apple’s initial public offering was the largest IPO since the Ford Motor went public in 1956. Nonetheless, it sold out in minutes. Originally priced to sell at \($14\) a share, the stock opened at \($22\)and all 4.6 million shares were sold almost immediately. The stock rose almost 32% that day to close at \($29\), giving the company a market evaluation of \($1.778 \)billions. The three founders of Apple Computer, Steve Jobs, Steve Wozniak and Mike Markkula weren’t only ones who did well that day. More than 40 of Apple’s 1,000 employees became instant millionaires thanks to the stock options.*CHM

**1980**, Leonardo daVinci's 36-sheet manuscript Codex Leicester was auctioned at Christie's. It was bought by Armand Hammer for $4.5 million. At the time, it was the highest price paid for a complete manuscript. (It has subsequently been resold). The Codex Leicester, written 1506-10, embraces a wide variety of topics, from astronomy to hydrodynamics, and includes Leonardo's observations and theories related to rivers and seas; the properties of water; rocks and fossils; air; and celestial light. All of this is expressed in his signature mirror writing, as well as in more than 300 pen-and-ink sketches, drawings, and diagrams, many of them illustrating imagined or real experiments.*TIS

**BIRTHS**

**1731 Erasmus Darwin **(12 Dec 1731; 18 Apr 1802) Prominent English physician , poet , philosopher, botanist, naturalist and the grandfather of naturalist Charles Darwin and the biologist Francis Galton. Erasmus Darwin was one of the leading intellectuals of 18th century England. As a naturalist, he formulated one of the first formal theories on evolution in Zoonomia, or, The Laws of Organic Life (1794-1796). Although he did not come up with natural selection, he did discuss ideas that his grandson elaborated on sixty years later, such as how life evolved from a single common ancestor, forming "one living filament". Although some of his ideas on how evolution might occur are quite close to those of Lamarck, Erasmus Darwin also talked about how competition and sexual selection could cause changes in species. *TIS

**1803 James Challis** (12 Dec 1803; 3 Dec 1882) British clergyman and astronomer, famous in the history of astronomy for his failure to discover the planet Neptune. Astronomer and mathematician John Couch Adams had studied the known deviations in the orbit of the planet Uranus which indicated a planet even further out. In 1845, Adams gave Astronomer Royal George Airy a calculated orbital path for the unknown planet. But Airy was more interested in the primary job of navigation and timekeeping observations. Airy informed Challis, who did not begin until July 1846, and actually sighted the new planet four times without recognising it. On 23 Sep 1845, the new planet was instead discovered from Berlin Observatory. Challis admitted that Adam's prediction was within 2° of the planet's position. *TIS

**1832 Peter Ludwig Mejdell Sylow **(12 Dec 1832 in Christiania (now Oslo), Norway - 7 Sept 1918 in Christiania (now Oslo), Norway) In his paper Théorèmes sur les groupes de substitutions which Sylow published in Mathematische Annalen Volume 5 (pages 584 to 594) appear the three Sylow theorems. Cauchy had already proved that a group whose order is divisible by a prime p has an element of order p. Sylow proved what is perhaps the most profound result in the theory of finite groups.

If p^{n} is the largest power of the prime p to divide the order of a group G then:

G has subgroups of order p^{n},

G has 1 + kp such subgroups,

any two such subgroups are conjugate.

Almost all work on finite groups uses Sylow's theorems.

Sylow became an editor of Acta Mathematica and, in 1894, he was awarded an honorary doctorate from the university of Copenhagen.

Lie had a special chair created for Sylow at Christiania University and Sylow taught at the university from 1898. *SAU

**1866 Kazimierz Ajdukiewicz** (12 Dec 1890; 12 Apr 1963) Polish logician and semanticist who was the chief contributor to the Warsaw school of philosophy and logic. He is credited with developing in 1920 the first deductive theory for the study of logic based on syntax. The dominant theme of Ajdukiewicz's thought was the problem of the dependence of our knowledge and conception of knowledge on language. His main contributions are in the field of logical syntax (with the theory of semantical categories) and in epistemology, with the so-called "radical conventionalism", a doctrine where he claimed that there exist conceptual apparatuses which are not intertranslatable and that scientific knowledge grows through the replacement of one such conceptual apparatus by another.*TIS

**1927 Robert (Norton) Noyce** (12 Dec 1927; Jun 1990) was a U.S. engineer and coinventor (1959), with Jack Kilby, of the integrated circuit, a system of interconnected transistors on a single silicon microchip. He held sixteen patents for semiconductor devices, methods, and structures. In 1968, he and colleague Gordon E. Moore cofounded N.M. Electronics, which later was renamed Intel Corporation. Noyce served as Intel's president and chairman (1968-75), then as vice chairman until 1979. *TIS

**1939 Michael Gazzaniga **(12 Dec 1939, )American cognitive neuroscientist and author who studies how the brain enables humans to perform those advanced mental functions that are generally associated with what we call the mind. In over four decades of split-brain research he has advanced understanding of how the brain works, by revealing the separate and highly specialized functions and abilities of each hemisphere. Gazzaniga has focused on how the brain facilitates such higher cognitive functions as remembering, speaking, interpreting, and making judgments. His most recent research uses three-dimensional magnetic resonance images of the brain's surface to compare normal brains with, for example, those having a mental disorders such as schizophrenia. *TIS

**DEATHS**

**1685 John Pell **(1 March 1611 in Southwick, Sussex, England - 12 Dec 1685 in Westminster, London, England) Malcolm wrote, "The mathematician John Pell is a significant figure in the intellectual history of 17th century England - significant, however, more because of his activities, contacts and correspondence than because of his published work. His few publications are, nevertheless, valuable sources of information about his intellectual biography.

Pell worked on algebra and number theory. He gave a table of factors of all integers up to 100000 in 1668. Pell's equation y^{2} = ax^{2} + 1, where a is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation. *SAU

He introduced the division sign (obelus, ÷) into England. The obelus was first used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra. Rahn's book was interpreted into English and published, with additions made by John Pell. According to some sources, John Pell was a key influence on Rahn and he may be responsible for the development of the symbol. The word obelus comes from a Greek word meaning a "roasting spit." The symbol wasn't new. It had been used to mark passages in writings that were considered dubious, corrupt or spurious.*TIS

**1889 Viktor Bunyakovsky** (16 Dec 1804 in Bar, Podolskaya gubernia (now Vinnitsa oblast), Ukraine - 12 Dec 1889 in St Petersburg, Russia) worked on Number Theory as well as geometry, mechanics and hydrostatics. He discovered the Cauchy-Schwarz inequality 25 years before Cauchy or Schwarz.*SAU

**1919 Paul Gustav Samuel Stäckel **(20 August 1862 — 12 December 1919) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime for the first time.*Wik

**1921 Henrietta Swan Leavitt** (4 Jul 1868, 12 Dec 1921) American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies. *TIS

**1965 Tibor Radó** (June 2, 1895 – December 12, 1965) was a Hungarian mathematician who moved to the USA after World War I. He was born in Budapest and between 1913 and 1915 attended the Polytechnic Institute. In World War I, he became a First Lieutenant in the Hungarian Army and was captured on the Russian Front. He escaped from a Siberian prisoner camp and, traveling thousands of miles across Arctic wasteland, managed to return to Hungary.

He received a doctorate from the University of Szeged in 1923. He taught briefly at the university and then became a research fellow in Germany for the Rockefeller Foundation. In 1929, he moved to the United States and lectured at Harvard University and the Rice Institute before obtaining a faculty position in the Department of Mathematics at Ohio State University in 1930. In 1935 he was granted American citizenship.

In the 1920s, he proved that surfaces have an essentially unique triangulation.

In 1933, Radó published "On the Problem of Plateau" in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions".

In World War II he was science consultant to the United States government, interrupting his academic career.

He became Chairman of the Department of Mathematics at Ohio State University in 1948.

His work focused on computer science in the last decade of his life and in May 1962 he published one of his most famous results in the Bell System Technical Journal: the Busy Beaver function and its non-computability ("On Non-Computable Functions").

In computability theory, a busy beaver (from the colloquial expression for an "industrious person") is a Turing machine that attains the maximum "operational busyness" (such as measured by the number of steps performed, or the number of nonblank symbols finally on the tape) among all the Turing machines in a certain class. The Turing machines in this class must meet certain design specifications and are required to eventually halt after being started with a blank tape. *Wik (*another source gives his death as Dec 29th of the same year??*)

**1977 Arthur Erdélyi **(2 Oct 1908 in Budapest, Hungary - 12 Dec 1977 in Edinburgh, Scotland) studied in Brno and Prague and came to Scotland before the Second World War to avoid the Nazi invasion of Czechoslovakia. He became a lecturer at Edinburgh and after a period in the USA he returned to Edinburgh as a Professor. He was an expert on Special Functions. He became President of the EMS in 1971. *SAU

**1994 Nicolaas Hendrik "Nico" Kuiper** (Dutch pronunciation: [kœypəʁ]; 28 June 1920, Rotterdam - 12 December 1994, Utrecht) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.

Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.

He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985. *Wik

**2014 Ivor Owen Grattan-Guinness **(23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics.

He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission for the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. In 2010, he was elected an Honorary Member of the Bertrand Russell Society.

He spent much of his career at Middlesex University. He was a fellow at the Institute for Advanced Study in Princeton, New Jersey, and is a member of the Académie Internationale d'Histoire des Sciences. *Wik

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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