The Knot gate at Cambridge Math Dept |

**…separation of the observer from the phenomenon to be observed is no longer possible.**

~Werner Heisenberg

The 340th day of the year; 340 is the sum of the first four powers of four.

340 can also be written as the sum of consecutive primes in three different ways.

340! +1 is prime. There are only thirteen day numbers of the year for which n! +1 is prime, and 340 is the last of these.

Jim Wilder@wilderlab pointed out that 340 = 4

^{1}+ 4

^{2}+ 4

^{3}+ 4

^{4}. Just think, tomorrow will be even a longer string of consecutive powers of four!

**EVENTS**

**1610**Benedetto Castelli, a former student of Galileo, wrote him, that if Copernicus was correct, Venus should sometimes appear “horned” and sometimes not. *VFR (Venus is at its brightest as it approaches Earth, when it appears as a crescent. Many cultures around the world describe it as the 'horned star', which suggests that early astronomers, although lacking telescopes, could somehow make out its crescent shape.)

Castelli wrote to Galileo

If the position of Copernicus, that Venus revolves around the sun, is true (as I believe), it is clear that it would necessarily sometimes be seen by us horned and sometimes not, even though the planet maintains the same position relative to the sun. ... Now I want to know from you if you, with the help of your marvellous glasses, have observed such a phenomenon, which will be, beyond doubt, a sure means to convince even the most obstinate mind. I also suspect a similar thing with Mars near the quadrature with the sun; I don't mean a horned or non-horned shape, but only a semicircular and a more full one.It is now impossible to prove whether this idea occurred to both Galileo and Castelli at the same time, or whether this letter of Castelli made Galileo turn his telescope on Venus to see if it showed phases. Certainly by 11 December Galileo had discovered that Venus did indeed appear as a crescent for on that day he wrote to Giuliano d'Medici expressing the discovery in code. It is of little consequence which scenario is correct, for in either case Castelli came up with one of the most important ideas of the time. *SAU

**1658**Simon Douw wins court judgement against Christian Huygen.

“Today, no clock by Simon Douw is known; I find that most curious, it is as if he has been excised from history, deliberately. Dutch Court papers described Douw as "City clockmaker of Rotterdam... a master in the art of great tower, domestic or office clocks", ("en meester in de kunst van groote Toorn, Camer ofte Comptoirwerken"). Yet his mechanical insights. his escapement, also his drive mechanisms, are best, and now only, revealed by his Patent Grant on* Keith Piggottm, antique Horology

August 9th, 1658, and by the evidence and judgement in a claim and counterclaim

started in the Provinces of Holland and West Friesland, but then

referred to the Court of The Netherlands in October 1658, with a Judgement

by Consent on December 5th, 1658. And that case went entirely in Douw's

favour, against the highly favoured joint Complainants Huygens and Coster.

In itself, that is remarkable. Huygens, the Noble patrician, the most famous

Dutch scientist, and the self-professed inventor of the pendulum clock, who

had in the course of this trial published "Horologium", was forced by the

judges to settle the case rather than face unfavourable verdict; also to concede

Consent; also one-third Royalties to Douw. It would have been a crushing

humiliation for Huygens, the seed of his libels. Subsequently, the Lower

Court of Holland, Zeeland and Friesland confirmed to Douw, on December

16th and 19th 1658, their Upper Court's judgement by consent”.

**1735**Euler presents his paper on “The sums of Series of reciprocals” to the St Petersburg Academy. Regarding the series 1+1/4 + 1/9 …. he writes, “I have shown the sum of the series to be approximately 1.644934066842264364 (“Euler calculates as other men breath”); multiplying the number by six, and then taking the square root.. “ and he shows that it is equal to pi, again expressed to nineteen digits accuracy. He then found the sum of the series of powers of the harmonic sequence for n= 4,6,8, 10 and 12

**1776**The ﬁrst scholastic fraternity in America, Phi Beta Kappa, was organized at William and Mary College in Virginia. *VFR

**1825**Abel wrote how delighted he was that Crelle was starting a new mathematics journal, for it meant he would now have a place to publish his researches. The ﬁrst volume contained seven papers by Abel*VFR

**1851**J. J. Sylvester Receives a letter from Arthur Cayley that "amounted to a birth certificate" of their theory of invariants. Giving a relationship between invariants and differential equations, Cayley states that "This will constitute the foundation of a new theory of invariants." *Karen Hunger Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World

**1883**Sylvester, in Baltimore, received a cable containing the single word “Elected,” informing him of his appointment as Savilian Professor of Geometry at Oxford. This ended his seven year stay at Johns Hopkins. *Osiris, 1(1936), 150

**1890**Harold Jacoby, later head of the Department of Astronomy at Columbia University, proposed at a meeting of the New York Mathematical Society that they publish a bulletin. In October 1891, the ﬁrst issue of the Bulletin of the New York Mathematical Society, A Historical and Critical Review of Mathematical Science appeared. *VFR

**1979**Iran issued a stamp commemorating the 600th anniversary of the death of the mathematician Ghyath-al-din Jamshid Kashani. He is pictured with an astrolabe in the background.*VFR

**1941**Zuse Completes Z3 Machine: Konrad Zuse completes his Z3 computer, the first program-controlled electromechanical digital computer. It followed in the footsteps of the Z1 - the world’s first binary digital computer - which Zuse had developed in 1938. Much of Zuse’s work was destroyed in World War II, although the Z4, the most sophisticated of his creations, survives. *CHM Thony C. at The Renaissance Mathematicus has a nice post about Zuse and Computing

**1965**The First Ph.D. Dissertation in Computer Science is Presented;

Richard L.Wexelblat was the first candidate in a computer science program to complete a dissertation. Many doctorate candidates had performed computer-related work, but Wexelblat’s diploma, presented by the University of Pennsylvania - the home of the ENIAC - was the first one to carry the designation computer science.*CHM

**2012**The Atlas computer was developed at Manchester, and the first production version of the machine ran almost 50 years ago, on 7 December 1962.

At the time of that switch-on, the Atlas was believed to be the most powerful machine in the world.

On 4 and 5 December, scientists and engineers who created Atlas as well as former students who learned to code on the machine will attend events to commemorate the achievement at Manchester's Museum of Science and Industry. *BBC

**BIRTHS**

**1863 Paul Painlevé**(5 Dec 1863; 29 Oct 1933) French politician, mathematician, and patron of aviation. Painlevé received a doctorate in mathematics from Paris in 1887. In his work on differential equations and mechanics, he solved, using Painlevé functions, differential equations which Poincaré and Picard had failed to solve. He took a special interest in aviation, applying his theoretical skills to study the theory of flight. He was Wilbur Wright's first passenger making a record 1 hr 10 min flight, then within a year he created the first university course in aeronautical mechanics. Although less skilled in politics than mathematics he began a political career in 1906 leading to two periods as French Prime Minister at a crucial period of World War I and again during the 1925 financial crisis. *TIS

**1868 Arnold Johannes Wilhelm Sommerfeld**(5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics. He was nominated a record 81 times for the Nobel Prize, and served as PhD supervisor for more Nobel prize winners in physics than any other supervisor before or since. He introduced the 2nd quantum number (azimuthal quantum number) and the 4th quantum number (spin quantum number). He also introduced the fine-structure constant, and pioneered X-ray wave theory.*Wik

**1895 Elbert Frank Cox**(December 5, 1895–November 28, 1969) was an American mathematician who became the first black person in the world to receive a Ph.D. in mathematics. He spent most of his life as a professor at Howard University in Washington, D.C., where he was known as an excellent teacher. During his life, he overcame various difficulties which arose because of his race. In his honor, the National Association of Mathematicians established the Cox-Talbot Address, which is annually delivered at the NAM's national meetings. The Elbert F. Cox Scholarship Fund, which is used to help black students pursue studies, is named in his honor as well.*Wik

**1901 Werner Karl Heisenberg**(5 Dec 1901; 1 Feb 1976) was the German physicist and philosopher who discovered a way to formulate quantum mechanics in terms of matrices (1925). For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his indeterminacy, or uncertainty, principle, upon which he built his philosophy and for which he is best known. He also made important contributions to the theories of the hydrodynamics of turbulence, the atomic nucleus, ferromagnetism, cosmic rays, and elementary particles, and he planned the first post-World War II German nuclear reactor, at Karlsruhe, then in West Germany. *TIS

**1903 Cecil Frank Powell**(5 Dec 1903; 9 Aug 1969) British physicist and winner of the Nobel Prize for Physics in 1950 for his development of the photographic method of studying nuclear processes and for the resulting discovery of the pion (pi-meson), a heavy subatomic particle. The pion proved to be the hypothetical particle proposed in 1935 by Yukawa Hideki of Japan in his theory. *TIS

**1932 Sheldon Lee Glashow**(5 Dec 1932, ) American theoretical physicist who, with Steven Weinberg and Abdus Salam, received the Nobel Prize for Physics in 1979 for their complementary efforts in formulating the electroweak theory, which explains the unity of electromagnetism and the weak force.*TIS

**1943 Robin James Wilson**(5 December, 1943 - ) is an emeritus professor in the Department of Mathematics at the Open University, having previously been Head of the Pure Mathematics Department and Dean of the Faculty. He was a Stipendiary Lecturer at Pembroke College, Oxford and, as of 2006, Professor of Geometry at Gresham College, London, where he has also been a visiting professor. On occasion, he guest teaches at Colorado College.

From January 1999 to September 2003, Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.[4]

He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He is married with two daughters.

Professor Wilson's academic interests lie in graph theory, particularly in colouring problems, e.g. the four colour problem, and algebraic properties of graphs.

He also researches the history of mathematics, particularly British mathematics and mathematics in the 17th century and the period 1860 to 1940 and the history of graph theory and combinatorics.

Due to his collaboration on a 1977 paper[6] with the noted Hungarian mathematician Paul Erdős, Wilson has an Erdős number of 1. *Wik

**DEATHS**

**1708 Takakazu Seki Kawa**(1642 in Fujioka, Kozuke, Japan

- 5 Dec 1708 in Edo (now Tokyo), Japan) a Japanese mathematician in the Edo period.

Seki laid foundations for the subsequent development of Japanese mathematics known as wasan; and he has been described as "Japan's Newton".

He created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. A contemporary of Gottfried Leibniz and Isaac Newton, Seki's work was independent. His successors later developed a school dominant in Japanese mathematics until the end of the Edo period.

While it is not clear how much of the achievements of wasan are Seki's, since many of them appear only in writings of his pupils, some of the results parallel or anticipate those discovered in Europe. For example, he is credited with the discovery of Bernoulli numbers. The resultant and determinant (the first in 1683, the complete version no later than 1710) are attributed to him. This work was a substantial advance on, for example, the comprehensive introduction of 13th-century Chinese algebra made as late as 1671, by Kazuyuki Sawaguchi. *Wik

**1770 James Stirling**(1692, 5 Dec 1770) Scottish mathematician who contributed important advances to the theory of infinite series and infinitesimal calculus. His most important book, Methodus Differentialis (1730), was written while in London. It is a treatise on infinite series, summation, interpolation and quadrature, and the text includes the asymptotic formula for n! for which Stirling is best known. In 1735 he returned to Scotland where he became manager of the 'Scotch mining company, Leadhills'. In 1745 Stirling published a paper on the ventilation of mine shafts. *TIS

**1859 Louis Poinsot**was the inventor of geometrical mechanics, investigating how a system of forces acting on a rigid body could be resolved into a single force and a couple.*SAU

**1973 Sir Robert Alexander Watson-Watt**(13 Apr 1892, 5 Dec 1973) Scottish physicist who is credited with the development of radar location of aircraft, in England. He studied at St Andrews University, taught at Dundee University, and in 1917 worked in the Meteorological Office, designing devices to locate thunderstorms, and investigating the ionosphere (a term he invented in 1926). He became head of the radio section of the National Physical Laboratory (1935), where he began work on locating aircraft. His work led to the development of radar (RAdio Detection And Ranging) which played a vital role in the defence of Britain against German air raids in 1940. He was knighted in 1942. *TIS

**1999 Nathan Jacobson**(October 5, 1910, Warsaw, Congress Poland, Russian Empire — December 5, 1999, Hamden, Connecticut) was an American mathematician.

Born in Warsaw, Jacobson emigrated to America with his Jewish family in 1918. Recognized as one of the leading algebraists of his generation, he was also famous for writing more than a dozen standard textbooks. *Wik

**2001 Franco Dino Rasetti**(August 10, 1901 – December 5, 2001) was an Italian scientist. Together with Enrico Fermi, he discovered key processes leading to nuclear fission. Rasetti refused to work on the Manhattan Project, however, on moral grounds.*Wik

**2005 Claude Ambrose Rogers**(1 Nov 1920, 5 Dec 2005) wrote extensively on Number Theory and on Sphere-packing problems.Roger's continues to produce a remarkable mathematical output having published to date over 170 papers. His early work was on number theory and he wrote on Diophantine inequalities and the geometry of numbers. Jointly with Erdős, he wrote The covering of n-dimensional space by spheres (1953) and Covering space with convex bodies (1961), writing many other articles on coverings and packings including Covering space with equal spheres with Coxeter. His later work covered a wide range of different topics in geometry and analysis including Borel functions, Hausdorff measure and local measure, topological properties of Banach spaces and upper semicontinuous functions. Rogers has written two important books, Packing and Covering in 1964 and Hausdorff Measures in 1970. *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

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