**The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before.**

~Freeman Dyson

The 350th day of the year; 350 is S(7,4), a Stirling Number of the second kind.

350

^{2}+1 = 122,501 is prime. The last day of the year for which n

^{2}+ 1 is prime.

Lucky Sevens, 350 = 7

^{3}+ 7

Both 350 and 351 are the product of four primes. 350 = 2x5x5x7 and 351 = 3x3x3x13. They are the third, and last pair of consecutive year days that are the product of four primes. (Don't just sit there, find the others!")

**EVENTS**

1610 Father Christoph Clavius SJ writes Galileo to ask about why his large aperture was partly covered; Galileo would answer on the 30th that he did this for two reasons:

The first is to make it possible to work it more accurately because a large surface is

more easily kept in the proper shape than a smaller one. The other reason is that if

one wants to see a larger space in one glance, the glass can be uncovered, but it is then

necessary to put a less acute glass near the eye and shorten the tube, otherwise the

objects will appear very fuzzy. *Aalbert Vvan Helden, Galileo and the Telescope; Origins of the Telescope - Royal Netherlands Academy of Arts and Sciences, 2010

**In 1612**, Simon Marius, namer of Jupiter's 4 inner satellites, is first to observe Andromeda galaxy through a telescope. He described it in the preface to his Mundus Jovialis as, 'like the flame of a candle seen through horn'. Marius vrs Galileo is well covered in this blog at the Renaissance Mathematicus .

**1693**The House of Commons established the British National Debt by issuing one-million GBP of annuities. *Against the Gods: The Remarkable Story of Risk By Peter L. Bernstein

**1742**Euler gave the ﬁrst clear statement of the fundamental theorem of algebra: every algebraic equation of degree n has exactly n complex roots. Imprecise statements of the result were given earlier by Peter Rothe (1608) and Albert Girard (1629). Incorrect proofs were given by d’Alembert (1746), Euler (1749), Foncenex (1759), Lagrange (1772) and Laplace (1795), but a correct proof (and the name) had to await Gauss’s doctoral dissertation of 1799, who discovered it in the fall of 1797 when he was 20. * E. Smith, Source Book, p. 292

**1859**Gustav R. Kirchhoff distillated from the sun spectra which elements are present in the sun. *SOLAR ECLIPSE NEWSLETTER

**1887**Nature quotes J. J. Sylvester: “Perhaps I may, without immodesty, lay claim to the appellation of the mathematical Adam, as I believe that I have given more names (passed into general circulation) to the creatures of the mathematical reason than all the other mathematicians of the age combined.” [p. 162] *VFR (

*Among the many terms he created were matrix, discriminant, invariant, totient, and Jacobian*)

**1890**Karl Pearson is appointed Gresham Professor of Geometry. The first whose name is commonly known since Robert Hooke died in 1703. The terms “standard deviation” and “histogram” were first used in his lectures at Gresham College. *Gresham Geometry lecture by Robin Wilson, 2008

**1896**Hollerith Agrees to Supply Machines for Russian Census:

Hollerith’s Census Machine was first employed by the U.S. Census Bureau in 1890 as the result of a crisis in counting a rapidly-increasing U.S. population. Methods based on Hollerith's machine served for almost 60 years until the Bureau adopted electron.*CHM (

*Image at Top, from officemuseum.com*)

**1928**To commemorate the International Congress of Medicine at Cairo, Egypt issued a postage stamp picturing Imhotep (c. 3000 BC). [Scott #153] *VFR

1965 Richard Feynman, having just won the Nobel Prize, makes a bet with CERN Director Viktor Weisskop that he will not hold a "responsible" position within the next ten years. A wager he will win. *Brain Pickings

1983 Grace Hopper was presented with the star to signify her promotion to Commodore (later Rear Admiral) by President Ronald Regan in a special White house ceremony. *WM

**In 2001**, the Leaning Tower of Pisa, Italy, was reopened to the public after a $27 million realignment that took over a decade. *TIS (

*sotto voce*"But still, it leans!")

**BIRTHS**

**1732 Wenceslaus Johann Gustav Karsten**(15 Dec 1732 in Neubrandenburg, Mecklenburg-Strelitz, Germany - 17 April 1787 in Halle, Germany) He wrote an important article in 1768 Von den Logarithmen vermeinter Grössen in which he discussed logarithms of negative and imaginary numbers, giving a geometric interpretation of logarithms of complex numbers as hyperbolic sectors, based on the similarity of the equations of the circle and of the equilateral hyperbola. *SAU

**1802 János Bolyai**(15 Dec 1802; 27 Jan 1860) Hungarian mathematician and one of the founders of non-Euclidean geometry - geometry that does not include Euclid's axiom that only one line can be drawn parallel to a given line through a point not on the given line. His father, Farkas Bolyai, had devoted his life to trying to prove Euclid's famous parallel postulate. Despite his father's warnings that it would ruin his health and peace of mind, János followed in working on this axiom until, in about 1820, he came to the conclusion that it could not be proved. He went on to develop a consistent geometry (published 1882) in which the parallel postulate is not used, thus establishing the independence of this axiom from the others. He also did valuable work in the theory of complex numbers. *TIS

**1823 Mikhail Vasilyevich Ostrogradsky**, (September 24, 1801 – January 1, 1862) was an Russian / Ukrainian mathematician, mechanician and physicist. Ostrogradsky is considered to be a disciple of Leonhard Euler and one of the leading mathematicians of Imperial Russia.

Ostrogradsky was born in Pashennaya, Poltava Governorate, Russian Empire (today Ukraine). From 1816 to 1820 he studied under Timofei Fedorovich Osipovsky (1765–1832) and graduated from the University of Kharkiv. When 1820 Osipovsky was suspended on religious grounds, Ostrogradsky refused to be examined and he never received his Doctor's degree. From 1822 to 1826 he studied at the Sorbonne and at the Collège de France in Paris, France. In 1828 he returned to the Russian Empire and settled in Saint Petersburg, where he was elected a member of the Academy of Sciences, Also he becomes the professor of the Main military engineering School of the Russian empire.

He worked mainly in the mathematical fields of calculus of variations, integration of algebraic functions, number theory, algebra, geometry, probability theory and in the fields of mathematical physics and classical mechanics. In the latter his most important work includes researches of the motion of an elastic body and the development of methods for integration of the equations of dynamics. Here he continued works of Euler, Joseph Louis Lagrange, Siméon-Denis Poisson and Augustin Louis Cauchy. His work in these fields was in Russia continued by Nikolay Dmitrievich Brashman (1796–1866), August Yulevich Davidov (1823–1885) and specially by the brilliant work of Nikolai Yegorovich Zhukovsky (1847–1921).

Ostrogradsky did not appreciate the work on non-Euclidean geometry of Nikolay Ivanovich Lobachevsky from 1823 and he rejected it, when it was submitted for publication in the Saint Petersburg Academy of Sciences.*Wik

**1827 Samuel Roberts FRS**(15 December 1827, Horncastle, Lincolnshire – 18 September 1913, London) was a British mathematician.

Roberts studied at Queen Elizabeth's Grammar School, Horncastle. He matriculated in 1845 at the University of London, where he earned in 1847 his bachelor's degree in mathematics and in 1849 his master's degree in mathematics and physics, as first in his class. Next he studied law and became a solicitor in 1853. After a few years of law practice he abandoned his law career and returned to mathematics, although he never had an academic position. He had his first mathematical paper published in 1848. In 1865 he was an important participant in the founding of the London Mathematical Society (LMS). From 1866 to 1892 he acted as legal counsel for LMS, from 1872 to 1880 he was the organization's treasurer, and from 1880 to 1882 its president. In 1896 he received the De Morgan Medal of the LMS. In 1878 he was elected FRS.

Roberts published papers in several fields of mathematics, including geometry, interpolation theory, and Diophantine equations.

Roberts and Pafnuty Chebyschev are jointly credited with the Roberts-Chebyshev theorem related to four-bar linkages *Wik

**1834 Charles Augustus Young**(15 Dec 1834; 3 Jan 1908) American astronomer who made the first observations of the flash spectrum of the Sun, proved the gaseous nature of the sun's corona and discovered the reversing layer of the solar atmosphere. He was a pioneer in the study of the spectrum of the sun and experimented in photographing solar prominences in full sunlight. On 22 Dec 1870, at the eclipse in Spain, he saw the lines of the solar spectrum all become bright for perhaps a second and a half (the "flash spectrum") and announced the "reversing layer." By exploring from the high altitude of Sherman, Wy. (1872), he more than doubled the number of bright lines he had observed in the chromosphere, By a comparison of observations, he concluded that magnetic conditions on the earth respond to solar disturbances. *TIS

**1847 Achille Marie Gaston Floquet**(December 15, 1847, Épinal–October 7, 1920, Nancy) was a French mathematician, best known for his work in mathematical analysis, especially in theory of differential equations.*Wik

**1852 Antoine-Henri Becquerel**(15 Dec 1852; 25 Aug 1908) was a French physicist who discovered radioactivity. In 1903 he shared the Nobel Prize for Physics with Pierre and Marie Curie. His early researches were in optics, then in 1896 he accidentally discovered radioactivity in fluorescent salts of uranium. He left some uranium mineral crystals in a drawer on a plate in black paper. Later, he developed the plate and found it was fogged, even though the crystals without ultraviolet radiation from sunlight were not fluorescing. Thus the salt was a source of a penetrating radiation. Three years afterwards he showed that it consists of charged particles that are deflected by a magnetic field. Initially, the rays emitted by radioactive substances were named after him. *TIS

**1912 Reuben Louis Goodstein**(15 December 1912 in London – 8 March 1985 in Leicester) was an English mathematician with a strong interest in the philosophy and teaching of mathematics. He earned his PhD from the University of London in 1946 while still working in Reading. Goodstein also studied under Wittgenstein and John Littlewood.

He published many works on finitism and the reconstruction of analysis from a finitistic viewpoint, for example "Constructive Formalism. Essays on the foundations of mathematics." Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems (such as second order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation sequence, together with the naming convention now used for these operations (tetration, pentation, etc.).*Wik

**1912 Emil Grosswald**(December 15, 1912 – April 11, 1989) was a Romanian-American mathematician who worked primarily in number theory. His career is closely associated with that of his teacher, Hans Rademacher. *Wik

**1916 Maurice Hugh Frederick Wilkins**(15 Dec 1916; 5 Oct 2004) was a New Zealand-born British biophysicist, whose X-ray diffraction studies of deoxyribonucleic acid (DNA) were significant in the determination of the molecular structure of DNA accomplished by James Watson and Sir Francis Crick. For this work the three scientists shared the 1962 Nobel Prize for Physiology or Medicine. *TIS

**1923 Freeman (John) Dyson**(15 Dec 1923, Feb 28, 2020 ) is an English-born American physicist and educator best known for his speculative work on extraterrestrial civilizations. As an imaginative scientist he proposed that a highly advanced technological civilization would ultimately completely surround its host star with a huge shell to capture 100% of the useful radiant energy. This "Dyson shell", would have a gigantic cluster of artificial planetoids ("Dyson cloud") with billions of billions of inhabitants who would make use of the energy captured by the Dyson shell. He also made the intriguing speculation that a Dyson shell viewed from other galaxies would have a highly distinctive, unnatural light. He suggests astronomers search for such tell-tale colored stars, which should signify advanced, intelligent life. *TIS (

*One of Dyson's earliest memories of his calculating power was at a time when he was still being put down for naps. He set about summing the fractions 1+1/2 + 1/4 ... and realized that they added up to two. At a time when most of us were still trying to figure out what fractions were, Dyson summed an infinite converging sequence.*)

I came across another beautiful anecdote about Dyson's incredible mental computational ability on the Math Frolic blog Posted by "Shecky Riemann":

Freeman Dyson sitting around a table with a bunch of scientists where the question arises, is there an integer such that by moving the last digit to the front (say 1234 to 4123) you can arrive at a result such that the new integer is exactly double the value of the original integer? In a matter of seconds, Dyson essentially responds (to a stunned group), “Oh, that’s not difficult, but of course the smallest such number is 18 digits long.” AND, he was right! If you can't, or just don't want to try to find it for yourself, I have posted it at the bottom.

He died in a Hospital near Princeton, where he was an emeritus professor.

**1921 Leo Königsberger**(15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject.

The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.

Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend. *Wik

**1958 Wolfgang Pauli**(25 Apr 1900, 15 Dec 1958) Austrian-born American winner of the Nobel Prize for Physics in 1945 for his discovery in 1925 of the Pauli exclusion principle, which states that in an atom no two electrons can occupy the same quantum state simultaneously. This principle clearly relates the quantum theory to the observed properties of atoms. *TIS

**1970 Sir Ernest Marsden**(19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

**1970 Theodore Samuel Motzkin**(26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.

He was appointed at UCLA in 1950 and worked there until retirement.

The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.

The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

**1971 Paul Pierre Lévy**(15 Sep 1886, 15 Dec 1971) was a French mining engineer and mathematician. He contributed to probability, functional analysis, partial differential equations and series. He also studied geometry. In 1926 he extended Laplace transforms to broader function classes. He undertook a large-scale work on generalized differential equations in functional derivatives. *TIS

2000 George Eric Deacon Alcock (August 28, 1912 – December 15, 2000)

George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder.

In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her.

Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. *TIA

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

I am calling this Dyson's Number, 105,263,157,894,736,842

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