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 349th day of the year; 349 is a prime, and the sum of three consecutive primes.
349 is the last day-number of the year that will be a member of a twin prime.
349 is also the largest day-number that is a prime such that p- product of its digits and p+product of its digits are both also prime; for 349, 349 + 3*4*9 = 457 and 349 - 3*4*9 = 241.. and 349, 457 and 241 are all prime. *Ben Vitale
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
Galileo's "cannocchiali" telescopes at the Museo Galileo, Florence
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 .
In 1614, Marius published his work Mundus Iovialis (English: World of Jupiter) describing the planet Jupiter and its moons (he previously had published the discovery in 1611 in a local almanac). Here he claimed to have discovered the planet's four major moons about a month before Galileo, who was naturally incensed. In The Assayer in 1623, he accused Marius of plagiarism. Regardless of priority, the mythological names by which these satellites are known today (Io, Europa, Ganymede and Callisto) are those given them by Marius.
Engraving of Marius in his book Mundus Iovialis (World of Jupiter), 1614
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
Peter Roth, in his book Arithmetica Philosophica (published in 1608, at Nürnberg, by Johann Lantzenberger),wrote that a polynomial equation of degree n (with real coefficients) may have n solutions. Albert Girard, in his book L'invention nouvelle en l'Algèbre (published in 1629), asserted that a polynomial equation of degree n has n solutions, but he did not state that they had to be real numbers. *Wik
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)
Hollerith Electrical Printing and Tabulating Machine
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 Reagan 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!")
The Leaning Tower of Pisa or simply, the Tower of Pisa , is the campanile, or freestanding bell tower, of Pisa Cathedral. It is known for its nearly four-degree lean, the result of an unstable foundation. The tower is one of three structures in the Pisa's Cathedral Square (Piazza del Duomo), which includes the cathedral and Pisa Baptistry.
Starting in 1993, 870 tonnes of lead counterweights were added, which straightened the tower slightly.
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
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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
He observed a solar flare with a spectroscope on 3 August 1872, and also noted that it coincided with a magnetic storm on Earth.
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
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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
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
Maurice Wilkins with one of the cameras he developed specially for X-ray diffraction studies at King's College London
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.
Dyson will always be a favorite of mine, for his presentation when I won the Presidential Award in Math Education. Within three minutes he had the entire audience dreading how long the speech of this demented mathematician might speak, then the audible concern as he seemed to be unaware of the podium he was leaning on rolled perilously close to the edge of the stage, and then the outburst of laughter as he stood up straight and said, "Well, I bet you'll all be relieved to know you don't have to listen to that for the next forty minutes." Then he dazzled us all with stories of his life in mathematics and his many recollections of his humorous experiences with people we had mostly only read about. "
1857, George Cayley, an English engineer, died Dec. 15, 1857, at age 83. Considering that Cayley has been called the father of aviation and the founder of aerodynamics and aeronautics, he is surprisingly little known, especially compared to the celebrated Wright brothers, Octave Chanute, and S.P. Langley. But one hundred years before Orville Wright took flight at Kitty Hawk, Cayley had worked out nearly all of the basic principles of fixed-wing aircraft. He knew the different functions and structural requirements of the wings, tail, stabilizer, and rudder, even the landing gear. He knew that lift, thrust, and control were all separate problems and had to be dealt with separately (most other would-be flight engineers of Cayley’s day were toying with ornithopters, or flapping machines, where lift and propulsion were to be supplied by the same mechanism). The only problem Cayley could not solve was power, since the engines of his day, especially the steam engine, were much too heavy and massive to be used on a flying machine. Thus a successful aircraft had to wait until lighter engines were available, which is one of the reasons why a century elapsed between Cayley and the Wrights. Cayley published the results of his theoretical work in three classic papers that appeared in 1809-1810 in three issues of A Journal of Natural Philosophy, Chemistry, and the Arts.
Cayley turned to balloons for many years, and then in 1852 he returned to the problem of heavier-than-air craft with a proposal for a glider, which he published in Mechanics' Magazine, coyly calling his invention a "governable parachute". This craft was actually built, and it flew briefly in 1853. Several replicas of Cayley's glider have been constructed and flown in modern times, including one in Yorkshire in 2009. *Linda Hall Org
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
Offer Pade' informed me that "He was the Ph.D advisor of Professor Igal Talmi of the weitzman Institute in Israel, Professor Talmi is one of the greatest physicist in Israel. Winner of the Israel Prize, Hans Bethe Prize and more."
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. 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
In mathematics, the nth Motzkin number is the number of different ways of drawing non-intersecting chords between n points on a circle . The following figure shows the 9 ways to draw non-intersecting chords between 4 points on a circle (M4 = 9):
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
2000 Zygmunt Wilhelm "Z. W." Birnbaum (18 October 1903 – 15 December 2000), often known as Bill Birnbaum, was a Polish-American mathematician and statistician who contributed to functional analysis, nonparametric testing and estimation, probability inequalities, survival distributions, competing risks, and reliability theory.
After first earning a law degree and briefly practicing law, Birnbaum obtained his PhD in 1929 at the University of Lwów under the supervision of Hugo Steinhaus, and was associated with the Lwów School of Mathematics. He visited University of Göttingen, Germany from 1929 to 1931, first working as an assistant for Edmund Landau.
After studying insurance mathematics and earning a diploma in actuarial science with Felix Bernstein in Göttingen, he worked as an actuary in Vienna during 1931–1932, and was then transferred to Lwów where he continued working as an actuary. After obtaining a position as a correspondent for a Polish newspaper, he arrived in New York as a reporter in 1937. He became a Professor of Mathematics at the University of Washington in 1939 (with help from Harold Hotelling and letters of reference from Richard Courant, Albert Einstein, and Edmund Landau).
Birnbaum was actively involved in reliability work with Boeing through the Boeing Scientific Research Laboratories during the late 1950s and 1960s, and was a key member of the "Seattle school of reliability", a group which also included Tom Bray, Gordon Crawford, James Esary, George Marsaglia, Al Marshall, Frank Proschan, Ron Pyke, and Sam Saunders.
Birnbaum served as Editor of the Annals of Mathematical Statistics (1967–1970) and as President of the Institute of Mathematical Statistics (1964). He received a Guggenheim Fellowship in 1960 (spent at the Sorbonne, Paris), and a Fulbright Program Fellowship in 1964 (spent at the University of Rome). *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
I am calling this Dyson's Number, 105,263,157,894,736,842
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