## Sunday, 22 January 2017

### On This Day in Math - January 22

 Niels & Harald Bohr talking football w/ children (see Deaths 1951)

Prudens interrogatio quasi dimidium sapientiae.
A prudent question is, as it were, one half of wisdom.
~Sir Francis Bacon

The 22nd day of the year; 22 is the smallest Hoax number (the sum of its digits is equal to the sum of the digits of its distinct prime factors). Can you find the next? [these sums that Hoax numbers add up to are an interesting study also]

Arrange the whole numbers from 1 to 22 into pairs so that the sum of the numbers in each pair is a perfect square. (Turns out that you can't, and 22 is the largest even number for which this is true) * Henri Picciotto@hpicciotto

Extra bonus: 22! has exactly 22 digits. *Mario Livio @Mario_Livio

22 is the smallest number which can be expressed as the sum of two primes in three ways.

EVENTS

1673 Leibniz presents a calculation machine at the Royal Society. Leibniz would complain to Oldenburg that Hooke took an "almost obscene" interest in the machine. Sure enough, by Feb 2 Hooke was actively working on an "arithmetic engine" that he would complete and show to the Royal Society within the month. By the following month his interest waned and he decided that no mechanical device could compare to paper and pencil or "Lord Napier's metal or parchment rods" (Napiers bones)*Stephen Inwood, The Forgotten Genius: The Biography Of Robert Hooke 1635-1703

1779 The parish register of Madron (the parish church) records ‘Humphry Davy, son of Robert Davy, baptized at Penzance, January 22nd, 1779. Davy was born in Penzance in Cornwall, United Kingdom, on 17 December 1778.

1833 In his notebook, Gauss introduces the linking number of two knots. "Gauss' note presents the first deep incursion into knot theory. *History of Topology edited by Ian Mackenzie James
From the Classic Carl Friedrich Gauss: Titan of Science By Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse, a partial translation comments on the developing theory of knots.

1876 The Johns Hopkins University Founded commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed $7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*JHU Web page 1879, the English were embroiled in a series of running conflicts in South Africa known as the Zulu War. On Jan. 22, 1879, a numerically superior Zulu force overwhelmed a smaller but technologically more advanced British contingent, in what became known as the Battle of Isandlwana. By coincidence, an annular solar eclipse (where the Moon is visually too small to cover the Sun) occurred around 2:30 p.m. at the tail end of the skirmish. The event would have been a deep partial from the battlefield, and the name “Isandlwana” in Zulu means “the day of the dead moon.” *listosaur.com web page 1889 Oskar Bolza gave his ﬁrst lecture to a non-German audience. At Johns Hopkins University he gave twenty lectures “on the theory of substitution groups and its application to algebraic equations.” This was the ﬁrst course on Galois theory in this country. It was published in 1891 in the American Journal of Mathematics.*VFR 1919 Richard Courant married Nina Runge in G¨ottingen. She was the daughter of the mathematician Carl Runge and granddaughter of the physiologist and philosopher of science Emil DuBois-Reymond. This provides another example of mathematical talent being passed from father to son-in-law. [Constance Reid, Courant in G¨ottingen and New York. The Story of an Improbable Mathematician (Springer 1976), p. 75–76] *VFR In 1980, Soviet dissident physicist Dr. Andrei Sakharov was arrested, stripped of his honors and exiled to Gorky from Moscow. *TIS 1984 Apple Computer Launches the Macintosh, the first successful mouse-driven computer with a graphic user interface, with a single$1.5 million commercial during the Super Bowl. Apple's commercial played on the theme of George Orwell's 1984 and featured the destruction of Big Brother -- a veiled reference to IBM -- with the power of personal computing found in a Macintosh.*CHM Surprise (to most) bit of feminism at the end, wait fore it.

In 1997, American Lottie Williams was reportedly the first human to be struck by a remnant of a space vehicle after re-entering the earth's atmosphere. At 3 a.m., while walking in a park in Tulsa, Oklahoma, she saw a light pass over her head. “It looked like a meteor,” she said. Minutes later, she was hit on the shoulder by a six-inch piece of blackened metallic material. The debris that struck Ms. Williams has not been examined to confirm its origin, but a used Delta II rocket, launched nine months earlier, had crashed into the Earth's atmosphere half an hour earlier. NASA scientists believe that Williams was hit by a part of it, making her the only person in the world known to have been hit by man-made space debris. *TIS

BIRTHS

1561 Sir Francis Bacon (22 Jan 1561; 9 Apr 1626) English philosopher remembered for his influence promoting a scientific method. He held that the aim of scientific investigation is practical application of the understanding of nature to improve man's condition. He wrote that scientists should concentrate on certain important kinds of experimentally reproducible situations, (which he called "prerogative instances"). After tabulating such phenomena, the investigator should also aim to make a gradual ascent to more and more comprehensive laws, and will acquire greater and greater certainty as he or she moves up the pyramid of laws. At the same time each law that is reached should lead him to new kinds of experiment, that is, to kinds of experiment over and above those that led to the discovery of the law. *TIS He died a month after performing his ﬁrst scientific experiment. He stuﬀed a chicken with snow to see if this would cause it to spoil less rapidly. The chill he caught during this experiment led to his death. [A. Hellemans and B. Bunch. The Timetables of Science, p . 32]. *VFR

1592 Pierre Gassendi (22 Jan 1592; 24 Oct 1655) French scientist, mathematician, and philosopher who revived Epicureanism as a substitute for Aristotelianism, attempting in the process to reconcile Atomism's mechanistic explanation of nature with Christian belief in immortality, free will, an infinite God, and creation. Johannes Kepler had predicted a transit of Mercury would occur in 1631. Gassendi used a Galilean telescope to observed the transit, by projecting the sun's image on a screen of paper. He wrote on astronomy, his own astronomical observations and on falling bodies.*TIS

1775 André-Marie Ampère (22 Jan 1775; 10 Jun 1836) French mathematician, physicist and chemist who founded and named the science of electrodynamics, now known as electromagnetism. His interests included mathematics, metaphysics, physics and chemistry. In mathematics he worked on partial differential equations. Ampère made significant contributions to chemistry. In 1811 he suggested that an anhydrous acid prepared two years earlier was a compound of hydrogen with an unknown element, analogous to chlorine, for which he suggested the name fluorine. He produced a classification of elements in 1816. Ampère also worked on the wave theory of light. By the early 1820's, Ampère was working on a combined theory of electricity and magnetism, after hearing about Oersted's experiments. *TIS (It is said that Ampere was capable of intense concentration leading to absent-mindedness. Once walking in Paris he had an insight and pulled a piece of chalk out of his pocket and finding the back of a cab he began to cover the back of the cab with equations, and was then shocked to see his solution begin to pull away and disappear down the street.)

1865 Louis Carl Heinrich Friedrich Paschen (22 Jan 1865; 25 Feb 1947) was a German physicist who was an outstanding experimental spectroscopist. In 1895, in a detailed study of the spectral series of helium, an element then newly discovered on earth, he showed the identical match with the spectral lines of helium as originally found in the solar spectrum by Janssen and Lockyer nearly 40 years earlier. He is remembered for the Paschen Series of spectral lines of hydrogen which he elucidated in 1908. *TIS

1866 Gustav de Vries (22 Jan 1866 in Amsterdam, The Netherlands
- 16 Dec 1934 in Haarlem, The Netherlands) was a Dutch mathematician who introduced the famous Korteweg-de Vries equation which characterizes traveling waves. *SAU

1874 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1880 Frigyes Riesz (22 Jan 1880; 28 Feb 1956) Hungarian mathematician and pioneer of functional analysis, which has found important applications to mathematical physics. His theorem, now called the Riesz-Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space. It was the mathematical basis for proving that matrix mechanics and wave mechanics were equivalent. This is of fundamental importance in early quantum theory. His book Leçon's d'analyse fonctionnelle (written jointly with his student B Szökefalvi-Nagy) is one of the most readable accounts of functional analysis ever written. Beyond any mere abstraction for the sake of a structure theory, he was always turning back to the applications in some concrete and substantial situation. *TIS

1908 Lev Davidovich Landau (22 Jan 1908; 1 Apr 1968) Soviet physicist who worked in such fields as low-temperature physics, atomic and nuclear physics, and solid-state, stellar-energy, and plasma physics. Several physics terms bear his name. He was awarded the 1962 Nobel Prize for Physics for his theory to explain the peculiar superfluid behaviour of liquid helium at very low temperature (2.18 K). Landau's further contributions are partly reflected in such terms as Landau diamagnetism and Landau levels in solid-state physics, Landau damping in plasma physics, the Landau energy spectrum in low-temperature physics, or Landau cuts in high-energy physics. *TIS

1929 Walter Volodymyr Petryshyn (Vladimir Petryshin) (22 January 1929, Liashky Murovani, Lviv - ) is a famous Ukrainian mathematician. He had commenced his studies in Lviv during World War II, but he became a displaced person at the end of the war and continued his schooling in Germany. In 1950 he emigrated from Germany to the United States and completed his education there, living in Paterson, New Jersey. He studied at Columbia University and was awarded a B.A. in 1953, an M.S. in 1954, and a Ph.D. in 1961. Petryshyn's main achievements are in functional analysis. His major results include the development of the theory of iterative and projective methods for the constructive solution of linear and nonlinear abstract and differential equations.*Wik

DEATHS

1779 Jeremiah Fenwicke Dixon (27 July 1733 – 22 January 1779) was an English surveyor and astronomer who is best known for his work with Charles Mason, from 1763 to 1767, in determining what was later called the Mason-Dixon line.
Dixon was born in Cockfield, near Bishop Auckland, County Durham, the fifth of seven children, to Sir George Fenwick Dixon 5th Bt. and Lady Mary Hunter. His father was a wealthy Quaker coal mine owner and aristocrat. His mother came from Newcastle, and was said to have been "the cleverest woman" to ever marry into the Dixon family. Dixon became interested in astronomy and mathematics during his education at Barnard Castle. Early in life he made acquaintances with the eminent intellectuals of Southern Durham: mathematician William Emerson, and astronomers John Bird and Thomas Wright. In all probability it was John Bird, who was an active Fellow of the Royal Society, who recommended Dixon as a suitable companion to accompany Mason.
Jeremiah Dixon served as assistant to Charles Mason in 1761 when the Royal Society selected Mason to observe the transit of Venus from Sumatra. However, their passage to Sumatra was delayed, and they landed instead at the Cape of Good Hope where the transit was observed on June 6, 1761. Dixon returned to the Cape once again with Nevil Maskelyne's clock to work on experiments with gravity.
Dixon and Mason signed an agreement in 1763 with the proprietors of Pennsylvania and Maryland, Thomas Penn and Frederick Calvert, sixth Baron Baltimore, to assist with resolving a boundary dispute between the two provinces. They arrived in Philadelphia in November 1763 and began work towards the end of the year. The survey was not complete until late 1766, following which they stayed on to measure a degree of Earth's meridian on the Delmarva Peninsula in Maryland, on behalf of the Royal Society. They also made a number of gravity measurements with the same instrument that Dixon had used with Maskelyne in 1761. Before returning to England in 1768, they were both admitted to the American Society for Promoting Useful Knowledge, in Philadelphia.
Dixon sailed to Norway in 1769 with William Bayly to observe another transit of Venus. The two split up, with Dixon at Hammerfest Island and Bayly at North Cape, in order to minimize the possibility of inclement weather obstructing their measurements. Following their return to England in July, Dixon resumed his work as a surveyor in Durham. He died unmarried in Cockfield on 22 January 1779, and was buried in an unmarked grave in the Quaker cemetery in Staindrop.
Although he was recognized as a Quaker, he was not a very good one, dressing in a long red coat and occasionally drinking to excess. *Wik

1904 The Reverend George Salmon (25 September 1819 - 22 January 1904) was, firstly, a mathematician whose publications in algebraic geometry were widely read in the second half of the 19th century. He was also an Anglican theologian who devoted himself mostly to theology for the last forty years of his life. His publications in theology were widely read, too. He spent his entire career at Trinity College Dublin. In 1848 Salmon had published an undergraduate textbook entitled A Treatise on Conic Sections. This text remained in print for over fifty years, going though five updated editions in English, and was translated into German, French and Italian. In the late 1840s and the 1850s Salmon was in regular and frequent communication with Arthur Cayley and J.J. Sylvester. The three of them together with a small number of other mathematicians (including Charles Hermite) were developing a system for dealing with n-dimensional algebra and geometry. During this period Salmon published about 36 papers in journals. In these papers for the most part he solved narrowly defined, concrete problems in algebraic geometry, as opposed to more broadly systematic or foundational questions. But he was an early adopter of the foundational innovations of Cayley and the others. In 1859 he published the book Lessons Introductory to the Modern Higher Algebra (where the word "higher" means n-dimensional). This was for a while simultaneously the state-of-the-art and the standard presentation of the subject, and went through updated and expanded editions in 1866, 1876 and 1885, and was translated into German and French. *Wik

1951 Harald August Bohr (22 Apr 1887, 22 Jan 1951) Danish mathematician who devised a theory that concerned generalizations of functions with periodic properties, the theory of almost periodic functions. His brother was noted physicist Niels Bohr.*TIS Harald was an excellent football(soccer) player in his youth and played for the National team. Niels played also, but not at the same high level. An interesting anecdote about Niels Bohr as an athlete is here.

1921 Marie Georges Humbert (7 Jan 1859 in Paris, France - 22 Jan 1921 in Paris, France) His doctorate extended Clebsch's work on curves. He then studied Abel's work which he developed and put into a geometric setting. It was as a direct consequence of his work on using abelian functions in geometry which won for him the 1892 Académie des Sciences prize for work on Kummer surfaces. As Costabel writes, "He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. "
He also extended work of Hermite considering applications to number theory throughout his life.
Humbert would be better known today if the area of mathematics in which he worked had remained in favor. Since it has now become merely something of an historical curiosity rather than mainstream mathematics, his contribution is less well known. It does, however, indicate the quality of his mathematics that, despite this, his name and results are known today. To some extent this is a consequence of the fact that although he worked in a specialized area he had a remarkably broad knowledge of mathematics and his results form links between areas. *SAU

1922 Camille Jordan (5 Jan 1838, 22 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik but 20 Jan by *TIS)

1936 V Ramaswami Aiyar (1871 in Coimbatore district, India - 22 Jan 1936 in Chittoor, India) was an enthusiastic amateur mathematician who worked as a civil servant in India. He was a founder of the Indian Mathematical Society. *SAU

1981 Rudolf Oskar Robert Williams Geiger (24 Aug 1894, 22 Jan 1981) German meteorologist, one of the founders of microclimatology, the study of the climatic conditions within a few metres of the ground surface. His observations, made above grassy fields or areas of crops and below forest canopies, elucidated the complex and subtle interactions between vegetation and the heat, radiation, and water balances of the air and soil.*TIS

1987 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1989 Sydney Goldstein (3 Dec 1903 in Hull, England - 22 Jan 1989 in Belmont, Massachusetts, USA) Goldstein's work in fluid dynamics is of major importance. He is described as, "... one of those who most influenced progress in fluid dynamics during the 20th century." He studied numerical solutions to steady-flow laminar boundary-layer equations in 1930. In 1935 he published work on the turbulent resistance to rotation of a disk in a fluid. His work was important in aerodynamics, a subject in which Goldstein was extremely knowledgeable. *SAU

1990 Bill Ferrar graduated from Oxford after an undergraduate career interrupted by World War I. He lectured at Bangor and Edinburgh before moving back to Oxford. He worked in college administration and eventually became Principal of Hertford College. He worked on the convergence of series. *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

## Saturday, 21 January 2017

### On THis Day in Math - January 21

*Wik

The whole of the developments and operations of analysis are now capable of being executed by machinery. ... As soon as an Analytical Engine exists, it will necessarily guide the future course of science.
C. Babbage

The 21st day of the year; To tile a square out of integer sided squares requires a minimum of 21 squares. (technically, this is true for what are called "simple" squared squares, one where no subset of the squares forms a rectangle or square. See the solution here) (btw: There are no cubed cubes!)
There are 21 possible ways to draw 5 circles that touch all the points on a 5x5 lattice.  *gotmath.com

21 repeated twenty-one times, following 1, forms a smoothly undulating palindromic prime
121212121212121212121212121212121212121 is prime

Blackjack primes are separated by exactly 21 consecutive composite numbers. Note that the pair {1129, 1151} is the smallest example.(Can you find more?) *Prime Curios

EVENTS

1472, the great daylight comet of 1472 passed within 10.5 million km of earth.*TIS (Johannes Müller von Königsberg (Regiomontanus) is said to have observed this comet)

1609 Modern astronomy dates all astronomical events using the Julian Day Count a system of dating that was first conceived by a Renaissance historian and Bible chronologist, Joseph Justus Scalier, who died on this day. The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC. At noon on the date of his death, the Julian Day 2308756 would have began. *Wik For a few details about his life see this post at the Renaissance Mathematicus.

1665 Samuel Pepys, having acquired a copy of Hooke’s Micrographia the day before, stays up to read it, “Before I went to bed I sat up till two o'clock in my chamber reading of Mr. Hooke's Microscopicall Observations, the most ingenious book that ever I read in my life.” *Pepy’s Diary

1807, the London Institution received a royal charter signed by King George III, to "promote the diffusion of Science, Literature, and the Arts, by means of Lectures and Experiments, and by easy access to an extensive collection of books, both ancient and modern, in all languages." The full name in the charter was the "London Institution for the Advancement of Literature and The Diffusion of Useful Knowledge." The first president was Sir Francis Baring. Its incorporation came after the Royal Society (1663) and Royal Institution (1800). The institution had an extensive lecture program. Instruction in practical chemistry was given in its laboratory, and significant chemistry research was done there through the 19th century. *TIS

1840, Charles Wheatstone and William F. Cooke were granted the earliest English alphabetic telegraph patent. Wheatstone made contributions to a broad range of fields in the mid 19th century. The ABC telegraph was popular in England and Europe because it did not require a trained telegraphist to read or send the messages. The operator simply rotates a wheel to the desired letter. During rotation the instrument sends out the proper number of electric pulses to an electromagnetically controlled pointer on a remote synchronized slave receiver with a similarly lettered wheel which moves to the sender's letter. Electric telegraphs of the 1840-50's are of special historic importance as the earliest practical application of serial binary coded digital communication. *TIS

1888 Babbage's Analytical Engine Passes the First Test
The Analytical Engine of Charles Babbage was never completed in his lifetime, but his son Henry Provost Babbage built the mill portion of the machine from his father's drawings, and on January 21, 1888 computed multiples of pi to prove the adequacy of the design. Perhaps this represents the first successful test of a portion of a modern computer. Recently a portion of his earlier machine, the Difference Engine, was sold at auction by Christies of London to the Powerhouse Museum in Sydney, Australia.*CHM

1954, the first atomic submarine, the U.S.S. Nautilus, was launched at Groton, Connecticut. Nautilus' nuclear propulsion system was a landmark in the history of naval engineering and submersible craft. All vessels previously known as "submarines" were in fact only submersible craft. Because of the nuclear power plant, the Nautilus could stay submerged for months at a time, unlike diesel-fueled subs, whose engines required vast amounts of oxygen. Nautilus demonstrated her capabilities in 1958 when she sailed beneath the Arctic icepack to the North Pole. Scores of nuclear submarines followed Nautilus, replacing the United States' diesel boat fleet. After patrolling the seas until 1980, the Nautilus is back home at Groton. *TIS

1979 Pluto moves closer to the sun than Neptune. *VFR Pluto is usually farther from the Sun. However, its orbit "crosses" inside of Neptune's orbit for 20 years out of every 248 years. Pluto last crossed inside Neptune's orbit on February 7, 1979, and temporarily became the 8th planet from the Sun. Pluto crossed back over Neptune's orbit again on February 11, 1999 to resume its place as the 9th planet from the Sun for the next 228 years (well, now it is now one of five known "dwarf planets").

BIRTHS

1793 Théodore Olivier (21 Jan 1793 in France - 5 Aug 1853 in France) From the 1840's Olivier wrote textbooks. His greatest fame, however, is as a result of the mathematical models which he created to assist in his teaching of geometry. Some of the models were of ruled surfaces, with moving parts to illustrate to students how the ruled surfaces were generated. Others were designed to illustrate the curves of intersection of certain surfaces. In fact Olivier earned quite a good income from selling these models, particularly in the United States.
The United States Military Academy at West Point had 23 mathematical models made for them by Olivier to use as teaching aids:=
These models are built on wooden boxes as bases, have metal supports, and consist of strings suspended from movable arms and arranged to form a variety of geometrical figures. The strings are held in place by lead weights that are concealed by the bases. The models illustrate such things as the intersection of two half cones, the intersection of a plane, hyperbolic paraboloid and a hyperboloid of one sheet, and the intersection of two half cylinders.
Other institutions in the United States such as the Columbia School of Mines also purchased models from Olivier while Princeton had copies of Olivier's models made for them. In 1849 Olivier presented a full set of the range of models he had created to the Conservatoire National des Arts et Métiers. The models had been manufactured by the firm of Pixii, Père et Fils, and later by the firm of Fabre de Lagrange which took over their manufacture. In 1857, four years after Olivier died, Harvard University purchased 24 of Olivier's models from Fabre de Lagrange and after the university received the order Benjamin Peirce gave a series of lectures on the mathematics which they illustrated. These models are still in Harvard's collection of scientific instruments.
Even after giving a complete set of his models to the Conservatoire National des Arts et Métiers, forty models were still in Olivier's possession at the time of his death. These were sold in 1869 to William Gillispie from Union College in Schenectady, east-central New York, United States. Gillispie exhibited the models at Union College which was appropriate since, twenty years earlier, Union College had became one of the first liberal arts colleges in the United States to give engineering courses. When Gillispie died Olivier's models were sold to the college. *SAU

1846 Pieter Hendrik Schoute (January 21, 1846, Wormerveer–April 18, 1923, Groningen) was a Dutch mathematician known for his work on regular polytopes and Euclidean geometry. *Wik Schoute was a typical geometer. In his early work he investigated quadrics, algebraic curves, complexes, and congruences in the spirit of nineteenth-century projective, metrical, and enumerative geometry. Schläfli's work of the 1850's was brought to the Netherlands by Schoute who, in three papers beginning in 1893 and in his elegant two-volume textbook on many-dimensional geometry 'Mehrdimensionale Geometrie' (2 volumes 1902, 1905), studied the sections and projections of regular polytopes and compound polyhedra. ... Alicia Boole Stott (1870-1940), George Boole's third daughter (of five), ... studied sections of four- and higher-dimensional polytopes after her husband showed her Schoute's 1893 paper, and Schoute later (in his last papers) gave an analytic treatment of her constructions. *SAU

1860 David Eugene Smith, Ph.D., LL.D. (January 21, 1860 in Cortland, New York – July 29, 1944 in New York) was an American mathematician, educator, and editor. David Eugene Smith attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884. He also knew Latin, Greek, and Hebrew. He became a professor at the Michigan State Normal College in 1891, the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901).
Smith became president of the Mathematical Association of America in 1920.[3] He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's Budget of Paradoxes (1915) and wrote many books on Mathematics and Mathematics History. *Wik

1874 René-Louis Baire (21 Jan 1874; 5 Jul 1932) French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

1897 Alexander Weinstein (21 Jan 1897 in Saratov, Russia - 6 Nov 1979 in Washington DC, USA) is famed for solving a variety of boundary value problems which have been used in a wide range of applications. Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. In examining singular partial differential equations he introduced a new branch of potential theory and applied the results to many different situations including flow about a wedge, flow around lenses and flow around spindles. *SAU

1908 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

1915 Yuri Vladimirovich Linnik (January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics.*Wik

1923 Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups.
After teaching mathematics to military personnel at Harvard before earning his doctorate, Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969, where he remained for the rest of his life. He was the founding director of DIMACS in 1989, and remained as its director until his death.[1]
Gorenstein was awarded many honors for his work on finite simple groups. He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in directing the classification proof, the largest collaborative piece of pure mathematics ever attempted. In 1972 he was a Guggenheim Fellow and a Fulbright Scholar; in 1978 he gained membership in the National Academy of Sciences and the American Academy of Arts and Sciences, and in 1989 won the Steele Prize for mathematical exposition. *Wik

DEATHS
1609 Joseph Justus Scaliger (5 Aug 1540, 21 Jan 1609) French scholar who was one of the founders of the science of chronology. Like Roger de Losinga, Bishop of Hereford, centuries before, Scaliger recognized that combining the three cycles of the 28-year solar cycle (S), the 19-year cycle of Golden Numbers (G) and the 15-year indiction cycle (I) produced one greater cycle of 7980 years (28×9×15). Scalinger applied this fact, called a Julian cycle, in his attempt to resolve a patchwork of historical eras and he used notation (S, G, I) to characterize years. The year of Christ's birth had been determined by Dionysius Exigus to be the number 9 on the solar cycle, by Golden Number 1, and by 3 of the indiction cycle, thus (9, 1, 3), which was 4713 of his chronological era. Hence, the year (1, 1, 1) was 4713 B.C. (later adopted as the initial epoch for the Julian day numbers).*TIS A formula for converting days to Julian day numbers is here.

1800 Jean-Baptiste Le Roy (15 August 1720;Paris, France - 21 January 1800, Paris) Son of the renowned clockmaker Julien Le Roy, Jean-Baptiste Le Roy was one of four brothers to achieve scientific prominence in Enlightenment France; the others were Charles Le Roy (medicine and chemistry), Julien-David Le Roy (architecture), and Pierre Le Roy(chronometry). Elected to the Académie Royale des Sciences in 1751 as adjoint géomètre, Le Roy played an active role in technical as well as administrative aspects of French science for the next half-century. He was elected pensionnaire mécanicies in 1770 and director of the Academy for 1773 and 1778, and became both a fellow of the Royal Society and a member of the American Philosophical Society in 1773.
Le Roy’s major field of enquiry was electricity, a subject on which European opinion was much divided at mid-century. The most prominent controversy engaged the proponents of the Abbé Nollet’s doctrine of two distinct streams of electric fluids (outflowing and inflowing) and the partisans of Benjamin Franklin’s concept of a single electric fluid. This debate intensified in France in 1753 with an attack on Franklin’s views by Nollet. Le Roy, later a friend and correspondent of Franklin, defended his single-fluid theory and offered considerable experimental evidence in support thereof. He played an important role in the dissemination of Franklin’s ideas, stressing particularly their practical applications, and published many memoirs on electrical machines and theory in the annual Histoires and Mémoires of the Academy and in the Journal de Physique.
A regular contributor to the Encyclopédie, Le Roy wrote articles dealing with scientific instruments. The most important of these included comprehensive treatments of “Horlogerie,” “Télescope,” and “Électrométre” (in which Le Roy claimed priority for the invention of the electrometer). He also promoted the use of lightning rods in France, urged that the Academy support technical education, and was active in hospital and prison reform. After the Revolutionary suppression of royal academies, Le Roy was appointed to the first class of the Institut National (section de mécanique) at its formation in 1795. *Encycopedia.com

1892 John Couch Adams (5 Jun 1819, 21 Jan 1892) In 1878 he published his calculation of Euler’s constant (Euler-Mascheronie constant) to 263 decimal places. (he also calculated the Bernoulli numbers up to the 62 nd) *VFR The Euler-Mascheronie constant is the limiting value of the difference between the sum of the first n values in the harmonic series and the natural log of n. (not 263 places, but the approximate value is 0.5772156649015328606065...)
He also predicted the location of the then unknown planet of Neptune, but it seems he failed to convince Airy to search for the planet. Independently, Urbanne LeVerrier predicted its locatin in Germany, and then assisted Galle in the Berlin Observatory in locating the planet on 23 September 1846. As a side note, when he was appointed to a Regius position at St. Andrews in Scotland, he was the last professor ever to have to swear and oath of “abjuration and allegience”, swearing fealty to Queen Victoria, and abjuring the Jacobite succession. The need for the oath was removed by the 1858 Universities Scotland Act. Adams made many other contributions to astronomy, notably his studies of the Leonid meteor shower (1866) where he showed that the orbit of the meteor shower was very similar to that of a comet. He was able to correctly conclude that the meteor shower was associated with the comet. *Wik & *TIS

1930 H(ugh) L(ongbourne) Callendar (18 Apr 1863, 21 Jan 1930) was an English physicist famous for work in calorimetry, thermometry and especially, the thermodynamic properties of steam. He published the first steam tables (1915). In 1886, he invented the platinum resistance thermometer using the electrical resistivity of platinum, enabling the precise measurement of temperatures. He also invented the electrical continuous-flow calorimeter, the compensated air thermometer (1891), a radio balance (1910) and a rolling-chart thermometer (1897) that enabled long-duration collection of climatic temperature data. His son, Guy S. Callendar linked climatic change with increases in carbon dioxide (CO2) resulting from mankind's burning of carbon fuels (1938), known as the Callendar effect, part of the greenhouse effect.*TIS

1931 Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician. He was born in Arezzo, and was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered what came to be called the Burali-Forti paradox of Cantorian set theory.*Wik

1946 Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician. He first grew to love mathematics at Manchester Grammar School, and in his final year, won a scholarship to Trinity College, Cambridge. There he distinguished himself in 1903 as Senior Wrangler (tied with P.E. Marrack) and by winning the Smith's Prize (1905). He studied in Göttingen and Paris, taught at the University of Liverpool and University of Manchester before moving to the US in 1910. First he taught at Bryn Mawr College and then Johns Hopkins University. There, working with Frank Morley in geometry, he achieved the Ph.D. In 1917 he took up his permanent position at California Institute of Technology, then still called Throop Polytechnic Institute.
Eric Temple Bell says, "Like his contemporaries and immediate predecessors among Cambridge mathematicians of the first decade of this century [1901–1910]... Bateman was thoroughly trained in both pure analysis and mathematical physics, and retained an equal interest in both throughout his scientific career."*Wik

1974 Arnaud Denjoy (5 January 1884 – 21 January 1974 in Paris) a French mathematician born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to integrate all derivatives. Among his students is Gustave Choquet.*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

## Friday, 20 January 2017

### On This Day in Math - January 20

If you are afraid of something, measure it, and you will realize it is a mere trifle.
~Renato Caccioppoli

The 20th day of the year; 20 is the smallest number that cannot be either prefixed or followed by one digit to form a prime. (What is next smallest?)

The 20th palindromic prime (929) has a digit sum of 20. *jim wilder ‏@wilderlab ... There is no larger nth prime palindrome for which digit sum = n less than $10^7$ *Derek Orr & *David ‏@InfinitelyManic

$e^\pi - \pi = 20$ Well, almost, it's 19.999099979...,  (The number $e^\pi$ is often called Gelfond's constant, after the mathematician Aleksandr Gelfond, who proved that it was transcendental.

EVENTS

In 1633, Galileo, at age 68, left his home in Florence, Italy, to face the Inquisition in Rome. By 22 Jun 1633, he buckled under the threats and interrogation by the Inquisition, and renounced his belief that the Earth revolved around the Sun. *TIS

1748 In a surprising letter of January 20, 1748, D'Alembert wrote to Euler [Euler 1980] to suggest a new theory: perhaps the moon (or at least its distribution of mass) was not spherical. If, after all, we only see one side from the Earth, we can't know how far back it truly extends. And perhaps if it extends far enough back, the apsidal motion would indeed be 3 degrees, as observed. In an even more surprising response written less than four weeks later [Euler 1980], Euler says that he too had considered this idea, and had worked out the details! He found that moon would have to extend back about 2 1/2 Earth diameters in the direction away from us, which seemed untenable. *VFR

1896, X-rays were reported by Henri Poincaré reading a letter from Wilhelm Roentgen to the weekly meeting of the Academie des Sciences in Paris, and members viewed some of his X-ray photographs. Henri Becquerel was present, and took note that X-rays seemed to come from the phosphorescent patch on the glass tube where the cathode rays struck it. This inspired him to study if the phosphorescence of minerals was related to X-rays. (Instead, a few weeks later, he discovered the radioactivity of a uranium mineral.) *TIS

1969, the New York Times made public the news of the discovery a few days earlier of the first optical pulsar by astronomers at the University of Arizona on 16 Jan 1969. It was the result of a year's search using a stroboscopic technique. Flashes of light in the optical range were found coming from the same location in the Crab Nebula as a previously known pulsar emitting radio bursts. The rate of pulsation of the two signals was found to be the same, and thus presumed to be from a single star. Other observatories were immediately notified and the flashing was confirmed by the McDonald Observatory and by the powerful 84-inch reflector telescope at the Kitt Peak National Observatory in Arizona. The star was flashing at a rate of about 30 times per second, with intermediate flashes of lesser intensity. *TIS

1983 The Department of Commerce officially withdrew the commercial standard for the sizing of women's apparel on January 20, 1983. In the mid-1940s, the Mail-Order Association of America, a trade group representing catalog businesses such as Sears Roebuck and Spiegel, asked the Commodity Standards Division of the National Bureau of Standards (NBS, now NIST )to conduct research to provide a reliable basis for industry sizing standards for women's clothing. Men's clothing had become somewhat standardized as early as the American Civil War due to demands for quick manufacture of uniforms. The resulting commercial standard was distributed by NBS to the industry for comment in 1953, formally accepted by the industry in 1957, and published as Commercial Standard (CS)215-58 in 1958.
However, with the passage of time, the standard became outdated. Both American men and women were becoming heavier. Whereas the average woman's figure once came a little closer to approaching the hourglass shape of the fashion magazines, she was now becoming more pear-shaped, with a thicker waist and fuller hips. At the same time that the average woman's body was changing shape, manufacturers discovered the advantage of appealing to women's vanity. They began selling bigger clothes labeled with smaller size numbers. Today only pattern makers consistently use the old commercial standard.*NIST

1989 Statistician and political scientist Edward R Tufte sent a letter to the New York Times with a copy of his book on statistical graphics. On a visit later to New York, the Times called it as "founding document of New York Times Graphics" *
Edward Tufte@EdwardTufte

BIRTHS

1573 Simon Marius (20 Jan 1573, 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611 *TIS Galileo initially named his discovery the Cosmica Sidera ("Cosimo's stars"), but names that eventually prevailed were chosen by Simon Marius and were suggested by Johannes Kepler, in his Mundus Jovialis​, published in 1614. *Wik You can find a nice blog about the conflict with Galileo by the Renaissance Mathematicus.

1775 André-Marie Ampère (20 January 1775 – 10 June 1836) was a French physicist and mathematician who is generally regarded as one of the main discoverers of electromagnetism. The SI unit of measurement of electric current, the ampere, is named after him.*Wik

1820 Alexandre-Emile Beguyer de Chancourtois (20 Jan 1820; 14 Nov 1886) French geologist who was the first to arrange the chemical elements in order of atomic weights (1862). De Chancourtois plotted the atomic weights on the surface of a cylinder with a circumference of 16 units, the approximate atomic weight of oxygen. The resulting helical curve which he called the telluric helix brought closely related elements onto corresponding points above or below one another on the cylinder. Thus, he suggested that "the properties of the elements are the properties of numbers." Although his publication was significant, it was ignored by chemists as it was written in the language of geology, and the editors omitted a crucial explanatory table. It was Dmitry Mendeleyev's table published in 1869 that became most recognized.*TIS

1831 Edward John Routh FRS (20 January 1831–7 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematise the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.*Wik

1834 William Watson born in Nantucket, MA. In 1862 he earned his Ph.D. at the University of Jena, being the ﬁrst American to receive a Ph.D. in mathematics at a foreign university. Later he taught at Harvard and MIT. In the same year Yale was the ﬁrst American school to grant a Ph.D. in mathematics (to J. H. Worall).*VFR

1895 Gabor Szego, Professor Emeritus at Stanford. He co-authored with George (originally Gy¨orogy) P´olya the renown book Problems and Theorems in Analysis. *VFR worked in the area of extremal problems and Toeplitz matrices.*SAU

1904 Renato Caccioppoli ( 20 January 1904 – 8 May 1959) was an Italian mathematician. His most important works, out of a total of around eighty publications, relate to functional analysis and the calculus of variations. Beginning in 1930 he dedicated himself to the study of differential equations, the first to use a topological-functional approach. Proceeding in this way, in 1931 he extended the Brouwer fixed point theorem, applying the results obtained both from ordinary differential equations and partial differential equations. *Wik

1931 David M. Lee (20 Jan 1931, ) American physicist who, with Robert C. Richardson and Douglas D. Osheroff, was awarded the Nobel Prize for Physics in 1996 for their joint discovery of superfluidity in the isotope helium-3.*TIS

DEATHS

1590 Giovanni Battista Benedetti died. In one of his books he forecast his death for 1592. Hence, on his deathbed, he recomputed his horoscope and declared that an error of four minutes must have been made in the original data, thus evincing his lifelong faith in the doctrines of judicial astrology.*VFR "The essence of Galileo’s laws of fall can be found in the work of Giambattista Bendetti: *RMAT

1760 John Colson (1680–20 January, 1760) was an English clergyman and mathematician, Lucasian Professor of Mathematics at Cambridge University.
Colson was educated at Lichfield School before becoming an undergraduate at Christ Church, Oxford, though he did not take a degree there. He became a schoolmaster at Sir Joseph Williamson's Mathematical School in Rochester, and was elected Fellow of the Royal Society in 1713. He was Vicar of Chalk, Kent from 1724 to 1740. He relocated to Cambridge and lectured at Sidney Sussex College, Cambridge. From 1739 to 1760 he was Lucasian Professor of Mathematics. He was also Rector of Lockington, Yorkshire.
In 1726 he published his Negativo-Affirmativo Arithmetik advocating a modified decimal system of numeration. It involved "reduction [to] small figures" by "throwing all the large figures 9, 8, 7, 6 out of a given number, and introducing in their room the equivalent small figures $1\bar{1}, 1\bar{2}, 1\bar{3}, 1\bar{4}$ respectively".
He translated several of Isaac Newton's works into English, including De Methodis Serierum et Fluxionum in 1736. It was Colsen who mistranslated the name of the curve that Maria Gaetana Agnesi called 'versiera' to become the Witch of Agnesi.*Wik

1864 Giovanni Antonio Amedeo Plana (6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician.
His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age.
The crater Plana on the Moon is named in his honor.*Wik

1907 Agnes Mary Clerke (10 Feb 1842, 20 Jan 1907) Irish astronomical writer who was a diligent compiler of facts rather than a practicing scientist. Nevertheless, by 1885, her exhaustive treatise, A Popular History of Astronomy in the Nineteenth Century gained international recognition as an authoritative work. In 1903, with Lady Huggins, she was elected an honorary member of the Royal Astronomical Society, a rank previously held only by two other women, Caroline Herschel and Mary Somerville. Her publications included several books and 55 pieces in the Edinburgh Review. She contributed some astronomer biographies to the Dictionary of National Biography and some astronomical entries in the Encyclopaedia Britannica. *TIS

1921 Mary Watson Whitney (11 Sep 1847, 20 Jan 1921) American astronomer who trained with Maria Mitchell and succeeded her as professor and director of the Vassar College Observatory. As Mitchell had before her, Whitney championed science education the advancement of professional opportunities for women. She developed the astronomy department. Four years before her 1910 retirement, there were 160 students and eight different astronomy courses, including some of the first courses anywhere on astrophysics and on variable stars. During her tenure as director, the Observatory staff published 102 papers in major astronomical journals reporting their work on comets, asteroids, and variable stars. From 1896, photographic plates were used to study and measure star clusters.*TIS

1922 Camille Jordan (5 Jan 1838, 20 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik)

1944 James McKeen Cattell (25 May 1860, 20 Jan 1944) American psychologist who had a talent in mathematics from a young age, and accordingly applied objective, quantitative methods with his career in experimental psychology. As a university professor, he was the first in America to teach a course in statistical analysis. From 1890, he termed his investigations “mental testing,” with such goals as measuring the amount of pressure required to produce pain, or reaction time to sounds. He developed the order of merit ranking method. Fields in which he applied psychology were broad, including education, business, industry, and advertising. The ideas in Galton's eugenics theory also interested him, and he did support such concepts as sterilization of persons of lower intelligence. He originated professional directories, published scientific periodicals and founded the Science Press (1923) *TIS

1971 Jan Arnoldus Schouten (28 Aug 1883 in Nieuwer Amstel (now part of Amsterdam), Netherlands - 20 Jan 1971 in Epe, The Netherlands) worked on tensor analysis and its applications. He produced 180 papers and 6 books on tensor analysis, applying tensor analysis to Lie groups, general relativity, unified field theory, and differential equations. Influenced by Weyl and Eddington, Schouten investigated affine, projective and conformal mappings. Klein's Erlanger Programm of 1872 looked at geometry as properties invariant under the action of a group. This approach had a large influence on Schouten's approach to his topic. *SAU

2001 Crispin St. John Alvah Nash-Williams (December 19, 1932 – January 20, 2001) was a British and Canadian mathematician. His research interest was in the field of discrete mathematics, especially graph theory. *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

## Thursday, 19 January 2017

### On This Day in Math - January 19

Suppose a contradiction were to be found in the axioms of set theory.
Do you seriously believe that a bridge would fall down?
~Frank P Ramsey

The 19th day of the year; 19 is the smallest number n such that nn contains all 10 digits *Number Gossip
19 is also the smallest base ten number that is NOT a palindrome in any base $2 \leq b \leq 10$ Seems strange that it is the first palindrome (with more than one character) in Roman Numerals XIX.

19⁵ + 19² + 19¹ + 19³ + 19⁵ + 19⁶ + 19⁴ + 19⁰ = 52135640 *Jim Wilder@wilderlab

This 19 digit number is a strobogrammatic palindrome prime (rotate it 180 degrees and it still is a palindrome prime ) and 666 in the middle. 1191196166616911911, with a hat tip to INDER JEET TANEJA@IJTANEJA

EVENTS

1581 Andreas Dudith (1533–1589), mathematician and opponent of astrology, argued in a letter that observations of the comet of 1577 proved the Aristotelian explanation fallacious (for Aristotle, comets were accidental exhalations of hot air from the earth that rise in the sublunar sphere). Dudith’s use of mathematically precise observations to criticize a general physical theory of Aristotle betokens Galileo’s work ﬁfty years later. *VFR Thony Christie points out that " problem is that Hagecius, and through him Dudith, were by no means the only people to accept that parallax measurements showed comets to be supra-lunar thus contradicting the Aristotelian theory of comets, as seems to be implied here. Amongst others, both Tycho and Michael Maestlin, Kepler’s teacher, who were much more influential than Dudith, had also reached this conclusion. In fact much earlier in the sixteenth century, based on their observations of the 1530s comets, Gemma Frisius, Jean Pena, Girolamo Fracastoro and Gerolamo Cardano had already reached the same conclusion"  *RMAT  You can read his entire post here.

1669/70 Newton writes to John Collins to provide a solution to a question about evaluating a series of fractions with a common numerator and denominators in an arithmetic sequence. Newton provides an exact solution and then an approximation that converges to the true solution. [a translation is here] *Newton Project

1671 Wren and Hooke make a joint presentation on Hooke’s idea of arch design by using gravity and chain links to form an inverted dome. *Lisa Jardine, Ingenious Pursuits, pg 72

1784 A huge Montgolfiere hot air balloon carried seven passengers to a height of 3,000 feet over the city of Lyons.
At the time, the Montgolfiers believed they had discovered a new gas (they called Montgolfier gas) that was lighter than air and caused the inflated balloons to rise. In fact, the gas was merely air, which became more buoyant as it was heated. *Mary Bellis, History of Airships and Balloons, About.com

182 J J Sylvester writes a letter to support a request of two associates that Christine Ladd's fellowship be continued for another year. She had been allowed to attend the all-male Johns Hopkins in 1878.
*James Joseph Sylvester: Life and Work in Letters By Karen Hunger Parshall

1887 The Great Southern Comet of 1887 was officially discovered by astronomer John Macon Thome at Córdoba, Argentina, at which point it was located in the constellation Grus. However, correspondence from William Henry Finlay suggests that it may also have been seen from Blauwberg, South Africa, on January 18. At the time of discovery the comet had already passed perihelion a week earlier, and its closest approach to Earth had been a month earlier. A curious feature of the comet was the fact that few, if any observations were made of a cometary head or nucleus. As a result, some older astronomical texts refer to it as the "Headless Wonder". *Wik *David Dickinson ‏@Astroguyz

1894, Professor James Dewar exhibited several properties of liquid air, and produced solid air, at the Friday meeting of the Royal Institution. He had previously there exhibited, on 5 Jun 1885, liquid air obtained at the temperature of -192ºC. By Mar 1893 he had produced solid air in the form of ice. *TIS

1983 The Apple Lisa, the 1st commercial personal computer from Apple to have a graphical user interface & a mouse, is announced. *@LouisTrapani

1986 First IBM PC computer virus is released. A boot sector virus dubbed (c)Brain, reportedly by Farooq Alvi Brothers in Pakistan. *@LouisTrapani

2006 The New Horizons probe, launched on Jan. 19, 2006, with Clyde Tombaugh's ashes on board, will arrive at Pluto on July 14, 2015. *The Las Cruces Sun-News

2016 Great Internet Mersenne Prime Search reported the discovery of the new record largest prime number, 274,207,281 -1. The huge number has 22,338,618 digits. The record prime was found on a computer loaned by Profesor Curtiss Cooper at the University of Central Missouri. This is the fourth record GIMPS project prime for Dr. Cooper and his university.
In a strange twist, Dr. Cooper's computer reported the prime in GIMPS on September 17, 2015 but it remained unnoticed until routine maintenance data-mined it on January 7th. The official discovery date is January 7th, the day a human took note of the result. The perfect number associated with this new Mersenne prime is over forty-four million digits long. *GIMPS

BIRTHS

1736 James Watt (19 Jan 1736; 19 Aug 1819) Scottish instrument maker and inventor whose steam engine contributed substantially to the Industrial Revolution. In 1763 he repaired the model of Newcomen's steam engine belonging to Glasgow University, and began experiments on properties of steam. The Newcomen engine was simple in design: it acted as a pump and a jet of cold water was used to condense the steam. Watt improved on this design by adding a separate condenser and a system of valves to make the piston return to the top of the cylinder after descending. He took out a patent for the separate condenser in 1769. He later adapted the engine to rotary motion, making it suitable for a variety of industrial purposes, and invented the flywheel and the governor. *TIS

1747 Johann Elert Bode (19 Jan 1747; 23 Nov 1826) German astronomer best known for his popularization of Bode's law. In 1766, his compatriot Johann Titius had discovered a curious mathematical relationship in the distances of the planets from the sun. If 4 is added to each number in the series 0, 3, 6, 12, 24,... and the answers divided by 10, the resulting sequence gives the distances of the planets in astronomical units (earth = 1). Also known as the Titius-Bode law, the idea fell into disrepute after the discovery of Neptune, which does not conform with the 'law' - nor does Pluto. Bode was director at the Berlin Observatory, where he published Uranographia (1801), one of the first successful attempts at mapping all stars visible to the naked eye without any artistic interpretation of the stellar constellation figures.*TIS

1833 Rudolf Friedrich Alfred Clebsch (19 Jan 1833 in Königsberg, Germany (now Kaliningrad, Russia) - 7 Nov 1872 in Göttingen, Germany) Clebsch described the plane representations of various rational surfaces, especially that of the general cubic surface. Clebsch must also be credited with the first birational invariant of an algebraic surface, the geometric genus that he introduced as the maximal number of double integrals of the first kind existing on it.
Clebsch's brilliant career came to a sudden end in 1872 when he died of diphtheria. Max Noether and Brill, who were among his students at Giessen, continued his work on curves. Two volumes of his lectures on geometry were published after his death in 1876 and 1891. A second edition of part of one of these volumes, with Clebsch as joint author, was published in three parts in 1906, 1910 and 1932. *SAU

1851 Jacobus Cornelius Kapteyn (19 Jan 1851; 18 Jun 1922) Dutch astronomer who used photography and statistical methods in determining the motions and spatial distribution of stars. Such work was the first major step after the works of William and John Herschel. He tried to solve the questions of space density of stars as a function of distance from the sun, and the distribution of starts according to brightness per unit volume. Some of his results had lasting value, but some were superceded because he had failed to account for the interstellar absorption. In studies using proper motion to determine stellar distances, he discovered stellar motions are not random, as previously thought, but that stars move in two "star streams" (1904). He introduced absolute magnitude and colour index as standard concepts.*TIS

1879 Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric.
Born in Venice, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. He gained some early fame when his 1900 doctoral thesis, entitled Clifford's parallelism in elliptic spaces, was discussed in a widely-read work on differential geometry published by Bianchi in 1902.
During this time his research focused primarily on topics in mathematical analysis, especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non-Euclidean geometry, and projective geometry, among other topics. With the outbreak of World War I, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics. *Wik

1908 Aleksandr Gennadievich Kurosh (19 Jan 1908 in Yartsevo (near Smolensk), Russia - 18 May 1971 in Moscow) proved important results in Group Theory and is best-known as the author of one of the standard text-books in the subject.*SAU

1911 Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA – November 22, 1996, Water Mill, New York, USA) was an American mathematician. He is best known for his work in lattice theory.During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines.
The mathematician George Birkhoff (1884–1944) was his father.*Wik

1912 Leonid Vitalyevich Kantorovich (19 Jan 1912; 7 Apr 1986) Soviet mathematician and economist who shared the 1975 Nobel Prize for Economics with Tjalling Koopmans for their work on the optimal allocation of scarce resources. Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication Mathematical methods of organising and planning production which he published in 1939. The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed. *TIS

1917 Graham Higman (19 Jan 1917 in Louth, Lincolnshire, England - 8 April 2008 in Oxford, England) is known for his outstanding work in all aspects of the theory of groups. He published on units in group rings, the subject of his doctoral thesis, in 1940 then there was a break in his publication record during the time he worked in the Meteorological Office. His 1948 papers are on somewhat different topics, being on topological spaces and linkages. They show the influences of Henry Whitehead and, to a lesser extent, Max Newman. *SAU

DEATHS
1755 Jean-Pierre Christin (May 31, 1683 – January 19, 1755) was a French physicist, mathematician, astronomer and musician. His proposal to reverse the Celsius thermometer scale (from water boiling at 0 degrees and ice melting at 100 degrees, to water boiling at 100 degrees and ice melting at 0 degrees) was widely accepted and is still in use today.
Christin was born in Lyon. He was a founding member of the Académie des sciences, belles-lettres et arts de Lyon and served as its Permanent Secretary from 1713 until 1755. His thermometer was known in France before the Revolution as the thermometer of Lyon. *Wik

1867 Horatio Nelson Robinson, (Jan 1, 1806; Hartwick, Otsego County, New York - 19 Jan, 1867; Elbridge, New York) received only a common-school education, but early evinced a genius for mathematics, making the calculations for an almanac at the age of sixteen. A wealthy neighbor gave him the means to study at Princeton, and at the age of nineteen he was appointed an instructor of mathematics in the navy, which post he retained for ten years. He then taught an academy at Canandaigua, and afterward one at Genesee, New York, until in 1844 he gave up teaching because his health was impaired, and removed to Cincinnati, Ohio. There he prepared the first of a series of elementary mathematical text-books, which have been adopted in many of the academies and colleges of the United States. In revising and completing the series he had the assistance of other mathematicians and educators. He removed to Syracuse, New York, in 1850, and to Elbridge in 1854. His publications include "University Algebra" (Cincinnati, 1847), with a "Key" (1847) ; "Astronomy, University Edition" (1849) ; " Geometry and Trigonometry" (1850) ; "Treatise on Astronomy" (Albany, 1850) ; "Mathematical Recreations" (Albany, 1851); "Concise Mathematical Operations" (Cincinnati, 1854); "Treatise on Surveying and Navigation" (1857), which, in its revised form, was edited by Oren Root (New York, 1863); "Analytical Geometry and Conic Sections" (New York, 1864) ; "Differential and Integral Calculus" (1861), edited by Isaac F. Quinby (l868). *famousamericans.net

1878 Henri-Victor Regnault (21 Jul 1810, 19 Jan 1878) French chemist and physicist noted for his work on the properties of gases. His invaluable work was done as a skilful, thorough, patient experimenter in determining the specific heat of solids, liquids, gases, and the vapour-tensions of water and other volatile liquids, as well as their latent heat at different temperatures. He corrected Mariotte's law of gases concerning the variation of the density with the pressure, determined the coefficients of expansion of air and other gases, devised new methods of investigation and invented accurate instruments. Two laws governing the specific heat of gases are named after him. *TIS

1913 Robert Gauss of Denver and his brother Charles H. Gauss of Saint Louis both died on this date. They are grandsons of the mathematician Carl Friedrich Gauss *VFR (Robert died within a few hours of his brother, Charles Henry Gauss. Both died from heart disease.)The names of all the grandchildren of Gauss were listed in a letter from Robert to Felix Klein regarding the biography of Gauss which was being prepared:
P. S. The names and the present places of residence of the grandchildren of Carl Friedrich Gauss, who were born in the United States and are now living, are as follows:
The children of Eugene Gauss: Charles Henry Gauss, St. Charles, Missouri; Robert Gauss, Denver, Colorado; Albert F. Gauss, Los Angeles, California.
The children of William Gauss: Charles Friedrich Gauss, St. Louis, Missouri; Oscar W. Gauss, Greeley, Colorado; Mary Gauss, St. Louis, Missouri; William T. Gauss, Colorado Springs, Colorado; Joseph Gauss, St. Louis, Missouri.
The only one of the great-grandchildren of Carl Friedrich Gauss born in the United States, who has ever visited Germany is Helen W. Gauss, daughter of William T. Gauss of Colorado Springs, Colorado. while in Germany last year she was present at the dedication of the Gauss tower on the Hohenhagen.

1930 Frank Plumpton Ramsey (22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik

1954 Theodor Franz Eduard Kaluza (9 November 1885, Wilhelmsthal, today part of Opole – 19 January 1954, Göttingen) was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in string theory. *Wik

2007 Asger Hartvig Aaboe (April 26, 1922 – January 19, 2007) was a historian of the exact sciences and mathematician who is known for his contributions to the history of ancient Babylonian astronomy. He studied mathematics and astronomy at the University of Copenhagen, and in 1957 obtained a PhD in the History of Science from Brown University, where he studied under Otto Neugebauer, writing a dissertation "On Babylonian Planetary Theories". In 1961 he joined the Department of the History of Science and Medicine at Yale University, serving as chair from 1968 to 1971, and continuing an active career there until retiring in 1992. In his studies of Babylonian astronomy, he went beyond analyses in terms of modern mathematics to seek to understand how the Babylonians conceived their computational schemes. *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