On This Day in Math - December 20

 

 

Our passion for learning is our tool for survival.
Somewhere, something incredible is waiting to be known.

~Carl Sagan

The 354th day of the year; 354 is the sum of the first four fourth powers 

and is also the sum of three distinct primes. (It is also the solution to one version of an unsolved recreational math problem called the Postage Stamp Problem, or sometimes Frobenius problem)

354 is the smallest number whose sum of its distinct prime factors is a cube, 2 + 3 + 59 = 64

 Of all the Primes less than 10^10, the largest difference between two consecutive primes is 354. *Derek Orr

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EVENTS

1587 In Viviani's biography of Galileo he tells of how as a young student of 18 in 1581 Galileo made his first discovery about pendulums which would later lead to his design just before his death of a pendulum clock.

"one afternoon performing his devotions in the Cathedral of Pisa, and in full view of Maestro Possenti's beautiful bronze lamp which hung (and still hangs) from the roof of the nave. In order to light it more easily the attendant drew it towards him, and then let it swing back. Galileo at first observed this simple incident, as thousands of other worshipers had done before him and have done since, i.e. in a casual way, but quickly his attention became riveted to the swinging lamp. The oscillations, which were at first considerable became gradually less and less, but, notwithstanding, he could see that they were all performed in the same time, as he was able to prove by timing them with his pulse the only watch he possessed!"

It is a beautiful story of a brilliant young mind who would go on to greatness, but J. J. FAHIE in his biography of Galileo points out:

"Whether this be only a pretty fable, like that of Newton and the apple, cannot now be decided, but it is, at least, certain that Possenti's lamp was not the one which Galileo observed, since it was not made until 1587, and was only hung in its present place on the 2Oth December in that year."

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1623 Wilhelm Schickard, in a letter to Kepler, described his calculating machine. *Dauben, A Selective Bibliography, p. 251
Only 3 documents about this machine have been found till now—two letters from Schickard to Kepler, and a sketch of the machine with instructions to the mechanician. I have also seen the date given as  February 25th, 1624, which may be more accurate.  *http://history-computer.com

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1883 On the night before J J Sylvester's departure from Johns Hopkins his friends hosted a gala in his honor at Hopkins Hall.

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In 1900, Michel Giacobini in France discovered a comet, which was rediscovered by a German, Ernst Zinner, on 23 Oct 1913, and since named the Giacobini-Zinner comet. It returns to the vicinity of the earth every six and two-thirds years. This comet became the first to be visited by a spacecraft. On 11 Sep 1985, the International Cometary Explorer (ICE) flew through its gas tail, 7,800-km downstream from the nucleus, at a speed of 21 km/sec. The nucleus was estimated to be 2.5-km across at its widest diameter. Instruments detected carbon monosulfide and hydroxyl molecules in the comet. The comet is the progenitor of the Draconid meteor shower, visible annually in early October, which produced intense meteor displays in 1933 and 1946.*TIS The most recent was on shower peaked on Oct 8, 2011.

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1906 Nature publishes a letter from Francis Galton on "Cutting a round cake on scientific principles." A Numberphile video by Alex Bellos explaining the method is here.

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In 1907, the first U.S. scientist to receive the Nobel Prize was Albert Michelson, a German-born ( actually born in Strzelno, Provinz Posen in the Kingdom of Prussia which is now part of Poland) American physicist who received the Nobel Prize for Physics "for his optical precision instruments and the spectroscopic and metrological investigations." He designed the highly accurate Michelson interferometer and used it to accurately measure the speed of light and establish it as a fundamental constant. With Edward Morley, he also used it in an attempt to measure the velocity of the earth through the ether (1887), yielding null results that eventually led Einstein to his theory of relativity. He measured the standard meter bar in Paris to be 1,553,163.5 wavelengths of the red cadmium line (1892-3) *TIS

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1910 New Zealand born physicist Ernest Rutherford made his seminal gold foil experiment which led to first insight about the nature of the inner structure of the atom and to the postulation of Rutherford's concept of the "nucleus. He had already received the 1908 Nobel Prize in Chemistry for demonstrating that radioactivity was the spontaneous disintegration of atoms. *Yovista

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1943 Norman Bel Geddes to Designs ASSC Machine Cover:
Thomas Watson Jr. informs Harvard University President James B. Conant that Norman Bel Geddes would be designing the cover of the Harvard Mark I computer. Bel Geddes was an American industrial designer who also worked on such things as Philco radio cabinets and a Graham Page car. He was deeply interested in the future, illustrating a book in 1932 that described, among other things, a huge passenger airplane with public lounges and an exercise center. Bel Geddes also desgined the GM pavilion at the 1939 World's Fair.*CHM

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1949 N. J. Woodland and Bernard Silver filed a patent application for "Classifying Apparatus and Method", in which they described both the linear and bullseye printing patterns, as well as the mechanical and electronic systems needed to read the code. The patent was issued on 7 October 1952 as US Patent 2,612,994. In 1951, Woodland moved to IBM and continually tried to interest IBM in developing the system. The company eventually commissioned a report on the idea, which concluded that it was both feasible and interesting, but that processing the resulting information would require equipment that was some time off in the future.
In 1952 Philco purchased their patent, and then sold it to RCA the same year.*Wik

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In 1951, at 1:50 p.m., the first electricity ever generated by atomic power began flowing from the EBR-1 turbine generator when Walter Zinn and his Argonne National Laboratory staff of scientists brought EBR-1 to criticality (a controlled, self-sustaining chain reaction) with a core about the size of a football. The reactor was started up and the power gradually increased over several hours. The next day, Experimental Breeder Reactor-1 generated enough electricity to supply all the power for its own building. Additional power and core experiments were then conducted until its decommissioning in Dec 1963. Construction began in 1949, between Idaho Falls and Arco, Idaho. Today, EBR-1 is a Registered National Historic Landmark.*TIS

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BIRTHS
1494 Oronce Fine (20 Dec 1494 in Briançon, France
- 8 Aug 1555 in Paris, France) was a French mathematician who published a major work on mathematics and astronomy. Before being awarded his medical degree, Fine had edited mathematics and astronomy books for a Paris printer. Among the texts which he edited were Peurbach's Theoricae Novae Planetarum, which presented Ptolemy's epicycle theory of the planets, and Sacrobosco's Tractatus de Sphaera, a book on astronomy in four chapters. The first book which Fine authored himself was published in 1526 and it was on the equatorium, an instrument which Fine was very interested in and which he worked on throughout his life, writing four further texts about it. The instrument can be used to determine the positions of the planets.*SAU

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1648 Thommaso Ceva (20 Dec 1648; 3 Feb 1737) Italian mathematician, poet, and brother of the mathematician Giovanni Ceva. At the age of fifteen he entered the Society of Jesus. His education was entirely within the Jesuit Order and he obtained a degree in theology. His first scientific work, De natura gravium (1669), dealt with physical subjects, such as gravity and free fall, in a philosophical way. Tommaso Ceva's mathematical work is summed up in Opuscula Mathematica (1699) which examines geometry (geometric-harmonic means, the cycloid, and conic sections), gravity and arithmetic. He also designed an instrument to divide a right angle into a given number of equal parts. He gave the greater part of his time to writing Latin prose. His poem Jesus Puer was translated into many languages. *TIS

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1838 Edwin Abbott Abbott (20 Dec 1838, 12 Oct 1926) His most famous work was Flatland: a romance of many dimensions (1884) which Abbott wrote under the pseudonym of A Square. The book has seen many editions, the sixth edition of 1953 being reprinted by Princeton University Press in 1991 with an introduction by Thomas Banchoff​. Flatland is an account of the adventures of A Square in Lineland and Spaceland. In it Abbott tries to popularise the notion of multidimensional geometry but the book is also a clever satire on the social, moral, and religious values of the period.
More recently, in 2002, an annotated version of Flatland has been produced with an introduction and notes by Ian Stewart who gives extensive discussion of mathematical topics related to passages in Abbott's text. *SAU
The Kindle edition of Flatland is available for less than $2.00 Flatland: A Romance of Many Dimensions [Illustrated] and the Stewart version is only a little more:

In a bold statement of personal opinion I add: This book should be read by every teacher and every student of mathematics.

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1843 Paul Tannery (20 Dec 1843 in Mantes-la-Jolie, Yvelines, France - 27 Nov 1904 in Pantin, Seine-St Denis, France) His main contributions were to the history of Greek mathematics and to the philosophy of mathematics. He published a history of Greek science in 1887, a history of Greek geometry in the same year, and a history of ancient astronomy in 1893.
Tannery did work of great importance as an editor of famous mathematics texts. He edited the work of Fermat in three volumes (jointly with C Henry) between 1891 and 1896. In addition he edited the work of Diophantus in two volumes (1893-95). He was an editor of the twelve volume complete works of Descartes Oeuvres de Descartes (1897-1913).
Tannery became so skilled in using Greek numerals in his historical work that he believed that they had certain advantages over our present system. *SAU

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1875 Francesco Cantelli (20 Dec 1875 in Palermo, Sicily, Italy
- 21 July 1966 in Rome, Italy)Cantelli's work in astronomy involved statistical analysis of data and his interests turned more towards the statistical style of mathematics and to applications of probability to astronomy and other areas. In particular he became interested in actuarial and social applications of probability theory. In 1903 took a job as an actuary at the Istituti di Previdenza where he undertook research into probability theory publishing some important papers, some which we mention below. He founded the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics. He edited the journal of the Institute Giornale dell'Istituto Italiano degli Attuari from 1930 to 1958 during which time it became one of the leading journals in its field. *SAU

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1876 Walter (Sydney) Adams (20 Dec 1876; 11 May 1956) was an American astronomer who is best known for his spectroscopic studies of sunspots, the rotation of the Sun, the velocities and distances of thousands of stars, and planetary atmospheres. He found (with Arnold Kohlschütter) that the relative intensities of stallar spectral lines depend on the absolute luminosities of the star, which in turn provides a spectroscopic method of determining stellar distances.By this method, he measured distances to hundreds of giant and main sequence stars. Adams identified Sirius B as the first white dwarf star known, and his measurement of its gravitational redshift was confirming evidence for the general theory of relativity. He was director of Mount Wilson (1923-46).*TIS

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1901 Robert Jemison Van de Graaff (20 Dec 1901; 16 Jan 1967) American physicist and inventor of the Van de Graaff generator, a type of high-voltage electrostatic generator that can be used as a particle accelerator in atomic research. The potential differences achieved in modern Van de Graaff generators can be up to 5 MV. It is a principle of electric fields that charges on a surface can leap off at points where the curvature is great, that is, where the radius is small. Thus, a dome of great radius will inhibit the electric discharge and added charge can reach a high voltage. This generator has been used in medical (such as high-energy X-ray production) and industrial applications (sterilization of food). In the 1950s, Van de Graaff invented the insulating core transformer able to produce high voltage direct current.*TIS

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DEATHS
1836 Johann Christian Martin Bartels​ (12 August 1769 – 7/20 December 1836) was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan.*Wik

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1891 George Bassett Clark (14 Feb 1827, 20 Dec 1891) Elder son in the American family of telescope makers and astronomers, Alvan Clark & Sons of Cambridge, Mass., who figured importantly in the great expansion of astronomical facilities which occurred during the second half of the 19th century. Before the family business began, George made a telescope in 1844 out of the melted-down brass of his school's broken dinner bell. His father, Alvan Clark, was at the time an established portrait painter, but his son's interest also spurred his father to begin making refractor telescopes. (Refractor telescopes use paired lenses to focus light.) The father taught himself to be a master optician, and eventually in business with his sons made the finest refractor telescopes of their time including five of the world's largest.*TIS

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1962 Emil Artin (3 Mar 1898; 20 Dec 1962 at age 64) Austro-German mathematician who worked in algebraic number theory, made a major contribution to field theory, and stated a law of reciprocity which included all previously known laws of reciprocity (1927). He also worked on the theory of braids (1925), and on rings with the minimum condition on right ideals, now called Artinian rings (1944). Artin has the distinction of solving (1927) one of the famous 23 problems previously posed by Hilbert in 1900. With his Jewish wife, he left Nazi Germany in 1937, and worked at universities in the U.S. until 1956, when he returned to his home country. *TIS He solved Hilbert’s seventeenth problem in 1927. *VFR (Can a multivariate polynomial that only has non-negative values over the reals be represented as a sum of squares of rational functions? Artin proved it could, An algorithm to do so was found by Charles Delzell.)

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1984 Max Deuring (9 December 1907, Göttingen, Germany – 20 December 1984, Göttingen, Germany) was a mathematician. He is known for his work in arithmetic geometry, in particular on elliptic curves in characteristic p. He worked also in analytic number theory.
Deuring graduated from the University of Göttingen in 1930, then began working with Emmy Noether, who noted his mathematical acumen even as an undergraduate. When she was forced to leave Germany in 1933, she urged that the university offer her position to Deuring. In 1935 he published a report entitled Algebren ("Algebras"), which established his notability in the world of mathematics. He went on to serve as Ordinarius at Marburg and Hamburg, then took a position as ordentlicher Lehrstuhl at Göttingen, where he remained until his retirement.*Wik

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1988 Elizabeth Scott (November 23, 1917 – December 20, 1988) was an American mathematician specializing in statistics.
Scott was born in Fort Sill, Oklahoma. Her family moved to Berkeley, California when she was 4 years old. She attended the University of California, Berkeley where she studied mathematics and astronomy. There were few options for further study in astronomy, as the field was largely closed to women at the time, so she completed her graduate studies in mathematics. She received her Ph.D. in 1949, and received a permanent position in the Department of Mathematics at Berkeley in 1951.
She wrote over 30 papers on astronomy and 30 on weather modification research analysis, incorporating and expanding the use of statistical analyses in these fields. She also used statistics to promote equal opportunities and equal pay for female academics.
In 1957 Elizabeth Scott noted a bias in the observation of galaxy clusters. She noticed that for an observer to find a very distant cluster, it must contain brighter than normal galaxies and must also contain a large number of galaxies. She proposed a correction formula to adjust for (what came to be known as) the "Scott effect".
The Committee of Presidents of Statistical Societies awards a prize in her honour to female statisticians.*Wik

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1993 W(illiam) Edwards Deming (14 Oct 1900, 20 Dec 1993) was an American statistician, the father of "Total Quality Management." After WW II, he contributed to Japan's economic recovery by recommending statistical methods of quality control in industrial production. His method embraced carefully tallying product defects, examining their causes, correcting the problems, and then tracking the results of these changes on subsequent product quality. In his career before the war, he had developed statistical sampling techniques that were first used in the 1940 U.S. census. From the 1980's in the U.S. Deming continued to teach quality control through the statistical control of manufacturing processes for companies such as Ford, Xerox, and GM.*TIS

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1996 Carl Edward Sagan 9 Nov 1934, 20 Dec 1996) U.S. astronomer and exobiologist and writer of popular science books. His studies were far-ranging. He coauthored a scientific paper about the dangers of nuclear winter. He researched the atmosphere of Venus, seasonal changes on Mars, surface conditions on planets, and created popular interest in the universe with his television series Cosmos. Sagan was a leading figure in the search for extraterrestrial intelligence. He urged the scientific community to listen with large radio telescopes for signals from intelligent extraterrestrial lifeforms. Sagan also played a prominent role in the U.S. space program, with his involvement in the Mariner, Viking, and Voyager spacecraft expeditions. *TIS  (and may I remind you all, in Carl's honor, that "we are all star-stuff."

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2002 Grote Reber (22 Dec 1911, 20 Dec 2002) U.S. amateur astronomer and radio engineer who self-financed and built the first radio telescope. He pioneered the new field of radio astronomy, and was the first to systematically study the sky by observing non-visible radiation. After reading about Jansky's discovery (1932) of natural radio emissions from space, Reber constructed a 9-meter dish antenna in his back yard and built three different detectors before finding 160 MHz signals (1939). In 1940 and 1944 he published articles titled Cosmic Static in the Astrophysical Journal. He was the first to express received radio signals in terms of flux density and brightness, first to find evidence that galactic radiation is non-thermal, and first to produce radio maps of the sky (1941).*TIS

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2005  Raoul Bott,(September 24, 1923 – December 20, 2005) was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. *Wik

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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

A Brief History of Blackboards and Slates

My career in education began with the use of chalk and a blackboard, transitioned into a room with only dry erase marker boards, and finished in a class with only an electronic smart board. Except for the few times I was inconvenience by a projector bulb picking a bad moment to go bad (and if a chalk board had been available, I would have been grateful) I loved the improvements that each transition brought to my ability to more effectively convey my ideas.
But for the period from 1800 to 2000 few things were as ubiquitous in a mathematics classroom as the blackboard. Today modern "white boards" may have taken their place in many institutions, or even an electronic version called a smart board; but board work still seems to be a part of the current classroom procedure. In a recent talk, Keith Devlin began by saying, "I step back from the (now largely metaphorical) blackboard and .. "
Whatever the present state of its demise, the classic chalkboard was so common a classroom presence that it was part of a frequently repeated gag sequence on the popular Simpsons cartoon series.(Not sure if the use shown above could be termed "educational")

It appears that the blackboard first came into American education around 1800. The National Museum of American History website on colonial education says,:

"Mathematics teachers with ties to England and France introduced blackboards into the United States around 1800. By the 1840s, these erasable surfaces were used for teaching a wide range of subjects in elementary schools, colleges, and academies. The Massachusetts educator William A. Alcott visited over 20,000 schoolhouses. “A blackboard, in every school house," he wrote, "is as indispensably necessary as a stove or fireplace."

James Pillan, a Scottish teacher and education reformer is often cited as the "inventor" of the blackboard, but this seems to be a misunderstanding based on a letter from Pillan which appeared in Jeremy Bentham's Chrestomathia (1815). It was entitled Successful application of the new system to language-learning, and dated 1814; it mentions the use of chalk and blackboard in teaching geography. But Pillan only began teaching in 1810, almost a decade after the board made its way to America, and as we shall see, literally hundreds of years too late to "invent" the chalkboard.  He may, however, be the inventor of colored chalk. He is reported to have had a recipe with ground chalk, dyes and porridge.

Blackboards and slates were seemingly used well before any of the previous examples in musical study. In Composers at Work, author Jessie Ann Owens devotes several pages to the existence of several types of slate and wood "cartella" which were used to write out musical ideas. She describes the discoveries of these with five or ten line staves dating to the 16th century. Much larger wall size examples seem to have been used but have only been confirmed by iconography. The book includes an image from a woodcut by Hieronymus Holtzel of Nuremberg in 1501.

In America they seem to have very quickly become and essential part of daily school life. [From a web page of Prof. Rickey]

Perhaps no one method has so influenced the quality of the instruction of the cadets as the blackboard recitations. Major Thayer (Superintendent from 1817) insisted on this form, although old records show that it was introduced at West Point by Mr. George Baron, a civilian teacher, who in the autumn of 1801 gave to Cadet Swift "a specimen of his mode of teaching at the blackboard." Today it is the prominent feature in Academic instruction. [Quoted from Richardson 1917, p. 25] There is indication that the blackboard was used in a few schools in the US before it was used at USMA. See Charnel Anderson, Technology in American Education, 1650-1900, published by the
US Dept of Health, Education, and Welfare 1961(I have read this document and he credits Frenchman Claude Crozet with introducing the blackboard to the USMA and that he built and painted one to teach his classes.  It may well be that after Baron left under a cloud in 1802, the method was not used by other teachers there until Crozet arrived in 1817. 

Thayer had visited the Ecole Polytechnique in France to study their methods and was heavily influence by the "French" method when he became superintendent, even to the point of extending instruction in French so that the students could better master the French texts in advanced math.. I can't find an early example of the use of chalk or slate in France, but they seem to have been very much a part of the educational process by the time Galois threw an eraser at his examiner in July of 1829.

Galois was not the only one who reacted negatively to some of the innovations in education connected to the blackboard. At Yale, there were two "rebellions" in which students refused to accept some changes in testing practice. Here is a paragraph from Stories in Stone: Travels Through Urban Geology By David B. Williams.

This "rebellion" occurred in 1830, with 43 rebels expelled, including Andrew Calhoun, the son of John C Calhoun, and Alfred Stillé, who eventually did get a degree from Yale and another from  U of Pennsylvania before he became a somewhat famous doctor, and one of the first to distinguish Typhus from Typhoid fever. His rebellious side wasn't limited to college however, as he refused to accept germ theory and laboratory medicine. There had been a similar event in 1825 at Yale, but those students recanted and were readmitted.

One of the earliest mentions of blackboards I have found has nothing to do with education, however. It seems that a custom developed in London's financial district in the later part of the 19th century to list the names of debtors on a blackboard to shame them into paying, and it seems to have persisted for a long time. Here is a description of the practice from Chronicles and Characters of the Stock Exchange
By John Francis, Daniel Defoe; printed in 1850.

From Wikipedia I learned that the Oxford English Dictionary provides a citation from 1739, to write "with Chalk on a black-Board". I know it is common in England for Pubs to advertise with a blackboard outside their doors on the sidewalk, but have no idea how far back this idea originated.
 
Prior to the use of blackboards students learned their early lessons from an object called a hornbook. Here is a description of one from the Blackwell Museum webpage at Northern Illinois University

Paper was pretty expensive once and hornbooks were made so children could learn to read without using a lot of paper. A hornbook was usually a small, wooden paddle with just one sheet of paper glued to it. But because that paper was so expensive, parents and teachers wanted to protect it. So they covered the paper with a very thin piece of cow's horn. The piece of cow's horn was so thin, you could see right through it. That's why these odd books were called "hornbooks."

Hornbooks seem to have been totally imported from England into the American Colonies, and almost all had a cross on the upper left, with the Lord's Prayer at bottom.  The American Revolution seemed to have almost completely eliminated the import of Hornbooks in rejection of all things English at the time.  The education conversion to the blackboard seems to have finished the hornbooks very quickly afterward judging from this quote from the OED about Hornbooks, (a1842 HONE in A. W. Tuer Hist. Horn-Bk. I. i. 7) " A large wholesale dealer in..school requisites recollects that the last order he received for Horn-books came from the country, about the year 1799. From that time the demand wholly ceased..In the course of sixty years, he and his predecessors in business had executed orders for several millions of Horn-books".
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Early blackboards were usually made of wood, (but some may have been made of paper mache') and painted with many coats as true slate boards were very expensive. Schools purchased large pots of "slate paint" for regular repainting of the boards. The Earliest quotes from the OED date to 1823.

1823 PILLANS Contrib. Cause Educ.    A large black board served my purpose. On it I wrote in chalk. 1835 Musical Libr. Supp., Aug. 77 The assistant wrote down the words..on a blackboard. 1846 Rep. Inspect. Schools I. 147 The uses of the black board are not yet fully developed.

However under "slates" I found other  earlier uses. In "1698 FRYER Acc. E. India & P. 112 A Board plastered over, which with Cotton they wipe out, when full, as we do from Slates or Table-Books" which indicates that boards covered with Plaster or other materials were used to write upon much earlier than the earliest use of "blackboards" in classrooms.

Another early use of slates is given in David E. Smith's Rara arithmetica of a book printed in 1483 in Padua of the arithmetic of Prosdocimo containing a mention of the use of a slate. This led Smith to conclude that at this time the merchants would actually erase and replace numbers (as was originally done by the Hindu mathematicians working in their sand trays) in division rather than showing the cross-outs that distinguish the galley method of division after it was adopted to use on paper.

The very earliest claim for slates I have found is of use in the 11th century. A work called Alberuni's Indica (Tarikh Al-Hind), "They use black tablets for the children in the schools, and write upon them along the long side, not the broadside, writing with a white material from the left to the right."

Chalkboards became so important for teaching that teachers in the 19th century sometimes went to extremes to create one. In Glen Allen, Virginia; a school is named for Elizabeth Holladay, a pioneer teacher who started the first pAublic school in the Glen Allen area of Henrico County at her home in 1886. On a note about the history of the school it says she had, "Black oilcloth tacked to another part of the shipping crate served as a blackboard." 

The slate was used even after paper became a relatively commonplace item. Many school histories report the use of slates into the 20th Century. This use may have been significant. The Binney & Smith company, better known to many for their creation of the Crayola Crayon, began the production of slate pencils, for writing on slate, in the year 1900. As an aside, they also won a Gold Medal at the St. Louis Fair.

Slate pencils prior to 1800 were known as Dutch Pencils in England, but increased slate mining in Wales around 1800 led to more domestic production, and use of slates, and slate pencils in England.   In the journal Australian Historical Archaeology, (2005) Peter Davies reports that in the excavation of a site called Henry Mill that was only operational from 1904 until around 1930 they found 30 slate pencils, remnants of four slates, and a single graphite pencil core. 

In "Slates Away!": Penmanship in Queensland, Australia, John Elkins, who started primary school in 1945, writes that he used slates commonly until around the third year of school.

I think in Prep 1 that we had some paper to write on with pencils, but my memory of the routine use of slates is much more vivid. Each slate was framed in wood and one side was inscribed with lines to guide the limits for the upper and lower extremities of letters. The slate "pencils" were made of some pale gray mineral softer than slate which had been milled into cylinders some one-eighth of an inch in diameter and inserted into metal holders so that about an inch protruded.
Each student was equipped with a small tobacco tin in which was kept a damp sponge or cloth to erase the marks. Sharpening slate pencils was a regular task. We rubbed them on any suitable brick or concrete surface in the school yard. Teachers also kept a good supply of spares, all writing materials and books being provided by the school. It is possible that the retention of slates stemmed from the political imperative that public education should be free.

Slates were advertised in newspapers in the US as early as 1737. Slates, as indicated above, show up as commonplace in quotes from the OED as early as 1698. It seems they may have been used for some artistic or educational purposes as early as the end of the 15th Century. In the famous painting of Luca Pacioli,
Ritratto di Frà Luca Pacioli, Pacioli is shown drawing on a slate to copy an example from Euclid in the open book before him. The closed book, which has the dodecahedron upon it, is supposedly Pacioli's Somma di aritmetica which was written in 1494.

In the Dec 2003 issue of Paradigm, the Journal of the Textbook Colloquium, is an article by Nigel Hall titled, "The role of the slate in Lancasterian schools as evidenced by their manuals and handbooks". A couple of snips from the article appear below:

The Oxford English Dictionary gives as its first citation for slate being used as a writing tool a quotation from Chaucer’s Treatise on the Astrolabe written about 1391. Whether usage began around this time or had begun much earlier is unknown, although as a technology it shared many characteristics with the wax tablet, used extensively from before the time of the Greeks until the 1600s in Europe, and even surviving in some usages until the early twentieth century (Lalou, 1989). Knowledge of the use of slate for writing after Chaucer is limited until one reaches the second half of the eighteenth century. The mathematician Digges (1591) refers to writing on slates and in the new colony of America an inventory (Plymouth Colony Archive, n.d.) made on 24 October 1633 of the possessions of the recently deceased Godbert and Zarah, noted among many items, ‘A writing table of slate’ (table here being a tablet of slate).

Hall goes on to suggest that, in fact, the use of slates may not have been very common in England until the end of the 18th Century because reading (beginning with hornbooks) was much more commonly taught than writing. He credits Lancaster for the promotion of slates for writing and math, but suggests that the slate was a principal element in the "monotorial system" in which more advanced students taught the lower group. An illustration showing the use of slates and the student monitor below is taken from the article. [See the full article here]

The blackboard was extended to some specialty uses as well. A "Slated Globe" was advertised in The New York Teacher, and the American Educational Monthly, Volume 6 in 1869 for use in spherical geometry and geography classes. A four inch diameter globe sold for $1.50

I also recently found this image on a Wikipedia article about Benjamin Pierce. He seems to be standing beside a stand with a spherical blackboard resting on it, but can not be sure that is what it was.

In an 1899 article for the proceedings of the Society for the Promotion of Engineering Education, Professor Arthur E Haynes of the University of Minnesota had an article for, "The Mounting and Use of a Spherical Blackboard, which included this image.

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Recently, J F Ptak posted an article on his Science Books blog from Scientific American, (Sep 13, 1890) about a pen-tip eraser for slate pens meant to be wetted to erase the marks on a slate by the pen.  The article described the invention with credit to the inventor, Mrs Emma C. Hudson

On This Day in Math - December 19

 

Nine Point Circle

If equations are trains threading the landscape of numbers,
then no train stops at pi.

~Richard Preston

The 353rd day of the year; 353 is the last day of the year that is a palindromic prime. It is the first multi-digit palindromic prime with all prime digits.

Also, it is the smallest number whose 4th power is equal to the sum of four other 4th powers, as discovered by R. Norrie in 1911: 353⁴ = 30⁴ + 120⁴ + 272⁴ + 315⁴. *Wik *R. Norrie, University of St. Andrews 500th Anniversary Memorial Volume, Edinburgh, 1911.

353 = 2^4 + 3^4 + 4^4 *Prime Curios

and similarly, 3^4 + 5^4 + 3^4 = 787, another palindromic prime.  *Prime Curios

EVENTSOn 19th December 1705 the demonstrator of experiments at the Royal Society turned the crank on the apparatus, that he had constructed especially for this demonstration, setting an evacuated glass globe in rotation against which he pressed a woollen cloth. There was “quickly produced a beautiful Phaenomenon, viz, a fine purple light and vivid to that degree, that all the included Apparatus was easily and distinctly discernable by the help of it.” *Renaissance Mathematicus

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1765 Joseph Priestley, visiting in London, is introduced to Benjamin Franklin, and other members of the "Honest Whigs" by John Canton in a popular coffee house in the shadow of St Pauls cathedral. Priestly had presented himself to Canton with a letter of introduction from Priestley's friend and rector at Warrington Academy that read, "You will find a benevolent, sensible man, with a considerable sense of learning. If Dr. Franklin be in Town,I believe Dr. Priestley would be glad to be made known of him." Before the night was over, Priestly had acquired their support for a book about their mutual efforts in the discovery of electricity. In 1767, the 700-page The History and Present State of Electricity was published to positive reviews. The first half of the text is a history of the study of electricity to 1766; the second and more influential half is a description of contemporary theories about electricity and suggestions for future research. Priestley reported some of his own discoveries in the second section. *Stephen Johnson, The Invention of Air

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1894 Karl Pearson introduced the Pearson family of densities. [Springer’s 1985 Statistics Calendar] *VFR

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1894 Karl Pearson first uses the term "Binomial Distribution" in Contributions to the Mathematical Theory of Evolution---II. Skew Variation in Homogeneous Material, Received by the Royal Society of London December 19, 1894, It would be read on January 24, 1895,” Philosophical Transactions of the Royal Society of London for the year MDCCCXCV. A footnote has: “This result seems of considerable importance, and I do not believe it has yet been noticed. It gives the mean square error for any binomial distribution, and we see that for most practical purposes it is identical with the value npq−−−√$\sqrt{npq}$ , hitherto deduced as an approximate result, by assuming the binomial to be approximately a normal curve.” Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

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1908 Scientific American offered a $500 prize for a simple explanation of the fourth dimension. They were surprised to receive a huge number of serious responses from around the globe. Many mentioned Charles Hinton, who was popularizing the idea of four-space (he invented the term tesseract, and the baseball pitching machine) but not one associated the fourth dimension with time, and none mentioned Einstein or his work.
* By Michio Kaku , Hyperspace: a scientific odyssey through parallel universes, time warps, and ... pg 75

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In 1958, the first known radio broadcast from outer space was transmitted. President Eisenhower's voice issued a Christmas greeting from a pre-recorded tape on a recorder aboard an orbiting space satellite. His full message was, "This is the President of the United States speaking. Through the marvels of scientific advance, my voice is coming to you from a satellite circling in outer space. My message is a simple one. Through this unique means I convey to you and all mankind America's wish for peace on earth and good will to men everywhere." The broadcast came from the first experimental satellite, Project SCORE, which had been launched two days earlier. The battery-operated 132 MHz all vacuum tubes transmitter had an 8-W output.*TIS

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In 1974, the pioneering Altair 8800 microcomputer was first put on sale in the U.S. as a do-it-yourself computer kit, for $397$\mathrm{\$}397$. It used switches for input and flashing lights as a display. Ed Roberts founded Micro Instrumentation and Telemetry Systems (MITS) to market his product that used the 8800 microprocessor. The demand for the $395.00$\mathrm{\$}395.00$ machine exceeded the manufacturer's wildest expectations. The Altair 8800 was featured on the cover of the Jan 1975 issue of Popular Electronics. The first commercially successful personal computer, the Commodore PET, which integrated a keyboard and monitor in its case, came out in early 1977. The Apple II followed later that year. *TIS

*PCMag,com

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BIRTHS
1615 Sir Charles Scarborough MP FRS FRCP (19 December 1615 – 26 February 1693) was an English physician and mathematician.
He was born in St. Martin's-in-the-Fields, London in 1615, the son of Edmund Scarburgh, and was sent to St. Paul's School, whence he proceeded to Caius College, Cambridge, and educated at St Paul's School, Gonville and Caius College, Cambridge (BA, 1637, MA, 1640) and Merton College, Oxford (MD, 1646). While at Oxford he was a student of William Harvey, and the two would become close friends. Scarborough was also tutor to Christopher Wren, who was for a time his assistant.
Following the Restoration in 1660, Scarborough was appointed physician to Charles II, who knighted him in 1669; Scarborough attended the king on his deathbed, and was later physician to James II and William and Mary. During the reign of James II, Scarborough served (from 1685 to 1687) as Member of Parliament for Camelford in Cornwall.
Scarborough was an original fellow of the Royal Society and a fellow of the Royal College of Physicians, author of a treatise on anatomy, Syllabus Musculorum, which was used for many years as a textbook, and a translator and commentator of the first six books of Euclid's Elements (published in 1705). He also was the subject of a poem by Abraham Cowley, An Ode to Dr Scarborough.
Scarborough died in London in 1693. He was buried at Cranford, Middlesex, where there is a monument to him in the parish church erected by his widow. *Wik

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1714 John Winthrop (December 19, 1714 – May 3, 1779) was the 2nd Hollis Professor of Mathematics and Natural Philosophy in Harvard College. He was a distinguished mathematician, physicist and astronomer, born in Boston, Mass. His great-great-grandfather, also named John Winthrop, was founder of the Massachusetts Bay Colony. He graduated in 1732 from Harvard, where, from 1738 until his death he served as professor of mathematics and natural philosophy. Professor Winthrop was one of the foremost men of science in America during the 18th century, and his impact on its early advance in New England was particularly significant. Both Benjamin Franklin and Benjamin Thompson (Count Rumford) probably owed much of their early interest in scientific research to his influence. He also had a decisive influence in the early philosophical education of John Adams, during the latter's time at Harvard. He corresponded regularly with the Royal Society in London—as such, one of the first American intellectuals of his time to be taken seriously in Europe. He was noted for attempting to explain the great Lisbon earthquake of 1755 as a scientific—rather than religious—phenomenon, and his application of mathematical computations to earthquake activity following the great quake has formed the basis of the claim made on his behalf as the founder of the science of seismology. Additionally, he observed the transits of Mercury in 1740 and 1761 and journeyed to Newfoundland to observe a transit of Venus. He traveled in a ship provided by the Province of Massachusetts - probably the first scientific expedition ever sent out by any incipient American state. *Wik

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1783 Birthdate of Charles-Julien Brianchon who, in 1820 published the nine-point circle theorem. Although this theorem has been independently discovered many times he gave the first complete proof and coined the phrase “nine-point circle”. *VFR He also published a geometrical theorem (named as Brianchon's theorem) while a student (1806). He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point. In fact, this theorem is simply the dual of Pascal's theorem which was proved in 1639. After graduation, Brianchon became a lieutenant in artillery fighting in Napoleon's army until he left active service in 1813 due to ill health.*TIS

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1813 Thomas Andrews (19 Dec 1813; 26 Nov 1885) Irish chemist and physicist, who demonstrated the continuity of the gaseous and liquid states whereby during changes between the two states, physical properties display no abrupt changes. He discovered the critical temperature for carbon dioxide (1861), above which the gas cannot be liquefied by pressure alone. He wrote: We may yet live to see...such bodies as oxygen and hydrogen in the liquid, perhaps even in the solid state. He accurately measured heats of neutralisation, formation and reaction; and latent heats of evaporation. Andrews was the first to use a "bomb calorimeter" - a strong, sealed, metal vessel for measuring heat of combustion. He studied ozone, and proved that is an allotrope - or altered form - of oxygen.*TIS

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1852 Albert Abraham Michelson (19 Dec 1852; 9 May 1931) was a German-born American physicist who accurately measured the speed of light and received the 1907 Nobel Prize for Physics "for his optical precision instruments and the spectroscopic and metrological investigations" he carried out with them. He designed the highly accurate Michelson interferometer and used it to establish the speed of light as a fundamental constant. With Edward Morley, he also used it in an attempt to measure the velocity of the earth through the ether (1887). The experiment yielded null results that eventually led Einstein to his theory of relativity. He measured the standard meter bar in Paris to be 1,553,163.5 wavelengths of the red cadmium line (1892-3).*TIS

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1854 Marcel Brillouin worked on topics ranging from history of science to the physics of the earth and the atom.*SAU

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1908 Anne Anastasi (19 Dec 1908; 4 May 2001) American psychologist, known as the "test guru," for her pioneering development of psychometrics, the measurement and understanding of psychological traits. Her seminal work, Psychological Testing (1954), remains a classic text in the subject. In it, she drew attention to the ways in which trait development is influenced by education and heredity. She explored how variables in the measurement of those traits include differences in training, culture, and language. In 1972, she became the first woman to be elected president of the American Psychological Association in half a century. For her accomplishments, she was awarded the National Medal of Science in 1987*TIS

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1887 Charles G Darwin was the grandson of the famous biologist and graduated from Cambridge. He lectured on Physics at Manchester and after service in World War I and a period back at Cambridge he became Professor of Physics at Edinburgh. He left eventually to become head of a Cambridge college. He worked in Quantum Mechanics and had controversial views on Eugenics. *SAU

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1910 Helmut Wielandt worked on finite groups and on finite and infinite permutation groups.*SAU

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1918 Leon Mirsky worked in Number Theory, Linear Algebra and Combinatorics.*SAU

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1921 APL Co-Inventor Adin D. Falkoff is born in New Jersey. He received a BChE in chemical engineering from the City College of New York in 1941 and MA in mathematics from Yale in 1963. He has worked for IBM since 1955. With Kenneth E. Iverson, Falkoff developed A Programming Language​ (APL). Iverson credited him for choosing the name APL and the introduction of the IBM golf-ball typewriter with the replacement typehead, which provided the famous character set to represent programs. Falkoff received IBM’s Outstanding Contribution Award for development APL and APL/360, and ACM’s Award for outstanding contribution to the development and application of APL. *CHM

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1932 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.
Hilton writes that "Themes running through his papers are Hamiltonian cycles, Eulerian graphs, spanning trees, the marriage problem, detachments, reconstruction, and infinite graphs." In his first papers Nash-William considered the knight's tour and random walk problems on infinite graphs; the latter paper included an important recurrence criterion for general Markov chains, and was also the first to apply electrical network techniques of Rayleigh to random walks. His graduate thesis, which he finished in 1958, concerned generalizations of Euler tours to infinite graphs. Welsh writes that his subsequent work defining and characterizing the arboricity of graphs (discovered in parallel and independently by W. T. Tutte) has "had a huge impact," in part because of its implications in matroid theory. Nash-Williams also studied k-edge-connected graphs, Hamiltonian cycles in dense graphs, versions of the reconstruction conjecture for infinite graphs, and the theory of quasi-orders. He also gave a short elegant proof on Kruskal's tree theorem.*Wik

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1937 Barry Charles Mazur (born December 19, 1937) is a professor of mathematics at Harvard.
Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. from Princeton University in 1959, becoming a Junior Fellow at Harvard from 1961 to 1964. He is currently the Gerhard Gade University Professor and a Senior Fellow at Harvard. In 1982 he was elected a member of the National Academy of Sciences. Mazur has received the Veblen Prize in geometry, the Cole Prize in number theory, the Chauvenet Prize for exposition, and the Steele Prize for seminal contribution to research from the American Mathematical Society.*Wik He is the author of the popular math book, Imaginary Numbers

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1943 Victor G. Kac (born 19 December 1943 in Buguruslan, Russia, USSR) is a Soviet and American mathematician at MIT, known for his work in representation theory. He discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. Kac studied mathematics at Moscow State University, receiving his M.S. in 1965 and his Ph.D. in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Engineering. He left the Soviet Union in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship in 1981 and a Guggenheim Fellowship in 1986 and the medal of the College de France (1981). He received the Wigner Medal(1994)"in recognition of work on affine Lie algebras that has had wide influence in theoretical physics". In 1978 he was an Invited Speaker (Highest weight representations of infinite dimensional Lie algebras) at the ICM in Helsinki, In 1988 a plenary speaker at the AMS centennial conference. In 2002 he gave a plenary lecture (Classification of Supersymmetries) at the ICM in Beijing. He is a Fellow of the American Mathematical Society., a Honorary member of the Moscow Mathematical Society, Fellow of the American Academy of Arts and Sciences and a Member of the National Academy of Sciences. The research of Victor Kac primarily concerns representation theory and mathematical physics. His work has been very influential in mathematics and physics and instrumental in the development of quantum field theory, string theory and the theory of integrable systems. Kac published 5 books and over 200 articles in mathematics and physics journals.
His brother Boris Katz is a principal research scientist at MIT. *Wik

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1944 Mitchell Jay Feigenbaum (born December 19, 1944) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.*Wik

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DEATHS
1887 Balfour Stewart (1 Nov 1828, 19 Dec 1887) Scottish meteorologist and geophysicist who studied terrestrial magnetism and radiant heat. His researches on radiant heat contributed to foundation of spectrum analysis. He was the first to discover that bodies radiate and absorb energy of the same wavelength. In meteorology, he pioneered in ionospheric science, making a special study of terrestrial magnetism. He proposed (1882) that the daily variation in the Earth's magnetic field could be due to air currents in the upper atmosphere, which act as conductors and generate electrical currents as they pass through the Earth's magnetic field. He also investigated sunspots. In 1887, he suffered a stroke while crossing to spend Christmas at his estate in Ireland and died soon after at the age of 59.*TIS

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1939 Dmitry Aleksandrovich Grave (September 6, 1863 – December 19, 1939) was a Russian and Soviet mathematician. Naum Akhiezer, Nikolai Chebotaryov, Mikhail Kravchuk, and Boris Delaunay were among his students.
Dmitry Grave was educated at the University of St Petersburg where he studied under Chebyshev and his pupils Korkin, Zolotarev and Markov. Grave began research while a student, graduating with his doctorate in 1896. He had obtained his masters degree in 1889 and, in that year, began teaching at the University of St Petersburg.
For his Master's Degree Grave studied Jacobi's methods for the three body problem, a topic suggested by Korkin. His doctorate was on map projections, again a topic proposed by Korkin, the degree being awarded in 1896. The work, on equal area plane projections of the sphere, built on ideas of Euler, Joseph Louis Lagrange and Chebyshev.
Grave became professor at Kharkov in 1897 and, from 1902, he was appointed professor at the University of Kiev, where he remained for the rest of his life. Grave is considered as the founder of the Kiev school of algebra which was to become the centre for algebra in the USSR.
At Kiev Grave studied algebra and number theory. In particular he worked on Galois theory, ideals and equations of the fifth degree. Among his pupils were O J Schmidt, N G Chebotaryov, B N Delone and A M Ostrowski. *WIK

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1946 Paul Langevin (23 Jan 1872, 19 Dec 1946) French physicist who was the first scientist to explain the effects of paramagnetism and diamagnetism (the weak attraction or repulsion of substances in a magnetic field), in 1905, using statistical mechanics. He further theorized how the effects could be explained by how electron charges behaved within the atom. He popularized Einstein's theories for the French public. During WW I, he began developing a source for high intensity ultrasonic waves, which made sonar detection of submarines possible. He created the ultrasound from piezoelectric crystals vibrated by high-frequency radio circuits. In WW II, he spoke out against the Nazis, for which he was arrested and imprisoned, though he managed to escaped and fled to Switzerland.*TIS

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1952 Otto Szász (11 December 1884, Hungary – 19 December 1952, Cincinnati, Ohio) was a Hungarian mathematician who worked on real analysis, in particular on Fourier series. He proved the Müntz–Szász theorem and introduced the Szász–Mirakyan operator. The Hungarian Mathematical and Physical Society awarded him the Julius König prize in 1939.*Wik

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1953 Robert Andrews Millikan (22 Mar 1868, 19 Dec 1953) American physicist who was awarded the 1923 Nobel Prize for Physics for "his work on the elementary charge of electricity and on the photoelectric effect." Millikan's famous oil-drop experiment (1911) was far superior to previous determinations of the charge of an electron, and further showed that the electron was a fundamental, discrete particle. When its value was substituted in Niels Bohr's theoretical formula for the hydrogen spectrum, that theory was validated by the experimental results. Thus Millikan's work also convincingly provided the first proof of Bohr's quantum theory of the atom. In later work, Millikan coined the term "cosmic rays" in 1925 during his study of the radiation from outer space.*TIS

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1983 Kate Sperling Fenchel (December 21, 1905 - December 19, 1983) Born in Berlin, Germany. Studied mathematics, philosophy, and physics at the University of Berlin from 1924 to 1928. She was encouraged to write a thesis, but she could not afford to continue her studies and research jobs for women appeared to be difficult to obtain. Thus she never received a Ph.D. in mathematics. From 1931 to 1933 she taught mathematics at the high school level, but was fired when the Nazis came to power in Germany because she was Jewish. She emigrated to Denmark with Werner Fenchel, a former fellow student, and the two married in December, 1933. Fenchel worked from 1933 to 1943 for a Danish mathematics professor. In 1943 she had to escape to Sweden with her husband and 3-year old son while Germany occupied Denmark. They returned to Denmark after the end of the war. Fenchel held a part-time lecturer's job at Aarhus University, Denmark, from 1965-1970.
Fenchel did research in finite nonabelian groups and published several papers, the last at the age of 73. *ASC

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1997 David N. Schramm (25 Oct 1945, 19 Dec 1997) American theoretical astrophysicist who was an authority on the particle-physics aspects of the Big Bang theory of the origin of the universe. He considered the nuclear physics involved in the synthesis of the light elements created during the Big Bang comprising mainly hydrogen, with lesser quantities of deuterium, helium, lithium, beryllium and boron. He predicted, from cosmological considerations, that a third family of neutrinos existed - which was later proven in particle accelerator experiments (1989). Schramm worked to evaluate undetected dark matter that contributed to the mass of the universe, and which would determine whether the universe would ultimately continue to expand. He died in the crash of a small airplane he was piloting.*TIS

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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

On This Day in Math - December 18

 

First celestial photograph, see 1839 below

Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid's Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid's presentation filled me with such vivid pleasure, that forthwith I felt as well as ever.
~Bernhard Bolzano

The 352nd day of the year; there are 352 ways to arrange 9 queens on a 9x9 chessboard so that none are attacking another. (Gauss worked on the generalized queens problem; Students might try to find the number for small n x n boards. A general algorithm is not yet known)

352 has all prime digits, and so does the 352nd prime, 2377.

352 can be written as the sum of  three squares, 8^12 + 12^2 + 12^2; and also as the sum of two consecutive primes, 173 + 179

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EVENTS
1680  C/1680 V1, also called the Great Comet of 1680, Kirch's Comet, and Newton's Comet, has the distinction of being the first comet discovered by telescope. Discovered by Gottfried Kirch on 14 November 1680, New Style, it became one of the brightest comets of the 17th century--reputedly visible even in daytime--and was noted for its spectacularly long tail. Passing only 0.4 AUs from Earth on 30 November, it sped around an incredibly close perihelion of .006 AU (898,000 km) on 18 December 1680, reaching its peak brightness on 29 December as it rushed outward again. It was last observed on 19 March 1681. As of December 2010 the comet was about 252.1 A.U. from the Sun. While the Kirch Comet of 1680-1681 was discovered and subsequently named for Gottfried Kirch , credit must also be given to the Jesuit, Eusebio Kino, who charted the comet’s course. During his delayed departure for Mexico, Kino began his observations of the comet in Cadíz in late 1680. Upon his arrival in Mexico City, he published his Exposisión astronómica de el [sic] cometa (Mexico City, 1681) in which he presented his findings. Kino’s Exposisión astronómica is among one of the earliest scientific treatises published by a European in the New World.  Aside from its brilliance, it is probably most noted for being used by Isaac Newton to test and verify Kepler's laws. *Wik 

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1703 The astronomer John Flamsteed was not pleased with the choice of successor to Wallis as the Savilian Professor of Geometry, Edmond Halley. In a letter of Flamsteed’s to Sharpe [he] reveals his irritation at the turn of events: Dr. Wallis is dead—Mr. Halley expects his place—who now talks, swears and drinks brandy like a sea-captain” *GERALD L. ALEXANDERSON, MAA Journal Volume 49, Number 3, July 2012,

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In 1839, John William Draper took a daguerreotype of the moon, the first celestial photograph made in the U.S. He exposed the plate for 20 minutes using a 5-inch telescope and produced an image one inch in diameter. Draper was a professor of chemistry at New York University, New York City. His research in the effect of light upon chemicals had led him to take up photography. He also made his first satisfactory photographic portrait in 1839. A picture he took (1840) of his sister is the oldest surviving photographic portrait. Draper made important scientific contributions in fields of radiant energy, photochemistry, photography, and electric telegraphy. He also anticipated development of spectrum analysis.*TIS

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In 1926, in a letter published in Nature, G.N. Lewis coined the word "photon" when he suggested that it "would seem inappropriate to speak of one of these hypothetical entities as a particle of light, a corpuscle of light, a light quantum, or a light quant, if we are to assume that it spends only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains as an important structural element within the atom. It would also cause confusion to call it merely a quantum, for later it will be necessary to distinguish between the number of these entities present in an atom and the so-called quantum number. I therefore [propose for this] which is not light but plays an essential part in every process of radiation, the name photon.*TIS

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In 1958, the first American communications satellite was launched. Project SCORE (Signal Communication by Orbiting Relay Equipment) was put into orbit from Cape Canaveral using an Atlas B missile, also the first successful trial of the Atlasas a space launch vehicle. The entire rocket was placed into low orbit with the communications equipment integrated into the fairing pods of the missile. The low orbit limited life expectancy of the satellite to only 2 to 3 weeks, thus limiting opportunities for real­time relay between two ground stations. Therefore, a store­and­forward mode was added by including a tape recorder, which also gave the satellite a worldwide broadcast capability - the world's first satellite to broadcast voice.*TIS

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1991 IBM and Siemens AG announce they have developed a prototype 64 megabyte DRAM chip. This development was in line with Moore’s Law which predicts a doubling of the number of transistors etched into silicon every 18 months. *CHM

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BIRTHS
1856 Sir J(oseph) J(ohn) Thomson (18 Dec 1856; 30 Aug 1940)  was an English physicist who helped revolutionize the knowledge of atomic structure by his discovery of the electron (1897). He received the Nobel Prize for Physics in 1906 and was knighted in 1908. Thomson experimented with currents of  electricity inside empty glass tubes, investigating a long-standing puzzle known as "cathode rays." His experiments prompted him to make a bold proposal: these mysterious rays are streams of particles much smaller than atoms. He called these particles "corpuscles," and suggested that they might make up all of the matter in atoms. It was startling to imagine a particles inside the atom at a time when most people thought that the atom was indivisible, the most fundamental unit of matter.*TIS 

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1917 Roger Conant Lyndon (18 Dec 1917 in Calais, Maine, USA - 8 June 1988 in Ann Arbor, Michigan) was an American mathematician, for many years a professor at the University of Michigan. He is known for Lyndon-words (a type of combinatorial string topic), the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence. *Wik 

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1942 Lenore Blum​ (December 18, 1942, New York) is a distinguished professor of Computer Science at Carnegie Mellon. She received her Ph.D. in mathematics from the Massachusetts Institute of Technology in 1968. Her dissertation was on Generalized Algebraic Structures and her advisor was Gerald Sacks. She then went to the University of California at Berkeley as a Postdoctoral Fellow and Lecturer in Mathematics. In 1973 she joined the faculty of Mills College where in 1974 she founded the Mathematics and Computer Science Department (serving as its Head or co-Head for 13 years). In 1979 she was awarded the first Letts-Villard Chair at Mills.
In 1983 Blum won an NSF CAREER award to work with Michael Shub for two years at the CUNY Graduate Center. They worked on secure random number generators and evaluating rational functions, see Blum Blum Shub. In 1987 she spent a year at IBM. In 1989 she published an important paper with Michael Shub and Stephen Smale on NP completeness, recursive functions and universal Turing machines, see Blum–Shub–Smale machine. In 1990 she gave an address at the International Congress of Mathematicians on computational complexity theory and real computation. In 1992 Blum became the deputy director of the Mathematical Sciences Research Institute, otherwise known as MSRI. After visiting the City University of Hong Kong for a year, she moved to her current position at Carnegie Mellon in 1999. [1] In 2002 she was selected to be a Noether Lecturer.
Lenore Blum is married to Manuel Blum and mother of Avrim Blum. All three are MIT alumni and professors of Computer Science at Carnegie Mellon.*Wik

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DEATHS
1559  Cuthbert Tunstall (1474 in Hackforth, Yorkshire, England - 18 Dec 1559 in Lambeth, London, England) wrote the first printed work published in England devoted exclusively to mathematics. It was an arithmetic book De arte supputandi libri quattuor (1522) based on Pacioli's Suma. It makes no claim to originality. *SAU   His life was primarily as a diplomat and bishop and shows no evidence of exceptional mathematical ability in what I have found, yet Grynaeus dedicated the first printed Greek edition of Euclid to him: "....since he has explained the calculating of numbers so clearly.   One of his biographers wrote of him, "A gentle man given to collecting coins and gardening, he was probably the most respected bishop and scholar in sixteenth century England."

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1799 Étienne Montucla (5 September 1725 – 18 December 1799) was a French historian of mathematics who wrote in 1754 a history of the problem of squaring the circle. He also wrote the first truly comprehensive classical history of mathematics,Histoire des mathématiques. Late in his life, Montucla's friends persuaded him to work on a new edition of his famous Histoire des mathématiques. In August 1799 Montucla published new editions through Agasse in Paris of the two volumes originally published in 1758. Montucla extensively revised and enlarged the two volumes. He had intended to extend his cover of history to the end of the 18th century and part of the third volume on this topic was printed by the time he died, four months after the publication of the new editions of 1799. Lalande, with the help of some other scientists, completed volumes three and four to give the coverage that Montucla had intended. Volume three covered 18th century pure mathematics, optics and mechanics in 832 pages, while the fourth volume covered 18th century astronomy, mathematical geography and navigation in 688 pages.*SAU In 1778 he re-edited Jacques Ozanam's Recreations mathématiques, afterwards published in English by Charles Hutton (4 vols, London, 1803).*Wik Huttons translation is free on Google Books

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1848 Bernhard Bolzano (5 Oct 1781, 18 Dec 1848) Bohemian mathematician and theologian who made significant contributions to both mathematics and the theory of knowledge. He provided a more detailed proof for the binomial theorem in 1816 and suggested the means of distinguishing between finite and infinite classes. Bolzano helped to establish the foundations of analysis (for example, the Bolzano-Weierstrass theorem), attempted to elaborate mathematical method, and anticipated some basic ideas of Cantor's set theory. His major work, Wissenschaftslehre (1837), contains various contributions to logic and semantics concerning the relations of compatibility, derivability, and consequence, the deduction theorem, and the logic of classes, entailment, and probability.*TIS 

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1855 Jacques Charles-François Sturm (29 Sep 1803, 18 Dec 1855) French mathematician whose work resulted in Sturm's theorem, an important contribution to the theory of equations. As tutor of the de Broglie family in Paris (1823-24), Sturm met many of the leading French scientists and mathematicians. In 1826, with the Swiss engineer Daniel Colladon, he made the first accurate determination of the velocity of sound in water and a year later wrote a prizewinning essay on compressible fluids. In 1829, he found the number of real roots of a given polynomial in a given interval. *TIS 

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1880 Michel Chasles (15 Nov 1793, 18 Dec 1880) French mathematician who, independently of the Swiss-German mathematician Jakob Steiner, elaborated the theory of modern projective geometry, the study of the properties of a geometric line or plane figure that remain unchanged when the figure is projected onto a plane from a point not on either the plane or the figure. In his text Traité de géométrie in 1852 Chasles discusses cross ratio, pencils and involutions, all notions which he introduced. Chasles was the victim of a celebrated fraud paying the equivalent of 20,000 pounds for various letters from famous men of science and others which turned out to be forged. *TIS 

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1970 Pao-Lu Hsu (1 Sept 1910 in Beijing, China - 18 Dec 1970 in Beijing, China) Hsu passed examinations in 1936 at Peking University and obtained a scholarship to enable him to continue his graduate studies in Britain. He spent four years in Britain mainly at University College, London but he also spent some time studying at Cambridge. Certainly University College, London was an excellent place for Hsu to study as his mathematical interests were in probability and statistics. Egon Pearson, following the retirment of his father Karl Pearson as Galton Professor of Statistics, had been made Reader and became Head of the Department of Applied Statistics three years before Hsu arrived there. Jerzy Neyman had been appointed in 1934 while R A Fisher held Karl Pearson's Galton Chair of Statistics and was Head of the Department of Eugenics at University College. Lehmann writes, "During this period Hsu wrote a remarkable series of papers on statistical inference which show the strong influence of the Neyman-Pearson point of view."
Hsu's first two papers were published in the Statistical Research Memoirs which were edited by Jerzy Neyman and Egon Pearson. One concerned what is now known as the Behrens-Fisher problem, while the second Hsu examined the problem of optimal estimators of the variance in the Gauss-Markov model.
In 1938 Hsu, while still undertaking research for his doctorate, too up a position as lecturer in Egon Pearson's Department. He was awarded the degree of Ph.D. and then that of D.Sc. from University College, London, in 1938 and 1940, respectively. Anderson, Chung and Lehmann write, "[Hsu's] British education formed his taste in mathematics; he preferred the hard and concrete to the general and abstract. "
By 1940 China was engaged in World War II fighting against the Japanese invasion and Britain was involved in the war against Germany. Hsu chose to leave Britain to return to his homeland of China where he was appointed as Professor at Peking University. It was a period of great difficulty and hardship for Hsu. He corresponded with Neyman during the years 1943-44, who by this time was at Berkeley in the United States, about statistical matters but he mentions in these letters the great hardship he was suffering, particularly suffering starvation.
It is a great tribute to Hsu's determination to devote himself to statistics that he managed to continue his research during these difficult war years. Many of his publications on multivariate analysis from this period show that he had been strongly influenced by R A Fisher while at University College. His role in promoting the use of matrix theory in statistics should also be emphasized. These papers brought him to, "... the forefront of the development of the mathematical theory of multivariate analysis. "
Attempts were made to get Hsu to the United States. In 1945 he arrived in the USA just in time for the First Berkeley Symposium on Probability and Statistics. During the next two years he taught at the University of California, Columbia University, and the University of North Carolina where he was offered an associate professorship.
After spending 1946-47 at the University of North Carolina at Chapel Hill, in 1947 Hsu returned to his professorship at Peking University. *SAU 

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1995 Konrad Zuse (22 Jun 1910, 18 Dec 1995) German engineer who in 1941 constructed the first fully operational program-controlled electromechanical binary calculating machine, or digital computer, called the Z3. Earlier, Zuse developed and built the Z1 the first binary digital computer in the world (1936-8) and two more machines before the end of WW II, but he was unable to convince the Nazi government to support his work. He created a basic programming system known as Plankalkül with which he designed a chess playing program.The Z3 was destroyed in 1944 during the war. Next came the more sophisticated Z4, which was the only Zuse Z-machine to survive the war, by several moves to new locations away from air raids. During the last days of war it was hidden. In 1950, he took it to Zurich. *TIS In an interesting coincidence, the first paper of Roger Lyndon, who was born on this date) was on the Zuse computer . In the paper he described the Z4, Zuse's relay-type digital computer which was discovered by advancing British and American troops. The nearly completed computer had been hidden by Zuse in the cellar of a house in the small village of Hinterstein in Bavaria. *SAU

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1995 Nathan Rosen (22 Mar 1909, 18 Dec 1995) U.S.-born Israeli theoretical physicist who in 1935 collaborated with Albert Einstein and Boris Podolsky on a much-debated refutation of the theory of quantum mechanics; he later came to accept the theory. The famous Einstein-Podolsky-Rosen critique of quantum mechanics was published in the 1935 Physical Review. (A New York Times obituary described The Physical Review as "one of the most impenetrable periodicals in the English language.") Rosen founded the Institute of Physics at Technion in Haifa.*TIS 

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2007 Samuel Karlin (June 8, 1924 - December 18, 2007) was an American mathematician at Stanford University in the late 20th century.
Karlin earned his undergraduate degree from Illinois Institute of Technology; and then his doctorate in mathematics from Princeton University in 1947 (at the age of 22) under the supervision of Salomon Bochner. He was on the faculty of Caltech from 1948–56, before becoming a professor of mathematics and statistics at Stanford.
Throughout his career, Karlin made fundamental contributions to the fields of mathematical economics, bioinformatics, game theory, evolutionary theory, biomolecular sequence analysis, and total positivity. He did extensive work in mathematical population genetics. In the early 1990s, Karlin and Stephen Altschul developed the Karlin-Altschul statistics, a basis for the highly used sequence similarity software program BLAST.
Karlin authored ten books and more than 450 articles. Karlin was a member of both the American Academy of Arts and Sciences and the National Academy of Sciences. In 1989, President George H. W. Bush bestowed Karlin the National Medal of Science "for his broad and remarkable researches in mathematical analysis, probability theory and mathematical statistics, and in the application of these ideas to mathematical economics, mechanics, and population genetics."
Karlin's three children all became scientists. One of his sons, Kenneth D. Karlin, is a professor of chemistry at Johns Hopkins University and the 2009 winner of the American Chemical Society's F. Albert Cotton Award for Synthetic Chemistry.  His other son, Manuel, is a physician in Portland, Oregon. His daughter, Anna R. Karlin, is a theoretical computer scientist, the Microsoft Professor of Computer Science & Engineering at the University of Washington. *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