**Nothing tends so much to the advancement of knowledge**

**as the application of a new instrument.**

The 351st day of the year; 351 is a triangular number, and the sum of five consecutive primes. It is also an element in the Padovan sequence, an interesting exploration for students.

351 can not be written as the sum of three squares. It is the 85th year day for which that is true, there is only one more this year. It is also not the sum of two squares.

351 is the smallest number n so that n, n+1, and n+2 are all the product of four or more primes.

**EVENTS**

1610 Father Christoph Clavius SJ, the senior mathematician at the Collegio Romano writes to inform Galileo that he and other Jesuits at the college had seen the four moons of Jupiter. Only two months earlier he had said that if Galileo saw "planets" around Jupiter in his glass, then he must have put them there. *David Leverington, Babylon to Voyager and Beyond: A History of Planetary Astronomy

December 17, **1750** - Mr. Theophilus Grew appointed first Master in Mathematics at Academy of Philadelphia (to become the Univ of Pennsylvania). Grew published the first American Trigonometry book while there, “The Description and Use of the Globes..”. His 1752 Barbados almanack, for the year of our Lord 1752, being bissextile, or leap-year. / By Theophilus Grew, professor of the mathematics was published in 1751 and printed by Ben Franklin. "This is the only recorded sheet almanac extant from the Franklin shop and the only one prepared by Grew which Franklin and Hall are known to have printed."--*C. W. Miller, Franklin (My blog notes about Grew here from U Pa.)

In **1790**, Mexico's greatest Aztec relic, an Aztec calendar stone is discovered in Mexico City. The 24-ton "Sun Stone" bears carved astronomical symbols. Based on the movements of the stars, it reflects the Aztecs’ knowledge of astronomy and mathematics. Used to predict the seasons and natural events, it also regulated economic and social activities as well as religious ceremonies. Making it took them 52 years (1427-79), and it is 103 years older than the Gregorian calendar in use in most cultures today. The Spanish buried this colossal monument during the Conquest where the Metropolitan Cathedral stands today in the main plaza of Mexico City. It was lost for 250 years until 1790, when it was accidentally uncovered during repair work on the Cathedral.*TIS

**1804 **One of the earliest science board games released.

An astronomical board game, folded into cardboard slip case, entitled 'Science in Sport, or the Pleasures of Astronomy; A New & Instructive Pastime. Revised & approved by Mrs. Bryan; Blackheath', 'Published, December 17th 1804, by the Proprietor, John Wallis, No. 16, Ludgate Street, London

The game is based on the traditional Game of the Goose, which was adapted to a wide range of themed boards, many produced by John Wallis, one of the leading publishers of board games in the early 19th century. Margaret Bryan (fl. 1795-1816) ran a girl's school in Blackheath and was author of a number of popular works on science (ZBA4475 is her portrait), and Wallis evidently felt that her association with this game would be a testament to its accuracy, as well as highlighting its suitability for girls' education. The board has 35 numbered 'squares' depicting astronomical objects, instruments and principles as well as astronomers (Ptolemy, Tycho Brahe, Nicholas Copernicus, Isaac Newton) and moral lessons (e.g. a studious and idle boy, the county gaol and an army volunteer). One square shows the man in the moon as an example of ignorance in astronomy. By spinning a 'te-totum', players can travel over the board, the object being to spin numbers up to 35 and reach the final 'square', depicting Flamsteed House: 'Whoever first arrives here is to take the title of Astronomer Royal'. The game involves much rote learning as well as moral lessons en route: within the rules of the game accuracy of knowledge and zeal are rewarded, while ignorance and idleness are punished. The requirements of each square and its consequences were recorded in an accompanying booklet, although this has been lost from this edition. This copy of the game belonged to William Proctor, the father of the astronomer and writer on science, Richard A. Proctor (1837-1888).

*National Maritime Museum, Greenwich, London

**1903** The Wright brothers ﬂew their ﬁrst plane at Kitty Hawk. Following unsuccessful attempt only three days before, the Wright brothers took their newly-built Wright Flyer to Kitty Hawk, North Carolina made "the first sustained and controlled heavier-than-air powered flight". In fact they made four flights that day. Orville made two and Wilber made two. The last of the four flights that day stayed aloft for 59 seconds and traveled 852 feet.

“Wishing to inform their father of the good news and make the press aware of the achievement, Orville sent him the following telegram just hours later.

Note: During the telegram's transmission, '59' seconds mistakenly became '57', and 'Orville' became 'Orevelle'.

176 C KA C8 33 Paid. Via Norfolk Va

Kitty Hawk N C Dec 17

Bishop M Wright

7 Hawthorne St

Success four flights Thursday morning all against twenty one mile wind started from Level with engine power alone average speed through air thirty one miles longest 57 seconds inform Press home Christmas.

Orevelle Wright 525P

*Letters of Note

In **1919,** Albert Porta an expert seismographer and meteorologist predicted that a conjunction of six planets on this date would spell the end of the world. The alignment of planets would cause a magnetic current which would pierce the sun and thereby engulf the earth in flames. As the date approached suicides and hysteria were reported throughout the world. *TIS

**1969** Egypt issued a stamp to publicize the International Congress for Scientific Accounting which began in Cairo on this date. Pictured are ancient arithmetic and modern computer cards. [Scott #815].

**BIRTHS**

**1706 Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet** (17 Dec 1706; 10 Sep 1749) was a French mathematician and physicist who was the mistress of Voltaire. She took to mathematics and the sciences, being exposed to distinguished guests of her aristocratic parents. Emilie was interested in the philosophies of Newton and Leibniz, and dressed as a man to enter the cafes where the scientific discussions of the time were carried on. Châtelet's major work was a translation of Newton's Principia, begun in 1745. Voltaire wrote the preface. The complete work appeared in 1759 and was for many years the only translation of the Principia into French. She died in 1749, a few days after giving birth to her daughter. *TIS

**1778 Sir Humphrey Davy** Born In his hometown of Penzance, Cornwall, a statue of Davy stands in front of the imposing Market House (now owned by Lloyds TSB) at the top of the town's main street Market Jew Street. The plaque is a nice description of a full life.

Nearby is a house on which a commemorative plaque claims the location as the site of his birth.

Penzance also has a secondary school named Humphry Davy School. Like James Prescott Joule and Isaac Newton, Davy is also remembered in his hometown by a pub – "The Sir Humphry Davy" at 32 Alverton Street, west of the Market House.

The first ever clerihew (a whimsical, four-line biographical poem invented by Edmund Clerihew Bentley) was written about Sir Humphry Davy:

Sir Humphrey [sic] Davy

Abominated gravy.

He lived in the odium

Of having discovered sodium.

Said to have been written as a schoolboy during a chemistry class at St. Paul's School.

**1797 Joseph Henry** (17 Dec 1797; 13 May 1878) One of the first great American scientists after Benjamin Franklin. Although Henry at an early age appeared to be headed for a career in the theater, a chance encounter with a book of lectures on scientific topics turned his interest to science. He aided Samuel F.B. Morse in the development of the telegraph and discovered several important principles of electricity, including self-induction, a phenomenon of primary importance in electronic circuitry. He was the first Secretary (director) of the Smithsonian Institution (1846-1878), where he established the foundation of a national weather service. For more than thirty years, Henry insisted that basic research was of fundamental importance. *TIS Henry was the first Secretary of the Smithsonian Museum.

1835 Felice Casorati is best remembered for the Casorati-Weierstrass theorem characterizing the behavior of a function near an essential singularity.*SAU

**1842 (Marius) Sophus Lie **(17 Dec 1842; 18 Feb 1899) was a Norwegian mathematician who made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. Lie was in Paris at the outbreak of the French-German war of 1870. Lie left France, deciding to go to Italy. On the way however he was arrested as a German spy and his mathematics notes were assumed to be coded messages. Only after the intervention of French mathematician, Gaston Darboux, was Lie released and he decided to return to Christiania, Norway, where he had originally studied mathematics to continue his work. *TIS

1861 Arthur Edwin Kennelly (17 Dec 1861; 18 Jun 1939) Irish-American electrical engineer who made innovations in analytic methods in electronics, particularly the definitive application of complex-number theory to alternating-current (ac) circuits. For six years he worked for Thomas Edison at West Orange Laboratory, then branched out as a consultant. Upon his co-discovery (with Oliver Heaviside) of the radio reflecting properties of the ionosphere in the upper atmosphere, the stratum was called the Kennelly- Heaviside layer*TIS

**1863 Henri Eugène Padé **(December 17, 1863 – July 9, 1953) was a French mathematician, who is now remembered mainly for his development of approximation techniques for functions using rational functions.*Wik He made advances with continued fractions.

**1894 Hendrik Anthony Kramers** (17 Dec 1894; 24 Apr 1952) Dutch physicist who, with Ralph de Laer Kronig, derived important equations relating the absorption to the dispersion of light. He also predicted (1924) the existence of the Raman effect, an inelastic scattering of light. Kramer's work covers almost the entire field of theoretical physics. He published papers dealing with mathematical formalism of quantum mechanics, and others on paramagnetism, magneto-optical rotation, ferro-magnetism, kinetic theory of gases, relativistic formalisms in particle theory, and on theory of radiation. His work shows outstanding mathematical skill and careful analysis of physical principles. *TIS

**1900 Dame Mary Lucy Cartwright** (17 Dec 1900 in Aynho, Northamptonshire, England

- 3 April 1998 in Cambridge, England) In 1930 Cartwright was awarded a Yarrow Research Fellowship and she went to Girton College, Cambridge, to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her theorem, now known as Cartwright's Theorem, gave an estimate for the maximum modulus of an analytic function which takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Ahlfors for conformal mappings.

Cartwright was appointed, on the recommendation of both Hardy and Littlewood, to an assistant lectureship in mathematics in Cambridge in 1934, and she was appointed a part-time lecturer in mathematics the following year. In 1936 she became director of studies in mathematics at Girton College, and in 1938 she began work on a new project which had a major impact on the direction of her research. The Radio Research Board of the Department of Scientific and Industrial Research produced a memorandum regarding certain differential equations which came out of modelling radio and radar work. They asked the London Mathematical Society if they could help find a mathematician who could work on these problems and Cartwright became interested in their memorandum.

The dynamics which lay behind the problems was unfamiliar to Cartwright and so she approached Littlewood for help with this aspect. They began to collaborate studying the equations. Littlewood wrote, "For something to do we went on and on at the thing with no earthly prospect of "results"; suddenly the whole vista of the dramatic fine structure of solutions stared us in the face. "

The fine structure which Littlewood describes here is today seen to be a typical instance of the "butterfly effect". The collaboration led to important results, and these have greatly influenced the direction that the modern theory of dynamical systems has taken. In 1947, largely on the basis of her remarkable contributions in the collaboration with Littlewood, she was elected a Fellow of the Royal Society and, although she was not the first woman to be elected to that Society, she was the first woman mathematician. *SAU

1908 Willard Frank Libby (17 Dec 1908; 8 Sep 1980) American chemist whose technique of carbon-14 (or radiocarbon) dating provided an extremely valuable tool for archaeologists, anthropologists, and earth scientists. For this development he was honoured with the Nobel Prize for Chemistry in 1960. Libby is a specialist in radiochemistry, particularly hot atom chemistry, tracer techniques, and isotope tracer work. He became well-known at Chicago University also for his work with natural tritium, and its use in hydrology and geophysics. On 18 May 1952, he determined that the age of Stonehenge was 1848 BC, based on analysis of radioisotopes in charcoal. *TIS

**1920 APL Co-Inventor Kenneth E. Iverson **is Born in Camrose, Alberta, Canada. He received a BA in mathematics from Queen’s University in Ontario, a MA and PhD in applied mathematics from Harvard. Iverson taught at Harvard, worked for IBM and I.P. Sharp Research Associates. With Adin D. Falkoff, he developed A Programming Language (APL). It was a triumphant start of his career, and for over 35 following years Iverson was able to transform his invention into a successful commercial property. He received the AFIPS Harry Goode Award in 1975, ACM Turing Award in 1979, IEEE Computer Pioneer Award in 1982, and the National Medal of Technology in 1991. *CHM

**1941 V. Frederick Rickey** born. The math historian who is the first source for this blog. V. Frederick Rickey, a logician turned historian, earned three degrees from the University of Notre Dame (Ph.D. 1968) and then went to Bowling Green State University where he rose through the professorial ranks to become Distinguished Teaching Professor Emeritus. He has broad interests in the history of mathematics and is especially interested in the development of the calculus.

He has been on leave six times, most recently during the 2007-2008 Academic Year when he was doing research for a book on the history of the Mathematics Department at West Point. His previous leave was spent in Washington D. C. where he was Visiting Mathematician at the MAA Headquarters. While there he was involved in the founding of Math Horizons, a magazine for mathematics undergraduates; became the first editor of electronic services for the MAA and built its first gopher and web pages (both long departed); and wrote a successful NSF proposal for an Institute for the History of Mathematics and Its Use in Teaching.

He loves teaching and enjoys giving lectures to mathematicians about the history of their field. He received the first award from the Ohio Section for Distinguished College or University Teaching of Mathematics, and was in the first group to receive a MAA National Award for teaching. *Biography from Professor Rickey's web page

**DEATHS**

**1851 Olinde Rodrigues** was a French mathematician best known for his formula for the Legendre polynomials.*SAU

**1857 Sir Francis Beaufort **(7 May 1774, 17 Dec 1857) Inventor of the wind force scale. In 1806, British Admiral Sir Francis Beaufort devised a simple scale that coastal observers could use to report the state of the sea to the Admiralty. Originally to describe wind effects on a fully rigged man-of-war sailing vessel, it was later extended to include descriptions of effects on land features as well. Officially adopted in 1838, it uses numbers 0 to 12, to designate calm, light air, light breeze, gentle breeze, moderate breeze, fresh breeze, strong breeze, moderate gale, fresh gale, strong gale, whole gale, storm, and hurricane. Zero (calm) is a wind velocity of less than 1 mph (0.6 kph) and 12 (hurricane) represents a velocity of over 75 mph (120kph). He was Hydrographer of the Navy from 1829-55.*TIS

**1907 William Thompson, Lord Kelvin**; died of a severe chill on 17 December 1907.

The Royal Society asked the Dean of Westminster if Kelvin could be buried in the Abbey and he agreed. The funeral was on 23 December and he lies to the south of Sir Isaac Newton's grave in the nave. On the previous night the coffin, covered by a purple pall, had rested in St Faith's chapel. The simple stone reads: WILLIAM THOMSON LORD KELVIN 1824-1907.

In 1913 a stained glass window, designed by J.Ninian Comper, was erected near the grave. This contains large figures of King Henry V and Abbot William Colchester and below is an inscription "In memory of Baron Kelvin of Largs. Engineer, Natural Philosopher. B.1824.D.1907". His coat of arms and those of Glasgow University are shown. The window was the gift of engineers from Great Britain and America.

**1912 Spiru C. Haret** (15 February 1851 – 17 December 1912) was a Romanian mathematician, astronomer and politician. He made a fundamental contribution to the n-body problem in celestial mechanics by proving that using a third degree approximation for the disturbing forces implies instability of the major axes of the orbits, and by introducing the concept of secular perturbations in relation to this.

As a politician, during his three terms as Minister of Education, Haret ran deep reforms, building the modern Romanian education system. He was made a full member of the Romanian Academy in 1892.

He also founded the Astronomical observatory in Bucharest, appointing Nicolae Coculescu as its first director. The crater Haret on the Moon is named after him. *Wik

Alicia Boole's sections of Polytopes |

**(June 8, 1860, Ireland – December 17, 1940, England) was the third daughter of George Boole and Mary Everest Boole, born in Cork, Ireland. Before marrying Walter Stott, an actuary, in 1890, she was known as Alicia Boole. She is best known for coining the term "polytope" to refer to a convex solid in four dimensions, and having an impressive grasp of four-dimensional geometry from a very early age.**

1940 Alicia Boole Stott

1940 Alicia Boole Stott

She found that there were exactly six regular polytopes in four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections.

After taking up secretarial work near Liverpool in 1889 she met and married Walter Stott in 1890. Stott learned of Pieter Schoute's work on central sections of the regular polytopes in 1895. Schoute came to England and worked with Alicia Stott, persuading her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.

The University of Groningen honoured her by inviting her to attend the tercentenary celebrations of the university and awarding her an honorary doctorate in 1914.

In 1930 she was introduced to Harold Coxeter and they worked together on various problems. Alicia Boole Stott made two further important discoveries relating to constructions for polyhedra related to the golden section. Coxeter described his time doing joint work with her saying, "The strength and simplicity of her character combined with the diversity of her interests to make her an inspiring friend." *Wik

**1964 Victor Francis Hess **(24 June 1883, 17 Dec 1964) Austrian-born physicist who was a joint recipient, with Carl D. Anderson of the United States, of the Nobel Prize for Physics in 1936 for his discovery of cosmic rays, high-energy radiation originating in outer space. *TIS

**1973 Charles Greeley Abbot** (31 May 1872, 17 Dec 1973) was an American astrophysicist who is thought to have been the first scientist to suspect that the radiation of the Sun might vary over time. In 1906, Abbot became director of the Smithsonian Astrophysical Observatory and, in 1928, fifth Secretary of the Smithsonian. To study the Sun, SAO established a network of solar radiation observatories around the world-- usually at remote and desolate spots chosen primarily for their high percentage of sunny days. Beginning in May 1905 and continuing over decades, his studies of solar radiation led him to discover, in 1953, a connection between solar variations and weather on Earth, allowing general weather patterns to be predicted up to 50 years ahead.*TIS

**1999 Juergen Kurt Moser **(July 4, 1928, Königsberg, East Prussia – December 17, 1999, Schwerzenbach, Kanton Zürich, Switzerland) was a German-American mathematician.

He won the first George David Birkhoff Prize in 1968 for contributions to the theory of Hamiltonian dynamical systems, the James Craig Watson Medal in 1969 for his contributions to dynamical astronomy, the L. E. J. Brouwer Medal of the Royal Dutch Mathematical Society in 1984, the Cantor Medal of the Deutsche Mathematiker-Vereinigung in 1992 and the Wolf Prize in 1995 for his work on stability in Hamiltonian systems and on nonlinear differential equations. He was elected to membership of the National Academy of Sciences in 1973 and was corresponding member of numerous foreign academies such as the London Mathematical Society and the Akademie der Wissenschaften und Literatur, Mainz . At three occasions he was an invited speaker at the quadrennial International Congress of Mathematicians, namely in Stockholm (1962) in the section on Applied Mathematics, in Helsinki (1978) in the section on Complex Analysis, and a plenary speaker in Berlin (1998). In 1990 he was awarded an honorary doctorate from the University of Bochum. The Society for Industrial and Applied Mathematics established a lecture prize in his honor in 2000. *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

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