**Those who study the stars have God for a teacher**.

~Tycho Brahe

The 348th day of the year; 348 is the sum of four consecutive primes. It is the last day of the year that is of such distinction.

348 is the smallest number whose fifth power contains exactly the same digits as another fifth power... find it.

348 is a practical number because any smaller number is the sum of distinct divisors of 348. Only three larger year days have that quality.

**EVENTS**

**1498** Luca Pacioli was professor in Milan 1496-1499. He was inspired to start his Divina Proportione on 9 Feb 1498 and completed it on 14 Dec 1498, though it was not published (in an expanded form) until 1509 . The period in Milan was the high point of his career, being a leading member of the glittering intellectual court of Lodovico Sforza. He lived at the monastery of San Simpliciano, writing his Divina Proportione, and De Viribus Quantitatis here . He was a good friend of LEONARDO DA VINCI who drew the pictures for Pacioli's book. Pacioli is our leading witness to Leonardo's work at this time, particularly the Last Supper in the Refectory of the Monastery of Santa Maria delle Grazie during 1495 1497, and he may well have advised on the perspective of the painting. Certainly Pacioli stimulated Leonardo's interest in perspective and it is possible that Leonardo's famous drawing of the proportions of the human body was inspired by Pacioli's comment on classical architecture; "For in the human body they found the two main figures ..., namely the perfect circle and the square." Pacioli seems to have made models of the polyhedra illustrated in his book, though we don't know if Leonardo used these for his drawings. A set was probably given to Pacioli's earlier patron, the Duke of Urbino, in 1494. Another set was paid for by Florence in 1504. *VFR

The first known printing of the Rhombicubeoctahedron, an Archimedian Solid with 26 faces, was Leonardo da Vinci's drawing in Divina Proportione

**In 1807**, the first meteorite strike to be recorded in the U.S. fell at Weston (now called Easton), Conn., at 6:30 a.m., making a hole 5-ft long and 4.5-ft wide. This was the New World's first witnessed fall of a meteorite, with subsequent recovery of specimens, since the arrival of the European settlers. Yale Professor Benjamin Silliman's description of the fall and his chemical analysis of the stone meteorite, the first performed in the U.S., received much attention in the national and international press. A thirty-pound fragment of this Chondrite H4 became the nucleus of Yale University’s Peabody Museum. This meteorite collection, the oldest in the country, was begun by Silliman.*TIS Eyewitnesses reported three loud explosions, and stone fragments fell in at least six locations. *Wik

**1844** Grassman had sent a copy of his book to Gauss who replied that a) I already did that fifty years ago, and b) I didn’t actually read it because I’m very busy and the terminology is difficult. Michael Cro. we described Grassmann’s book, “Grassmann’s Die lineale Ausdehnungslehre (Linear Extension Theory) demonstrated deep mathematical insights. It also in one sense contained much of the modern system of vector analysis. This, however, was embedded within a far broader system, which included n-dimensional spaces and as many as sixteen different products of his base entities (including his inner and outer products, which are respectively somewhat close to the our modern dot and cross products). Moreover, Grassmann justifies his system by philosophical discussions that may have put off many of his readers.” *A history of vector analysis: the evolution of the idea of a vectorial system, By Michael J. Crowe pg 78

**1893** The American, Dorothea Klumpke defended her thesis on Saturn’s rings for a doctorate in mathematics at the Sorbonne, before an expectant gathering of professors and several hundred spectators. “Your thesis,” said one of the examining professors during the awards ceremony, “is the ﬁrst which a woman has presented and successfully sustained with our faculty to obtain this degree. You worthily open the way.” Indeed she did, for she became a distinguished astronomer. *Sky & Telescope, August 1986, pp. 109–110. Reprinted in AWM Newsletter, 17, no. 5, p. 12-13.

**In 1900,** German physicist Max Planck made public his ideas on quantum physics at a meeting of the German Physics Society, revolutionizing scientists' understanding of physics. Planck demonstrated that in certain situations energy exhibits characteristics of physical matter, something unthinkable at the time. He suggested the explanation energy exists in discrete packets, which he called "quanta."*TIS

**1911** “So we arrived and were able to plant our ﬂag at the geographical South Pole. God be thanked!” From the diary of the Norwegian explorer, Roald Amundsen, the ﬁrst person to reach the South Pole. He was accompanied by four companions and ﬁfty-two sled dogs. *VFR

**In 1933,** Rutherford suggested the names diplogen for the newly discovered heavy hydrogen isotope and diplon for its nucleus. He presented these ideas in the Discussion on Heavy Hydrogen at the Royal Society. For ordinary hydrogen, the lightest of the atoms, having a nuclues of a sole proton, he coined a related name: haplogen. (Greek: haploos, single; diploos, double.) In 1931, Harold Urey had discovered small quantities of atoms of heavy hydrogen wherever ordinary hydrogen occurred. The mass of its nucleus was double that of ordinary hydrogen. This hydrogen-2 is now called deuterium, as named by Urey (Greek: deuteros, second). Its nucleus, named a deuteron, has a neutron in addition to a proton. *TIS

**1946 **Denmark issued a stamp commemorating the 400th anniversary of the birth of the mathematician and astronomer Tycho Brahe. [Scott #300]. (TOP)*VFR

**1981** The New Yorker carried a long interview with Marvin Minsky, tracing his biography and the development of artiﬁcial intelligence. [Mathematics Magazine 55(1982), p. 245]. *VFR

**1952** U.S. Navy Approaches MIT to create Whirlwind

U.S. Navy issues a formal Letter of Intent to MIT for development of the Airplane Stability and Control Analyzer (ASCA) program, the beginning of the project Whirlwind. Constructed under the leadership of Jay. W. Forrester, the Whirlwind was the first high-speed electronic digital computer that was able to operate in real time with the remarkable electronic reliability. By December 1954, the computer comprised 12,500 vacuum tubes and 23,800 crystal diodes, occupying a two-story building. It operated until 1959.

Whirlwind served as an experimental prototype for the IBM’s AN/FSQ-7 manufactured for the SAGE air defense system, and influenced the early IBM 700 series computers and computers developed by Digital Equipment Corporation. *CHM

**In 1967**, the first synthesis of biologically active DNA in a test tube was announced at a press conference by Arthur Kornberg who had worked with Mehran Goulian at Stanford and Robert L. Sinsheimer of MIT. Kornberg chose to replicate the relatively simple DNA chain of the Phi X174 virus, which infects bacteria (a bacteriophage). It has a single strand of DNA only about 5500 nucleotide building blocks long, and with about 11 genes, it was easier to purify without breaking it up. Having isolated the Phi X174 DNA, they used the DNA from E. coli, a common bacterium in the human intestine that could copy a DNA template from any organism. The viral DNA template thus copied was found to be able to infect bacteria - it was error-free, active DNA. *TIS

2009 On 14 December 2009, the Orient Express ceased to operate and the route disappeared from European railway timetables, reportedly a "victim of high-speed trains and cut-rate airlines" *Wik

2014. The annual Geminids meteor shower will reach its peak late on Saturday night and into early Sunday morning.

The meteors will appear to radiate from a point near the star Castor, in the constellation Gemini.

In the Northern hemisphere, that will be westward and nearly overhead in the early hours of Sunday. *BBC News

**BIRTHS**

**1503 The astrologer Nostradamus** is born. [Muller] *VFR

**1546 Tycho Brahe** (14 Dec 1546; 24 Oct 1601) Danish astronomer whose work in developing astronomical instruments and in measuring and fixing the positions of stars paved the way for future discoveries. He studied the nova of 1572 ("Tycho's star") showed that it was a fixed star. His report, De nova...stella (1573), was taken by many as proof of the inadequacy of the traditional Aristotelian cosmology. In 1577, he moved to his own observatory on Hven Island (financed by King Frederick II). Before the invention of the telescope, using his nine-foot armillary sphere and his fourteen-foot mural quadrant, he charted the positions of 777 stars with an unparallelled accuracy. In 1599 he moved to Prague, with Johannes Kepler as his assistant. *TIS

**1760 The Very Reverend James Wood **(14 December 1760 – 23 April 1839) was a mathematician, Dean of Ely and Master of St John's College, Cambridge.

Wood was born in Holcombe where his father ran an evening school and taught his son the elements of arithmetic and algebra. From Bury Grammar School he proceeded to St John's College, Cambridge in 1778, graduating as senior wrangler in 1782. On graduating he became a fellow of the college and in his long tenure there produced several successful academic textbooks for students of mathematics. (The Elements of Algebra (1795); The Principles of Mechanics (1796); The Elements of Optics (1798))

Wood remained for sixty years at St. John's, serving as both President (1802–1815) and Master (1815–1839); on his death in 1839 he was interred in the college chapel and bequeathed his extensive library to the college, comprising almost 4,500 printed books on classics, history, mathematics, theology and travel, dating from the 17th to the 19th centuries.[3]

Wood was also ordained as a priest in 1787 and served as Dean of Ely from 1820 until his death.{He was succeeded by another eminent mathematician, George Peacock)*Wik

**1904 Nikolai Grigor'evich Chudakov** (1904–1986) was a Russian and Soviet mathematician. He was born in Lysovsk, Novo-Burassk, Saratov, Russian Empire. His father worked as a medical assistant.

He first studied at the Faculty of Physics and Mathematics at Saratov State University, but then he transferred to Moscow University. He then graduated in 1927. In 1930, he was named head of higher mathematics at Saratov University. In 1936, he successfully defended his thesis and became a Doctor of Science. Among others, he considerably improved a result from Guido Hoheisel and Hans Heilbronn on an upper bound for prime gaps. *Wik

**1914 Solomon Spiegelman** (14 Dec 1914; 21 Jan 1983) American microbiologist and geneticist who discovered that only one of two strands of molecules that make up DNA, carried the genetic information to produce new substances. The carrier was called ribonucleic acid (RNA). In 1962, he developed a technique that allowed the detection of specific RNA and DNA molecules in cells. This technique, called nucleic acid hybridization, is credited for helping to lay the groundwork for current advances in recombinant DNA technology. Much earlier, his Ph.D. thesis (1944) was the first work to establish that genes are activated and deactivated by compounds that he called inducers, which thus radically affect the pattern of proteins that a cell fabricates without actually altering the genes themselves. *TIS

**1922 Nikolay Gennadiyevich Basov** (14 Dec 1922, )Soviet physicist, best known for the development of the maser, the precursor of the laser. In 1955, while working as a research student with Aleksandr Prokhorov (1916- ) at the Soviet Academy of Sciences, he devised a microwave amplifier based on ammonia molecules. The two scientists shared the 1964 Nobel Prize (with American Charles Townes (1915- ), who independently developed a maser), for basic research in quantum electronics that led to the development of both the maser and the laser. These devices produce monochromatic, parallel, coherent beams of microwaves and light, respectively. Basov went on to develop the laser principle, and introduced the idea of using semiconductors to achieve laser action (1958). *TIS

**1936 Charles Terence Clegg ("Terry") Wall** (born 14 December 1936 in Bristol, England) is a leading British mathematician, educated at Marlborough and Trinity College, Cambridge. He is an emeritus professor of the University of Liverpool, where he was first appointed Professor in 1965. From 1978 to 1980 he was the President of the London Mathematical Society.

His early work was in cobordism theory in algebraic topology; this includes his 1959 Cambridge Ph.D thesis entitled "Algebraic aspects of cobordism", written under the direction of Frank Adams and Christopher Zeeman. His research was then mainly in the area of manifolds, particularly geometric topology and related abstract algebra included in surgery theory, of which he was one of the founders. His 1970 research monograph "Surgery on Compact Manifolds" is a major reference work in geometric topology.

In 1971 he conjectured that every finitely generated group is accessible. This conjecture is known as "Wall's conjecture". It motivated much progress in the understanding of splittings of groups. In 1985 Martin J. Dunwoody proved the conjecture for the class of finitely presented groups. The resolution of the full conjecture took until 1991 when, surprising to most mathematicians at the time, Dunwoody found a finitely generated group that is not accessible and hence the conjecture turned out to be not correct in its general formulation.

C.T.C Wall's work since the mid-1970s has mostly been in singularity theory as developed by R. Thom, J. Milnor and V. Arnold, and especially concerns the classification of isolated singularities of differentiable maps and of algebraic varieties. He has written two research monographs on singularity theory, "The Geometry of Topological Stability" (1989) (containing a great deal of original work) with Andrew du Plessis, and "Singular Points of Plane Curves" (2004).*Wik

**DEATHS**

**1710 Henry Aldrich **(1647 – 14 December 1710) was an English theologian and philosopher.He had wide interests including mathematics, music, and architecture. He was well known as a humorist and Suttle describes him as".. a punner of the first value. "

In 1674 he published Elementa geometricae which led to him being described by his Christ Church colleagues as ".. a great mathematician of our house."

In 1691 he published Artis logicae compendium a treatise on logic which was to be the main text on the topic for 150 years in England. Even when Richard Whately published Elements of logic in 1826 it still took Aldrich's work as his starting point. *SAU

**1897 Francesco Brioschi** (22 December 1824 – 13 December 1897) was an Italian mathematician born in Milan in 1824. From 1850 he taught analytical mechanics in the University of Pavia. After the Italian unification in 1861, he was elected depute in the Parliament of Italy and then appointed twice secretary of the Education Minister. In 1863 he founded the Politecnico di Milano university, where he worked until death. In 1870 he became member of the National Academy of the Lincei and in 1884 he succeed Quintino Sella as president of the National Academy of the Lincei. He directed the Il Politecnico (English translation: The Polytechnic) review and, between 1867 and 1877, Annali di matematica pura e applicata (English translation: Annals of pure and applied mathematics). He died in Milan in 1897.

As mathematician, Brioschi publicized in Italy various algebraic theories and studied the problem of solving fifth and sixth grade equations using elliptic functions. Brioschi is also remembered as a distinguished teacher: among his students in the University of Pavia there were Eugenio Beltrami, Luigi Cremona and Felice Casorati.*Wik

**1927 Yulian-Karl Vasilievich Sokhotsky **(2 Feb 1842 in Warsaw, Poland - 14 Dec 1927 in Leningrad, USSR (now St Petersburg, Russia)) The magister's thesis of Sokhotskii was the first research paper on complex analysis published in Russian. It contains many important results which were later ascribed to other mathematicians. First of all, there is the famous theorem on the behaviour of an analytic function in a neighbourhood of an essential singularity. This theorem was published by Sokhotskii (in his magister's thesis) and by Casorati in 1868, whereas Weierstrass published it eight years later - in 1876. Furthermore, Sokhotskii was the first to apply the calculus of residues to Legendre polynomials. The credit for this procedure is usually given to Hermann Laurent. Finally, the so-called Plemelj formulas are also due to Sokhotskii, who published them in his doctor's thesis in 1873, that is to say 35 years before Plemelj. *SAU

**1976 Donald H(oward) Menzel **(11 Apr 1901, 14 Dec 1976) was an American astronomer best known for his arguments against the existance of extraterrestrial UFO's. Menzel was one of the first practitioners of theoretical astrophysics in the United States and pioneered the application of quantum mechanics to astronomical spectroscopy. An authority on the sun's chromosphere, he discovered with J. C. Boyce (1933) that the sun's corona contains oxygen. With W. W. Salisbury he made (1941) the first of the calculations that led to radio contact with the moon in 1946. He supervised the assignment of names to newly discovered lunar features. *TIS

**1989 Andrey Dmitriyevich Sakharov** (21 May 1921, 14 Dec 1989) Soviet nuclear physicist, an outspoken advocate of human rights in the Soviet Union. At the end of World War II, Sakharov returned to pure science and the study of cosmic rays. Two years later, he began work with a secret research group on the development of the hydrogen bomb, and he is believed to have been principally responsible for the Soviets' success in exploding their first thermonuclear bomb (1954). With I.E. Tamm, he proposed controlled thermonuclear fusion by confining an extremely hot ionized plasma in a torus-shaped magnetic bottle, known as a tokamak device. He became politically more active in the 1960s, campaigned against nuclear proliferation, and from 1980 to 1986, he was banished and kept under police surveillance.*TIS

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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