Science can amuse and fascinate us all, but it is engineering that changes the world.

~Isaac Asimov

The 2nd day of the year; the smallest prime, and the only even prime. Euler's beautiful theorem for polyhedra shows that , the number of vertices plus the number of faces minus the number of edges will equal two.

The sum of the reciprocals of the triangular numbers is 2, 2 = 1/1 + 1/3 + 1/6 + 1/10 + ...

And perhaps the most beautiful way to define perfect numbers: Let n be a perfect number. Then the reciprocals of n's divisors sum to 2 *Algebra Fact @AlgebraFact

And a special one for the 2nd and 3rd day of 2016, sent from Robert Mařík @robert_marik

: \( 2016^2 + 2016^3 = 8197604352 \) a pandigital number using all ten decimal digits once each.

**EVENTS**

1663 The Republic of Venice offered Stefano DegliAngeli (1623–1697) the professorship of mathematics at the University of Padua, a post that Galileo held earlier. He was a student of Cavalieri who generalized the Archimedian spiral.*VFR

1665 Samuel Pepys sees a copy of Hooke’s Micrographia at his bookseller and orders a copy. “Thence to my bookseller's and at his binder's saw Hooke's book of the Microscope, which is so pretty that I presently bespoke it.” *Pepy’s Diary

1690 The Hamburg Mathematical Society was founded. It is the oldest mathematical society now in existence. The second oldest is the Amsterdam Mathematical Society founded in 1788. The Hamburg Mathematical Society was founded by school-master Henry Meissner and Master Reckoner Valentin Heins. *R C Archibald, Scripta Mathematica 1932 (With *Wik assistance from @rmathematicus and @MathBooks)

1697 In his New Year’s greetings to Duke Rudolph August, Leibniz sent a “thought-penny or medal” showing his invention of the binary system. Leibniz argued that just as all numbers can be created from the symbols 0 and 1, so God created all things. [The Monist 26 (1916), p 561]. *VFR

1738/9 At age 23, John Winthrop, former pupil of Isaac Greenwood, succeeded him as the second Hollis Professor at Harvard. [I. B. Cohen, Some Early Tools of American Science, p. 36]

1769 Originally called the Philosophical Society, on January 2, 1769, it united with the American Society for Promoting Useful Knowledge under the name "American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge". the Society was founded in 1743 by Benjamin Franklin and John Bartram as an offshoot of an earlier club, the Junto.

Since its inception, the Society attracted America's finest minds. Early members included George Washington, John Adams, Thomas Jefferson, Alexander Hamilton, James McHenry, Thomas Paine, David Rittenhouse, Nicholas Biddle, Owen Biddle, Benjamin Rush, James Madison, Michael Hillegas, John Marshall, and John Andrews. The Society also recruited philosophers from other countries as members, including Alexander von Humboldt, the Marquis de Lafayette, Baron von Steuben, Tadeusz Kościuszko, and Princess Dashkova.

By 1746 the Society had lapsed into inactivity. In 1767, however, it was revived, in 1769, it united with the American Society for Promoting Useful Knowledge Benjamin Franklin was elected the first president. During this time, the society maintained a standing Committee on American Improvements; one of its investigations was to study the prospects of a canal to connect the Chesapeake Bay and the Delaware River. The canal, which had been proposed by Thomas Gilpin, Sr., would not become reality until the 1820s *Wik

In 1839, French pioneering photographer Louis Daguerre took the first photograph of the moon. *TIS It seems it no longer survives. Earliest known surviving photograph of the Moon is a daguerreotype taken in 1851 by John Adams Whipple, shown at right. *Wik

**1860**Le Verrier announced the discovery of Vulcan by to a meeting of the Académie des Sciences in Paris. The discoverer was French physician and amateur astronomer Edmond Modeste Lescarbault, who claimed to have seen a transit of the hypothetical planet earlier in the 1859 . For half a century or more many sightings of Vulcan were reported by both professional and amateur astronomers.

Vulcan is a small hypothetical planet that was proposed to exist in an orbit between Mercury and the Sun. Attempting to explain peculiarities of Mercury's orbit, the 19th-century French mathematician Urbain Le Verrier hypothesized that they were the result of another planet, which he named "Vulcan".

A number of reputable investigators became involved in the search for Vulcan, but no such planet was ever found, and the peculiarities in Mercury's orbit have now been explained by Albert Einstein's theory of general relativity. *Wik

**1879**West Point cadet J. W. Acton wrote in his copy of Charles Davies’ Algebra (1877 edition) that he had been examined on logarithms and “fessed cold,” which was cadet slang for ﬂunking. Then he added this ditty:

This study was ordained in hell

to torment those who on earth dwell

And it suits its purpose well

Glory Hallelujah!! Amen! Amen! Amen!

Apparently Acton never mastered logarithms for he did not graduate from USMA. *VFR

1890 President Benjamin Harrison received, from the International Bureau of Weights and Measures in France, an exact duplicate of the standard kilogram; it is housed at the Bureau of Standards in Washington, D.C

1936 In a letter From R. A. Fisher to E.B.Ford, he writes, “had the shocking experience lately of coming to the conclusion that the data given in Mendel’s paper must be practically all faked.” *R A Fisher Digital Archive, University College London

1947 Matt Weinstock’s column in the Los Angeles Daily News began: “Readers of Esquire magazine [January 1948] ... are slowly losing their minds over a story by Martin Gardner” entitled the “No-Sided Professor.” This story is the ﬁrst time that the Mobius strip, a one-sided surface, was used in a piece of fantasy. The story is reprinted in Gardner’s The No-Sided Professor (1987), pp 45–58.*VFR

In 1960, John H Reynolds, (

*American physicist and a specialist in mass spectrometry*), set the age of solar system at 4,950,000,000 years.*TIS

1975 Gates and Allen name "Micro-Soft". Microsoft founders Bill Gates and Paul Allen write a letter to MITS, the Albuquerque, N.M., company that manufactured the Altair computer, offering a version of BASIC for MITS's "Altair 8800" computer. The contract for BASIC reflected the first time Gates and Allen referred to themselves as the company Microsoft, spelled in the document as "Micro-Soft." *CHM

1979 Software Arts incorporated. They designed and programmed VisiCalc, the best-selling micro-computer program ever made. *VFR VisiCalc was the first spreadsheet program available for personal computers, originally released for the Apple II. It is often considered the application that turned the microcomputer from a hobby for computer enthusiasts into a serious business tool. VisiCalc sold over 700,000 copies in six years. *Wik

**BIRTHS**

1729 Johann Daniel Titius (2 Jan 1729; 11 Dec 1796) Prussian astronomer, physicist, and biologist whose formula (1766) expressing the distances between the planets and the Sun was confirmed by J.E. Bode in 1772, when it was called Bode's Law. Titius suggested that the mean distances of the planets from the sun very nearly fit a simple relationship of A=4+(3x2n) giving the series 4, 7, 10, 16, 28, *, 52, 100, corresponding to the relative distance of the six known planets, up to Saturn, and an unassigned value (*) between Mars and Jupiter. Olbers searched for a planetary object at this empty position, thus discovering the asteroid belt. However, since the discovery of Neptune, which did not fit the pattern, the "law" is regarded as a coincidence with no scientific significance.*TIS

1822 Rudolf (Julius Emanuel) Clausius (2 Jan 1822; 24 Aug 1888) was a German mathematical physicist who was one of the founders of thermodynamics. In 1850, he stated the second law of thermodynamics. As a theoretical physicist, he also researched in molecular physics and electricty. In his published work in thermodynamics (1865) he gave the First and Second laws of thermodynamics in the following form: (1) The energy of the universe is constant. (2) The entropy of the universe tends to a maximum. In all Clausius wrote eight important papers on the topic. He restated Sadi Carnot's principle of the efficiency of heat engines. The Clausius-Clapeyron equation expresses the relation between the pressure and temperature at which two phases of a substance are in equilibrium. *TIS

1905 Lev Genrikhovich Schnirelmann (January 2, 1905 in Gomel – September 24, 1938 in Moscow) was a Soviet mathematician who sought to prove Goldbach's conjecture. In 1931, using the Brun sieve, he proved that any natural number greater than 1 can be written as the sum of not more than 20 prime numbers.

His other fundamental work is joint with Lazar Lyusternik. Together, they developed the Lyusternik-Schnirelmann category, as it is called now, based on the previous work by Henri Poincaré, David Birkhoff, and Marston Morse. The theory gives a global invariant of spaces, and has led to advances in differential geometry and topology. According to Pontryagin's memoir, Schnirelmann committed suicide in Moscow. *Wik

1920 Isaac Asimov (2 Jan 1920; 6 Apr 1992) American author and biochemist, who was a prolific writer of science fiction and of science books for the layperson. Born in Petrovichi, Russia, he emigrated with his family to New York City at age three. He entered Columbia University at the age of 15 and at 18 sold his first story to Amazing Stories. After earning a Ph.D., he taught biochemistry at Boston University School of Medicine after 1949. By 18 Mar 1941, Asimov had already written 31 stories, sold 17, and 14 had been published. As an author, lecturer, and broadcaster of astonishing range, he is most admired as a popularizer of science (The Collapsing Universe; 1977) and a science fiction writer (I, Robot;1950). He coined the term "robotics." He published about 500 volumes.*TIS

1923 Philip J. Davis (January 2, 1923; ) is an American academic applied mathematician and writer.

He is known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics. Currently a Professor Emeritus from the Division of Applied Mathematics at Brown University, he earned his degrees in mathematics from Harvard University

He was awarded the Chauvenet Prize for mathematical writing in 1963 for an article on the gamma function, and has won numerous other prizes, including being chosen to deliver the 1991 Hendrick Lectures of the MAA . In addition, he has authored several books. Among the best known are The Mathematical Experience (with Reuben Hersh), a popular survey of modern mathematics and its history and philosophy; Methods of Numerical Integration (with Philip Rabinowitz), long the standard work on the subject of quadrature; and Interpolation and Approximation, still an important reference in this area. *Wik

1938 Anatoly Mykhailovych Samoilenko (2 Jan 1938 in Potiivka, Radomyshl, Zhytomyr oblast, Ukraine, ) is a Ukrainian mathematician who worked on linear and nonlinear ordinary differential equations. *SAU

1940 Sathamangalam Ranga Iyengar Srinivasa Varadhan (2 January 1940, ) FRS is an Indian-American mathematician from Madras (Chennai), Tamil Nadu, India. Varadhan is currently a professor at the Courant Institute. He is known for his work with Daniel W. Stroock on diffusion processes. He was awarded the Abel Prize in 2007 for his work on large deviations with Monroe D. Donsker *Wik

1941 Donald B. Keck (2 Jan 1941 in Lansing, Michigan, ) American research physicist, who with his colleagues at Corning Glass, Dr. Robert Maurer and Dr. Peter Schultz, invented fused silica optical waveguide - optical fiber. This was a breakthrough creating a revolution in telecommunications, capable of carrying 65,000 times more information than conventional copper wire. In 1970, Maurer, Keck, and Schultz solved a problem that had previously stumped scientists around the world. They designed and produced the first optical fiber with optical losses low enough for wide use in telecommunications. The light loss was limited to 20 decibels per kilometer (at least one percent of the light entering a fiber remains after traveling one kilometer).*TIS

**DEATHS**

1892 Sir George Biddell Airy (27 Jul 1801, 2 Jan 1892) English astronomer who became the seventh Astronomer Royal (1836-92). In his life he studied interference fringes in optics, made a mathematical study of the rainbow and computed the density of the Earth by swinging a pendulum at the top and bottom of a deep mine, determined the mass of the planet Jupiter and its period rotation, calculated the orbits of comets and cataloged stars. He designed corrective lenses for astigmatism (1825), the first that worked. His motivation was his own astigmatism. Airy had a long-standing battle with Babbage. In 1854, the conflict continued between the two during the battle of the incompatible railway gauges in England. Airy championed the railway narrow gauge and Babbage for the wide gauge. *TIS

1913 Léon (-Philippe) Teisserenc de Bort (5 Nov 1855, 2 Jan 1913) French meteorologist who discovered the stratosphere (1902). He established own observatory at Trappes (1896) and pioneered in the use of unmanned, instrumented balloons to investigate atmosphere. Teisserenc de Bort found that above an altitude of 7 miles (11 km) temperature ceased to fall and sometimes increased slightly. He named this upper part of the atmosphere the stratosphere, because he thought that the different gases would lie in distinct strata as, without temperature differentials, there would be no mechanism to disturb them. The lower part of the atmosphere he named the troposphere (Greek: "sphere of change") as here, with abundant temperature differentials, constant change and mingling of atmospheric gases occurred. *TIS

1972 Lillian Evelyn Gilbreth (née Moller)(24 May 1878, 2 Jan 1972) American efficiency expert, who as wife of Frank Bunker Gilbreth, contracting engineer, together developed the method of time-and-motion study. Upon her marriage, 19 Oct 1904, she became a partner in her husband's fledgling motion study business. As a contractor, he was already applying ideas to improve the speed of building. After a few years, they applied motion study to industry. Each step of work activity was to be studied in detail (employing motion pictures for analysis) to determine the optimal way to execute a given task. By choosing a method of least exertion, the employees would be more healthy, more productive, and economically improve the business. She continued after her husband's death in 1924. *TIS

1992 Brian Kuttner (11 April 1908 in London, England - 2 Jan 1992 in Birmingham, England) Most of Kuttner's early work is on Fourier series and summability. Hardy quotes some of these early results of Kuttner's in his treatise Divergent series (1949). Throughout his career he continued to publish a steady stream of high quality research papers right up to the time of his death. There was no signs that his output was decreasing when he retired, rather the reverse since the publication of 8 papers in 1978 indicates that his research activity increased after he retired from the Birmingham chair in 1975. Mathematical Reviews lists over 120 of his papers, and the continuation of joint papers appearing after his death show clearly that even into his 80s his love for his favourite topics of analysis remained as strong as ever. *SAU

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell