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
EVENTS
1663 The Republic of Venice offered Stefano Degli Angeli (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
Cavalieri's indivisibles and Galileo Galilei's heliocentrism were systematically opposed by the Jesuits and attacked through a spectrum of means, be it mathematical, academic, political, or religious. Bettini called the method of indivisibles "counterfeit philosophizing" and sought to discredit it through a discussion of a paradox presented in Galileo's Discorsi. Angeli analyzes Bettini's position and proves it untenable.
On 6 December 1668 Pope Clement IX issued a brief suppressing the Jesuati order counting Angeli among its members, on the grounds that "no advantage or utility to the Christian people was to be anticipated from their survival." Writes Alexander: "It was a stunningly violent and unexpected end to an old and venerable order. Founded by the Blessed John Colombini in 1361 to tend for the poor and the sick, it had survived for [over] three centuries." While Angeli had previously published no fewer than nine books promoting and using the method of indivisibles, he did not publish a word on the topic ever again.
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.” *Pepys' Diary
Hooke most famously describes a fly's eye and a plant cell (where he coined that term because plant cells, which are walled, reminded him of the cells in a honeycomb). Known for its spectacular copperplate of the miniature world, particularly its fold-out plates of insects, the text itself reinforces the tremendous power of the new microscope. The plates of insects fold out to be larger than the large folio itself, the engraving of the louse in particular folding out to four times the size of the book. Although the book is best known for demonstrating the power of the microscope, Micrographia also describes distant planetary bodies, the wave theory of light, the organic origin of fossils, and other philosophical and scientific interests of its author.
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 It was founded with six resident members and nine non-residents.Mathematical Society was founded by school-master Henry Meissner and Master Reckoner Valentin Heins.
Heins wrote several textbooks that made him known beyond the country's borders. They were printed until the beginning of the 19th century; the Tyrocinium mercatorio-arithmeticum alone had 24 editions.
*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]
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.[citation needed] 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, he was one of the first American intellectuals to be taken seriously in Europe. He was elected to the revived American Philosophical Society in 1768. 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 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.Winthrop was recorded as owning two enslaved men, George and Scipio, in 1759 and 1761 respectively.
Portrait by John Singleton Copley, c. 1773
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, John Winthrop, 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
The Chesapeake and Delaware (C&D) Canal connects the Delaware River to the Chesapeake Bay. The C&D Canal system provides a continuous sea level channel connecting the Port of Baltimore to the ports of Wilmington (DE), Philadelphia, and the northern trade routes.
*U S Army Corp of Engineers
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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
Unfortunately, in March of that same year, Daguerre's entire laboratory burnt to the ground, destroying all his written records and much of his early experimental work–and that historical image of the moon. On March 22, 1840, John William Draper, an American doctor and chemist, took his own daguerreotype of the moon, the first known image of the full moon.
Appropriately, it was an astronomer who coined the term photography in 1839, when Johann Heinrich von Madler combined “photo” (from the Greek word for “light”) and “graphy” (“to write”). *APS.org Madler's claim rests on a paper supposedly written on 25 February 1839 in the German newspaper Vossische Zeitung. Many still credit Sir John Herschel both for coining the word and for introducing it to the public. His uses of it in private correspondence prior to 25 February 1839 and at his Royal Society lecture on the subject in London on 14 March 1839 have long been amply documented and accepted as settled facts.
On this day in 1851, George Boole wrote in a letter to William Thomson
I am now about to set seriously to work upon preparing for the press an account of my theory of Logic and Probabilities which in its present state I look upon as the most valuable if not the only valuable contribution that I have made or am likely to make to Science and the thing by which I would desire if at all to be remembered hereafter ...
*SAU
1860 Le Verrier announced the discovery of Vulcan 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
Vulcan in a lithographic map from 1846
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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
Charles Davies (1798-1876) was a graduate of the United States Military Academy at West Point, New York, who returned to teach there as a mathematics professor. His career as a teacher at West Point spanned the period 1816-1837. Both as a student and a professor at the Academy, Davies became aware of the attraction and usefulness of French mathematics texts and began translating and adapting them for American students. He soon became the most popular American author of mathematics texts designed for higher education. His partnership with the book publisher A. S. Bames also helped to promote his texts.
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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
The allegation that has impugned Mendel's integrity is Fisher's assertion that “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel's expectations,” a discovery that Fisher regarded as “abominable” and “shocking” . Much of the discrepancy results from the absence of extreme deviates, and this can largely be explained by unconscious bias in classifying ambiguous phenotypes, stopping the counts when satisfied with the results, recounting when the results seem suspicious, and repeating experiments whose outcome is mistrusted. *Natl Library of Medicine
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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
A Google Ngram view indicates the term was little known or used up to that time.
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
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
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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. 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
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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 – March 14, 2018) 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
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
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
She is also credited with the invention of the foot-pedal trash can, adding shelves to the inside of refrigerator doors (including the butter tray and egg keeper), and wall-light switches, all now standard.
Lou Hoover urged Gilbreth to join the Girl Scouts as a consultant in 1929. She remained active in the organization for more than twenty years, becoming a member of its board of directors.[45] During the Great Depression, President Hoover appointed Gilbreth to the Organization on Unemployment Relief as head of the "Share the Work" program.
Gilbreth is the recipient of twenty-three honorary degrees from schools such as Rutgers University, Princeton University, Brown University, Smith College, and the University of Michigan.*Wik
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
1912 Tibor Gallai (born Tibor Grünwald, 15 July 1912 – 2 January 1992) was a Hungarian mathematician. He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős. He was a student of Dénes Kőnig and an advisor of László Lovász. He was a corresponding member of the Hungarian Academy of Sciences (1991).
The Edmonds–Gallai decomposition theorem, which was proved independently by Gallai and Jack Edmonds, describes finite graphs from the point of view of matchings. Gallai also proved, with Milgram, Dilworth's theorem in 1947, but as they hesitated to publish the result, Dilworth independently discovered and published it.
Gallai was the first to prove the higher-dimensional version of van der Waerden's theorem.
With Paul Erdős he gave a necessary and sufficient condition for a sequence to be the degree sequence of a graph, known as the Erdős–Gallai theorem.
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
