Sunday, 19 April 2015

On This Day in Math - April 19

People must understand that science is inherently neither a potential for good nor for evil. It is a potential to be harnessed by man to do his bidding.
~Glenn T. Seaborg

The 109th day of the year; 109 is a twin prime with 107. I just found out that the product of twin primes (greater than 5) will have a digit root of 8..
5 * 7 = 35, 3 + 5 = 8
11 * 13 = 143, 1 + 4 + 3 = 8
17 * 19 = 323, 3 + 2 + 3 = 8
Hat tip to Ben Vitale

109 = 1*2+3*4+5*6+7*8+9.
The period of the reciprocal of 109 ends with 853211 (the beginning of the Fibonacci sequence reversed).

1739  John Winthrop (12 Dec 1714-1779) of Cambridge, Mass., the first astronomer of note in the U.S. began sunspot observations and continued over the next two days. No observations were possible on 21 Apr due to cloudy weather. His observations exist as one-page reports in the University Archives of Harvard University, though they were never published. In 1761, he went on an expedition to St. John’s, Newfoundland, to observe the transit of Venus across the sun on 6 Jun 1761, which measurements could be used to compute the distance between the sun and the Earth. He also observed the transit of 1769 from Cambridge.*TIS

1760 Euler writes the first of many “Letters to a German Princess”.. Madam, The hope of having the honor to communicate, in person, to your Highness, my lessons in geometry, becoming more and more distant, which is a very sensible mortification to me, I feel myself impelled to supply personal instruction by writing, as far as the nature of the objects can permit.” Thus begins the letter on “of maginitude or extension” . the letters will continue, two or more per week, for the next three years. *VFR

1879 “A red letter day in Massachusetts. On that day the second circular which launched the Harvard ‘Annex’, later Radcliffe College, was sent out ... ” Mathematics 2 dealt with plane geometry and algebra through quadratics. [Scripta Mathematica, 11(1945), p. 260] *VFR

1957 First FORTRAN program run.[The first FORTRAN program (other than internal IBM testing) runs at Westinghouse, producing a missing comma diagnostic. A successful attempt followed.*CHM] I think the first actual program run of Fortran is described here. It was a calculation using gamma function.

1958 France issued a stamp to honor Jean Cavailles (1903–1944) as a hero of the French Underground during World War II. [Scott #879] *VFR He was a French philosopher and mathematician, specialized in philosophy of science. He took part in the French Resistance within the Libération movement and was shot by the Gestapo on February 17, 1944. *Wik

1975 India’s first scientific satellite was successfully launched from a Soviet cosmodrome with the help of the Soviet rocket carrier at 1300 hours Indian standard time. The satellite was named Aryabhata, after the famous Indian astronomer and mathematician, who was born in Kusuma­pura, near present-day Patna, in A.D. 476. [Eves, Return to Mathematical Circles,7◦]*VFR

1977 The German Democratic Republic issued a stamp commemorating the 200th anniversary of Gauss’s birth, 30 April 1777. Besides a portrait of Gauss there is a geometric construction (dealing with the constructible regular polygons?). Why wasn’t it issued on the anniversary day? [Scott #1811] *VFR I found a different stamp than the one Professor Rickey describews issued for the same reason showing complex plane. (pb) also found this anecdote about Gauss recently, "Such was his admiration of Karl Friedrich Gauss that the German mathematician Peter Dirichlet is said to have slept with Gauss's Disquisitiones Arithmeticae under his pillow. [The admiration was mutual: "The total number of Dirichlet's publications is not large," Gauss once remarked. "Jewels are not weighed on a grocery scale." (Gauss's motto? "Few, but ripe.")] *anecdotatge web site and one more note for students.. To understand a little more about "constuctable" see this post by Alexander Bogomolny at "Cut the Knot".

1988 In an article entitled “Hot hands phenomenon: A myth?” the New York Times (pp. 23, 25) reported on work of the Stanford Psychologist A. Iversky. Most fans believe that a player who has made a string of baskets is likely to succeed on the next try. By examining thousands of shots of the Philadelphia 76ers over a season and a half, Iversky has shown otherwise: Outcomes of successive shots are independent. [Mathematics Magazine 61 (1988), p. 268].*VFR [The article is here (pb)]

1748 D'Amondans Charles de Tinseau (19 April 1748 in Besançon, France - 21 March 1822 in Montpellier, France) wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes that Tinseau's works, "... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space." Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites. He also wrote Solution de quelques questions d'astronomie on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics. *SAU

1801 Gustav Theodor Fechner (19 Apr 1801; 18 Nov 1887 at age 86) German physicist and philosopher who was a key figure in the founding of psychophysics, the science concerned with quantitative relations between sensations and the stimuli producing them. He formulated the rule known as Fechner’s law, that, within limits, the intensity of a sensation increases as the logarithm of the stimulus. He also proposed a mathematical expression of the theory concerning the difference between two stimuli, advanced by E. H. Weber. (These are now known to be only approximately true. However, as long as the stimulus is of moderate intensity, then the laws will give us a good estimate.) Under the name “Dr. Mises” he also wrote humorous satire. In philosophy he was an animist, maintaining that life is manifest in all objects of the universe. *TIS

1880 Evgeny Evgenievich Slutsky (19 April 1880 in Novoe, Yaroslavl guberniya, Russia - 10 March 1948 in Moscow, USSR) Slutsky was important in the application of mathematical methods in economics. Slutsky introduced stochastic concepts of limits, derivatives and integrals between 1925 to 1928 while he worked at the Conjuncture Institute. In 1927 he showed that subjecting a sequence of independent random variables to a sequence of moving averages generated an almost periodic sequence. This work stimulated the creation of stationary stochastic processes. He also studied correlations of related series for a limited number of trials. He obtained conditions for measurability of random functions in 1937. He applied his theories widely, in addition to economics mentioned above he also studied solar activity using data from 500 BC onwards. Other applications were to diverse topics such as the pricing of grain and the study of chromosomes. *SAU

1883 Richard von Mises (19 Apr 1883; 14 Jul 1953 at age 70.) Austrian-American mathematician and aerodynamicist who notably advanced statistics and the theory of probability. Von Mises' contributions range widely, also including fluid mechanics, aerodynamics, and aeronautics. His early work centred on aerodynamics. He investigated turbulence, making fundamental advances in boundary-layer-flow theory and airfoil design. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. He introduced a stress tensor which was used in the study of the strength of materials.Von Mises' primary work in statistics concerned the theory of measure and applied mathematics. His most famous, yet controversial, work was in probability theory *TIS

1912 Glenn T. Seaborg (19 Apr 1912; - 25 Feb 1999 at age 86) American nuclear chemist. During 1940-58, Seaborg and his colleagues at the University of California, Berkeley, produced nine of the transuranic elements (plutonium to nobelium) by bombarding uranium and other elements with nuclei in a cyclotron. He coined the term actinide for the elements in this series. The work on elements was directly relevant to the WW II effort to develop an atomic bomb. It is said that he was influential in determining the choice of plutonium rather than uranium in the first atomic-bomb experiments. Seaborg and his early collaborator Edwin McMillan shared the 1951 Nobel Prize for chemistry. Seaborg was chairman of the US Atomic Energy Commission 1962-71. Element 106, seaborgium (1974), was named in his honor. *TIS

1966 Brett J. Gladman (April 19, 1966 - ) is a Canadian astronomer and a full professor at the University of British Columbia's Department of Physics and Astronomy in Vancouver, British Columbia. He holds the Canada Research Chair in Planetary Astronomy.
Gladman is best known for his work in dynamical astronomy in the Solar System. He has studied the transport of meteorites between planets, the delivery of meteoroids from the main asteroid belt, and the possibility of the transport of life via this mechanism, known as panspermia. He also studies planet formation, especially the puzzle of how the giant planets came to be.
He is discoverer or co-discoverer of many astronomical bodies in the solar system, asteroids, Kuiper Belt comets, and many moons of the giant planets:

Uranus: Caliban, Sycorax, Prospero, Setebos, Stephano, and Ferdinand
Saturn: A dozen satellites in several groups, each named after a theme of Canadian Inuit gods, French deities, and Norse gods
Neptune: The satellite Neso
Jupiter: Discovery and co-discovery of 6 moons

Gladman is a member of the Canada France Ecliptic Plane Survey (CFEPS), which has detected and tracked the world's largest sample of well-understood Kuiper Belt comets, including unusual objects like Buffy = 2004 XR190 and Drac. *Wik

1567  Michael Stifel (1487 in Esslingen, Germany - 19 April 1567 in Jena, Germany). This number mystic (for his “beasting” of Pope Leo X, see Eves, History,p. 199) became the greatest German algebraist of the sixteenth century. He died on the same date in 1567. [Muller] *VFR His most important work is "Arithmetica integra" (1544) contained important innovations in mathematical notation. It has the first use of multiplication by juxtaposition (with no symbol between the terms) in Europe. He is the first to use the term "exponent". The book contains a table of integers and powers of 2 that some have considered to be an early version of a logarithmic table. In 1532 Stifel published anonymously his "Ein Rechenbuchlin vom EndChrist. Apocalyps in Apocalypsim" (A Book of Arithmetic about the AntiChrist. A Revelation in the Revelation). This predicted that Judgement Day the world would end at 8am on October 19, 1533. When this prediction failed, he did not make any other predictions. *Wik (Some sources say he was also born on April 19)
Here is a clip from Louis Karpinski's Unified Mathematics about Stifel's contribution to logarithms:

1739 Nicholas Saunderson died of scurvy at age 56. At age 1 he became blind from smallpox. This did not prevent him from learning Greek, Latin and French and “hearing” the works of Euclid, Archimedes, and Diophantus in the original, learning some parts by heart. He created a “palpable arithmetic,” a nailboard for doing arithmetic and forming diagrams with silk threads—the forerunner of the geoboard. He became Lucasian professor at Cambridge in 1711 and earned a reputation as an excellent teacher.*VFR Would love to have an image of one of these he actually used... anyone?
According to Stephen M. Stigler, he may have been the earliest discoverer of Bayes theorem

1791 Richard Price (23 February 1723 – 19 April 1791) was a British moral philosopher and preacher in the tradition of English Dissenters, and a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He fostered connections between a large number of people, including writers of the Constitution of the United States. He spent most of his adult life as minister of Newington Green Unitarian Church, where possibly the congregant he most influenced was early feminist Mary Wollstonecraft, who extended his ideas on the egalitarianism inherent in the spirit of the French Revolution to encompass women's rights as well. In addition to his work as a moral and political philosopher, he also wrote on issues of statistics and finance, and was inducted into the Royal Society for these contributions. Price was a friend of the mathematician and clergyman Thomas Bayes. He edited Bayes' most famous work "An Essay towards solving a Problem in the Doctrine of Chances" which contains Bayes' Theorem, one of the most fundamental theorems of probability theory, and arranged for its posthumous publication. Price wrote an introduction to Bayes' paper which provides some of the philosophical basis of Bayesian statistics.
Besides the above-mentioned, Price wrote an Essay on the Population of England (2nd ed., 1780) which directly influenced Thomas Robert Malthus.*Wik

1882 Charles Robert Darwin (12 Feb 1809, 19 Apr 1882 at age 73) was an English naturalist who presented facts to support his theory of the mode of evolution whereby favourable variations would survive which he called "Natural Selection" or "Survival of the Fittest," and has become known as Darwinism. His two most important books were On the Origin of Species by Means of Natural Selection (1859) and The Descent of Man, and Selection in Relation to Sex.

1889 Warren De la Rue (15 Jan 1815, 19 Apr 1889 at age 74)English astronomer who pioneered in astronomical photography, the method by which nearly all modern astronomical observations are made. *TIS In 1854 he turned his attention to solar physics, and for the purpose of obtaining a daily photographic representation of the state of the solar surface he devised the photoheliograph, described in his report to the British Association, On Celestial Photography in England (1859), and in his Bakerian Lecture (Phil. Trans. vol. clii. pp. 333–416). Regular work with this instrument, inaugurated at Kew by De la Rue in 1858, was carried on there for fourteen years; and was continued at the Royal Observatory, Greenwich, from 1873 to 1882. The results obtained in. the years 1862–1866 were discussed in two memoirs, entitled Researches on Solar Physics, published by De la Rue, in conjunction with Professor Balfour Stewart and Mr B Loewy, in the Phil. Trans. *Wik

1906 Pierre Curie (15 May 1859, 19 Apr 1906 at age 46)French physical chemist and cowinner of the Nobel Prize for Physics in 1903. His studies of radioactive substances were made together with his wife, Marie Curie, whom he married in 1895. They were achieved under conditions of much hardship - barely adequate laboratory facilities and under the stress of having to do much teaching in order to earn their livelihood. Together, they discovered radium and polonium in their investigation of radioactivity by fractionation of pitchblende (announced in 1898). Later they did much to elucidate the properties of radium and its transformation products. Their work in this era formed the basis for much of the subsequent research in nuclear physics and chemistry. *TIS

1933 Ernest William Hobson FRS (27 October 1856 – 19 April 1933) was an English mathematician, now remembered mostly for his books, some of which broke new ground in their coverage in English of topics from mathematical analysis. He was Sadleirian Professor at the University of Cambridge from 1910 to 1931. He was the brother of the economist John A. Hobson. He became a Fellow of Christ's almost immediately after graduation. He made his way into research mathematics only gradually, becoming an expert in the theory of spherical harmonics. His 1907 work on real analysis was something of a watershed in the British mathematical tradition; and was lauded by G. H. Hardy. It included material on general topology and Fourier series that was topical at the time; and included mistakes that were picked up later (for example by R. L. Moore).*Wik He fought against “the superstition that it is impossible to be ‘rigorous’ without being dull.” “Althouth he lived to be seventy-six he was active almost up to his death; his last book (and perhaps in some ways his best) was published when he was seventy-four. He was a singular exception to the general rule that good mathematicians do their best work when they are young.” See The Mathematical Intelligencer, 6(1984), no. 2, p. 9. *VFR

1914 Charles Sanders Peirce (10 Sep 1839, 19 Apr 1914 at age 74)American scientist, logician, and philosopher who is noted for his work on the logic of relations and on pragmatism as a method of research. He was the first modern experimental psychologist in the Americas, the first metrologist to use a wave-length of light as a unit of measure, the inventor of the quincuncial projection of the sphere, the first known conceiver of the design and theory of an electric switching-circuit computer, and the founder of "the economy of research." He is the only system-building philosopher in the Americas who has been both competent and productive in logic, in mathematics, and in a wide range of sciences. *TIS Charles Sanders Peirce was the son of Sarah Hunt Mills and Benjamin Peirce, himself a professor of astronomy and mathematics at Harvard University, perhaps the first serious research mathematician in America. At 12 years of age, Charles read an older brother's copy of Richard Whately's Elements of Logic, then the leading English-language text on the subject. Thus began his lifelong fascination with logic and reasoning. *Wik

1974 Alexander Dinghas (February 9, 1908 – April 19, 1974) was a Turkish mathematician. He is known for his work in different areas of mathematics including differential equations, functions of a complex variable, functions of several complex variables, measure theory and differential geometry. His most important contribution was his work in function theory, in particular Nevanlinna theory and the growth of subharmonic functions.*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

Saturday, 18 April 2015

On This Day in Math - April 18

It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry.
~Albert Einstein

The 108th day of the year; 108 can be written as the sum of a cube and a square (a^3 + b^2) in two ways. This is the smallest number with this property. *Prime Curios
AND 108 = 1¹ • 2² • 3³ *jim wilder ‏@wilderlab
The concatenation of 108 with its previous and next number is prime, i.e., 108107 and 108109 are primes.
108 is the smallest possible sum for a set of six distinct primes such that the sum of any five is prime: {5, 7, 11, 19, 29, 37}.

1557 Maurolico completed the first volume of his Arithmetic at three o’clock in the morning on Easter Sunday. [Jean Cassinet, Mathematics from Manuscript to Print, 1300–1600, p. 162; Thanks to Dave Kullman]*VFR Throughout his lifetime, he made contributions to the fields of geometry, optics, conics, mechanics, music, and astronomy. He edited the works of classical authors including Archimedes, Apollonius, Autolycus, Theodosius and Serenus. He also composed his own unique treatises on mathematics and mathematical science. *Wik

1694 An ad for William Leybourne's Pleasure with Profit appears in The Proceedings of the Old Bailey:
Pleasure with Profit: Consisting of Recreations of divers kinds, viz. Numerical, Geometrical, Mathematical, Astronomical, Arithmetical, Cryptographical, Magnetical, Authentical, Chymical, and Historical. Published to Recreate Ingenious Spirit, and to induce them to make further scrutiny how these (and the like) Sublime Sciences. And to divert them from following such Vices, to which Youth (in this Age) are so much inclin'd. By William Laybourn, Philomathes.
A nice discussion of the "Uphill Climber", one of the problems in the book, is explained by the excellent mathematical writer, Julian Havel. *

1775 Paul Revere’s Ride. The revolutionary War began the next day. Now you probably think this has nothing to do with mathematics, but how do you suppose he got that lantern up in the church steeple? Easy, he used a key to get in. Since he was a change ringer, a highly mathematical activity, he needed a key to get up to the bells. *VFR

1796 Professor E. A. W. Zimmerman sends a short notice of Gauss’s work on constructibility of regular polygons (see March 30, 1796) to the Jenenser Intelligenzblatt. He adds, “It is worthy of notice that Herr Gauss is now in his 18th year and has devoted himself here in Brunswick to philosophy and classical literature with just as great success as to higher mathematics.” [Tietze, 204] *VFR (found this on Twitter from Matt Henderson....and loved it..
"Erdős believed God had a book of all perfect mathematical proofs.
God believes Gauss has such a book.")

1810 Gauss elected a member of the Berlin Academy of Sciences. *VFR

1831 Founding of the University of the City of New York. [Muller] *VFR

1905 The first mention of the word genetics seems to occur in a letter from William Bateson to Adam Sedgwick. A photo of the letter is here

1942 GE builds first US Jet Aircraft Engine: In1941, the U.S. Army Air Corps picked GE's Lynn, Massachusetts, plant to build a jet engine based on the design of Britain's Sir Frank Whittle. Six months later, on April 18, 1942, GE engineers successfully ran the I-A engine.
In October 1942, at Muroc Dry Lake, California, (today, Edwards Air Force Base) two I-A engines powered the historic first flight of a Bell XP-59A Airacomet aircraft, launching the United States into the Jet Age. *About GE website

1958 India issued a stamp commemorating the centenary of the birth of Dr. Dhondo Keshav Karve (1858–1922), pioneer of women’s education. [Scott #299]*VFR

1986 IBM First to Use Megabit Chip:
Newspapers report that IBM had become the first computer manufacturer to use a megabit chip -- a memory chip capable of storing 1 million bits of information -- in a commercial product, its Model 3090. The announcement is heralded as a notable triumph for American computer makers, whose work had been perceived as having fallen behind that of the Japanese electronics industry.*CHM

2011 Scientists demonstrate mathematically that asymmetrical materials should be possible; such material would allow most light or sound waves through in one direction, while preventing them from doing so in the opposite direction; such materials would allow the construction of true one-way mirrors, soundproof rooms, or even quantum computers that use light to perform calculations. *Wik

1772 David Ricardo (18 April 1772 – 11 September 1823) was an English political economist, often credited with systematizing economics, and was one of the most influential of the classical economists, along with Thomas Malthus, Adam Smith, and John Stuart Mill. He was also a member of Parliament, businessman, financier and speculator, who amassed a considerable personal fortune. Perhaps his most important contribution was the law of comparative advantage, a fundamental argument in favor of free trade among countries and of specialization among individuals. Ricardo argued that there is mutual benefit from trade (or exchange) even if one party (e.g. resource-rich country, highly skilled artisan) is more productive in every possible area than its trading counterpart (e.g. resource-poor country, unskilled laborer), as long as each concentrates on the activities where it has a relative productivity advantage. *Wik

1863 H(ugh) L(ongbourne) Callendar (18 Apr 1863, 21 Jan 1930) was an English physicist famous for work in calorimetry, thermometry and especially, the thermodynamic properties of steam. He published the first steam tables (1915). In 1886, he invented the platinum resistance thermometer using the electrical resistivity of platinum, enabling the precise measurement of temperatures. He also invented the electrical continuous-flow calorimeter, the compensated air thermometer (1891), a radio balance (1910) and a rolling-chart thermometer (1897) that enabled long-duration collection of climatic temperature data. His son, Guy S. Callendar linked climatic change with increases in carbon dioxide (CO2) resulting from mankind's burning of carbon fuels (1938), known as the Callendar effect, part of the greenhouse effect.*TIS

1892 Dmitrii Evgenevich Menshov (18 April 1892 in Moscow, Russia - 25 Nov 1988)
For his work on the representation of functions by trigonometric series, Menshov was awarded a State Prize in 1951. He was then elected a Corresponding Member of the USSR Academy of Sciences in 1953. In 1958 Menshov attended the International Congress of Mathematicians in Edinburgh and he was invited to address the Congress with his paper On the convergence of trigonometric series. *SAU

1907 Lars Valerian Ahlfors (18 Apr 1907; 11 Oct 1996 at age 89) Finnish mathematician who was awarded one of the first two Fields Medals in 1936 for his work with Riemann surfaces. He also won the Wolf Prize in 1981.*TIS

1904 Stefan E Warschawski (18 April 1904 in Lida, Russia (now Belarus)- 5 May 1989 in San Diego, California, USA) With careful scholarship, he made lasting contributions to the theory of complex analysis, particularly to the theory of conformal mappings. With keen judgment, he guided two mathematics departments to eminence. With modest gratitude, he cemented many friendships along the way.*SAU

1911 Maurice Goldhaber (18 Apr 1911; 11 May 2011 at age 100) Austrian-American physicist who devised an experiment to show that neutrinos always rotate in one direction (only counterclockwise). His method was simple, elegant, and used an apparatus small enough to fit on a benchtop, rather than employing a huge accelerator. He also discovered that the nucleus of the deuterium atom consists of a proton and a neutron. In the decade (1961-73) that he headed the Brookhaven National Laboratory in New York, he oversaw the experiments there which led to three Nobel Prizes. He died at age 100.*TIS

1916 Ellis Robert Kolchin (April 18, 1916 – October 30, 1991) was an American mathematician at Columbia University. Kolchin earned a doctorate in mathematics from Columbia University in 1941 under supervision of Joseph Ritt. He was awarded a Guggenheim Fellowship in 1954 and 1961.
Kolchin worked on differential algebra and its relation to differential equations, and founded the modern theory of linear algebraic groups.*Wik

1918 Hsien Chung Wang (18 April 1918 in Peking (now Beijing), China - 25 June 1978 in New York, USA)worked on algebraic topology and discovered the 'Wang sequence', an exact sequence involving homology groups associated with fibre bundles over spheres. These discoveries were made while he worked with Newman in Manchester. Wang also solved, at that time, an important open problem in determining the closed subgroups of maximal rank in a compact Lie group. *SAU

1928 Mikio Sato (April 18, 1928 - ) is a Japanese mathematician, who started the field of algebraic analysis. He studied at the University of Tokyo, and then did graduate study in physics as a student of Shin'ichiro Tomonaga. From 1970 Sato has been professor at the Research Institute for Mathematical Sciences, of Kyoto University.
He is known for his innovative work in a number of fields, such as prehomogeneous vector spaces and Bernstein–Sato polynomials; and particularly for his hyperfunction theory. This initially appeared as an extension of the ideas of distribution theory; it was soon connected to the local cohomology theory of Grothendieck, for which it was an independent origin, and to expression in terms of sheaf theory. It led further to the theory of microfunctions, interest in microlocal aspects of linear partial differential equations and Fourier theory such as wave fronts, and ultimately to the current developments in D-module theory. Part of that is the modern theory of holonomic systems: PDEs over-determined to the point of having finite-dimensional spaces of solutions.
He also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension. In number theory he is known for the Sato–Tate conjecture on L-functions.*Wik

1945 Joseph Bernstein (April 18, 1945, ) is an Israeli mathematician working at Tel Aviv University. He works in algebraic geometry, representation theory, and number theory.
Bernstein received his Ph.D. in 1972 under Israel Gelfand at Moscow State University. He was a visiting scholar at the Institute for Advanced Study in 1985-86 and again in 1997-98.
Bernstein was elected to the Israel Academy of Sciences and Humanities in 2002 and was elected to the United States National Academy of Sciences in 2004. In 2004, Bernstein was awarded the Israel Prize for mathematics. In 2012 he became a fellow of the American Mathematical Society. *Wik

1949 Charles Louis Fefferman born in Washington, D.C. In 1978 he received a Fields Medal for his work on complex analysis.*VFR As a child prodigy, his accelerated schooling resulted a B.S. degrees in physics and mathematics by age 17 and a Ph.D. in mathematics at age 20 from Princeton University (1969). When in he became a professor (1971) at the University of Chicago at the age of 22, he was the youngest full professor ever in the U.S. Two years later, he returned to Princeton as a professor (1973). His Ph.D. dissertation was on "Inequalities for Strongly Regular Convolution Operators." His field of study includes his interest in physics - applied mathematics in vibrations, heat, turbulence, though he is best known for his theoretical work. *TIS

1756 Jacques Cassini (18 Feb 1677; 18 Apr, (or Sometimes given 16 Apr) 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1674 John Graunt- (24 Apr 1620, 18 Apr 1674 at age 54) English statistician, generally considered to be the founder of the science of demography, the statistical study of human populations. His analysis of the vital statistics of the London populace influenced the pioneer demographic work of his friend Sir William Petty and, even more importantly, that of Edmond Halley, the astronomer royal. *TIS
John Graunt was the first person to compile data that showed an excess of male births over female births. He also noticed spatial and temporal variation in the sex ratio, but the variation in his data is not significant. John Arbuthnott was the first person to demonstrate that the excess of male births is statistically significant. He erroneously concluded that there is less variation in the sex ratio than would occur by chance, and asserted without a basis that the sex ratio would be uniform over all time and space. (pb)

1803 Louis François Antoine Arbogast (October 4, 1759 – April 8, or April 18, 1803) His contributions to mathematics show him as a philosophical thinker somewhat ahead of his time. As well as introducing discontinuous functions, he conceived the calculus as operational symbols. The formal algebraic manipulation of series investigated by Lagrange and Laplace in the 1770s was put in the form of operator equalities by Arbogast in 1800 in Calcul des dérivations.*SAU

1883 Édouard Albert Roche (17 Oct 1820, 18 Apr 1883 at age 62) was a French mathematical astronomer who studied the internal structure of celestial bodies and was the first to propose a model of the Earth with a solid core. He determined (1850) the Roche Limit for a satellite to have a stable orbit around a planet of equal density. The smaller body could not lie within 2.44 radii of the larger body without breaking apart from effect of the gravitational force between them. He later made a rigorous mathematical analysis of Pierre Laplace's nebular hypothesis and showed (1873) the instability of a rapidly rotating lens-shaped body.*TIS

1923 Pieter Hendrik Schoute (January 21, 1846, Wormerveer–April 18, 1923, Groningen) was a Dutch mathematician known for his work on regular polytopes and Euclidean geometry. *Wik Schoute was a typical geometer. In his early work he investigated quadrics, algebraic curves, complexes, and congruences in the spirit of nineteenth-century projective, metrical, and enumerative geometry. Schläfli's work of the 1850's was brought to the Netherlands by Schoute who, in three papers beginning in 1893 and in his elegant two-volume textbook on many-dimensional geometry 'Mehrdimensionale Geometrie' (2 volumes 1902, 1905), studied the sections and projections of regular polytopes and compound polyhedra. ... Alicia Boole Stott (1870-1940), George Boole's third daughter (of five), ... studied sections of four- and higher-dimensional polytopes after her husband showed her Schoute's 1893 paper, and Schoute later (in his last papers) gave an analytic treatment of her constructions. *SAU

1945 Sir John Ambrose Fleming (29 Nov 1849, 18 Apr 1945 at age 95)English engineer who made numerous contributions to electronics, photometry, electric measurements, and wireless telegraphy. In 1904, he discovered the one directional current effect between a positively biassed electrode, which he called the anode, and the heated filament in an evacuated glass tube; the electrons flowed from filament to anode only. Fleming called the device a diode because it contained two electrodes, the anode and the heated filament. He noted that when an alternating current was applied, only the positive halves of the waves were passed - that is, the wave was rectified (from a.c. to d.c.). It would also take a radio frequency wave and produce d.c.corresponding to the on and off of the Morse code transmitted signals. *TIS

1955 Albert Einstein (14 Mar 1879; 18 Apr 1955 at age 76) German-American physicist who developed the special and general theories of relativity and won the Nobel Prize for Physics in 1921 for his explanation of the photoelectric effect. Recognized in his own time as one of the most creative intellects in human history, in the first 15 years of the 20th century Einstein advanced a series of theories that proposed entirely new ways of thinking about space, time, and gravitation. His theories of relativity and gravitation were a profound advance over the old Newtonian physics and revolutionized scientific and philosophic inquiry.*TIS
An NBC News broadcast of his death is here.

1999 Gian-Carlo Rota Rota worked on functional analysis for his doctorate and, up to about 1960, he wrote a series of papers on operator theory. Two papers in 1959-60, although still in the area of operator theory, looked at ergodic theory which is an area which requires considerable combinatorial skills. These papers seem to have led Rota away from operator theory and into the area of combinatorics. His first major work on combinatorics, which was to change the direction of the whole subject, was On the Foundations of Combinatorial Theory which Rota published in 1964.
Rota received the Steele Prize from the American Mathematical Society in 1988. The Prize citation singles out the 1964 paper On the Foundations of Combinatorial Theory as:-... the single paper most responsible for the revolution that incorporated combinatorics into the mainstream of modern mathematics. *SAU

2003 Edgar Frank Codd British-American computer scientist and mathematician who laid the theoretical foundation for relational databases, for storing and retrieving information in computer records. He also contributed knowledge in the area of cellular automata. *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

Friday, 17 April 2015

On This Day in Math - April 17

Origami Soma Cubes (see Piet Hein, Deaths, 1996)*The New Origami by Steve and Megumi Biddle

A Man of Knowledge like a rich Soil, feeds
If not a world of Corn, a world of Weeds.
~Benjamin Franklin

The 107th day of the year; There is no integer N such that N! has exactly 107 zeros in it. The same is true if we replace 107 by the primes 3, 31, or 43.*Prime Curios (This seems a most remarkable set of facts to me.)
Interestingly, the sum of the first 107 digits of pi is prime, and the sum of the first 107 digits of e is prime. This is trivially true for the first digit of each, but can you find the one (I believe) other number between 1 and 107 for which the sum of the digits of e and pi are both prime?

2107 - 1 is the largest known Mersenne prime not containing all the individual digits.

Allan Brady proved in 1983 that the maximal number of steps that a four-state Turing machine can make on an initially blank tape before eventually halting is 107.

1397 Geoffrey Chaucer told the Canterbury Tales for the first time at the court of Richard II, *The British Library ‏@britishlibrary
Another significant work of Chaucer's is his Treatise on the Astrolabe, possibly for his own son, that describes the form and use of that instrument in detail and is sometimes cited as the first example of technical writing in the English language. Although much of the text may have come from other sources, the treatise indicates that Chaucer was versed in science in addition to his literary talents. Another scientific work discovered in 1952, Equatorie of the Planetis, has similar language and handwriting compared to some considered to be Chaucer's and it continues many of the ideas from the Astrolabe. Furthermore, it contains an example of early European encryption. The attribution of this work to Chaucer is still uncertain. *Wik

1732 Laura Maria Caterina Bassi defends forty-nine academic theses in public display:
The University of Bologna is the oldest university in Europe and at the beginning of the eighteenth century students were still examined by public disputation, i.e. the candidate was expected to orally defend a series of academic theses. At the beginning of 1732 Bassi took part in a private disputation in her home with members of the university faculty in the presence of many leading members of Bolognese intellectual society. As a result of her performance during this disputation she was elected a member of the prestigious Bologna Academy of Science on 20th March. Rumours of this extraordinary young lady quickly spread and on 17th April she defended forty-nine theses in a highly spectacular public disputation. On 12th May following a public outcry she was awarded a doctorate from the university in a grand ceremony in the city hall of Bologna. Following a further public disputation the City Senate appointed her professor of philosophy at the university, making her the first ever female professor at a European university.
See more at *Thony Christie, The Renaissance Mathematicus

1799 Humphry Davy announced in Nicholson's Journal that N2O can be inhaled by humans *A.J. Wright ‏@AJWrightMLS
1912 Two days after the sinking of the Titanic a solar eclipse occurred in England and Europe. It was a hybrid event, starting and ending as an annular eclipse, with only a small portion of totality. Totality was visible over the sea between Spain and France, with annularity continued northeast across Europe and Asia.
This eclipse occurred two days after the RMS Titanic sank in the northwestern Atlantic ocean under the darkness of new moon. *Wik
Eclipse poster from the London Underground for the 1912 Eclipse.

1935 Turkey issued a series of semi-postal stamps commemorating the 12th congress of the Women’s International Alliance. One pictured a school teacher. Another was the first stamp honoring Marie SkLlodowska Curie. [Scott #B55, B67]*VFR

*Louis Paul Hennefeld, Out of the Closet

1944 Harvard Mark I Operating:
Harvard University President James Conant writes to IBM founder Thomas Watson Sr. to let him know that the Harvard Mark I, developed in cooperation between the two, was operating smoothly. The project was one of the many examples of wartime collaboration among the federal government, universities, and private corporations. In his letter, Conant noted that the Mark I already was "being used for special problems in connection with the war effort." *CHM

2013 Yitang Zhang announced a proof that there are infinitely many pairs of prime numbers which differ by 70 million or less. This proof is the first to establish the existence of a finite bound for prime gaps, resolving a weak form of the twin prime conjecture. *Wik

1598 Giovanni Battista Riccioli (17 April 1598 – 25 June 1671) Italian astronomer who was the first to observe (1650) a double star (two stars so close together that they appear to be one) - Mizar in Ursa Major, the middle star in the handle of the Big Dipper. He also discovered satellite shadows on Jupiter. In 1651, he assigned the majority of the lunar feature names in current use. He named the more prominent features after famous astronomers, scientists and philosophers, while the large dark and smooth areas he called "seas" or "maria". The lunar seas were named after moods (Seas of Tranquillity, Serenity) or terrestrial phenomena (Sea of Rains, Ocean or Storms) His map was published in Almagestum Novum in1651.*TIS
Riccioli studied seventy-seven objections to the Copernican thesis and after studying them Riccioli said that the weight of argument favored a “geo-heliocentric” hypothesis such as that advocated by the great Danish astronomer Tycho Brahe. Riccioli's preference for Tycho's model illustrates something important about how science is done. While today anti-Copernicans are often portrayed as Einstein characterized them (opposed to rational thinking, opposed to science), Riccioli, perhaps the most prominent of the anti-Copernicans, examined the available evidence diligently and rationally. The conclusion he reached was indeed wrong, but wrong because at that time neither the diffraction of light and the Airy disk, nor the details of the Coriolis effect, were understood. Riccioli's anti-Copernican arguments were so solid that they would become subjects of further investigation in physics, long after the Copernican theory had triumphed over the Tychonic theory.*Christopher M. Graney, Teaching Galileo, Physics Teacher V50,1
An interesting blog about Riccioli is at the Renaissance Mathematicus

1656 William Molyneux (17 April 1656 in Dublin, Ireland - 11 Oct 1698 in Dublin, Ireland) was an Irish scientist and philosopher who worked on optics.After leaving Bologna, Angeli continued his contacts with Cavalieri(who had been his teacher in Bologna) by correspondence, and was entrusted to publish Cavalieri's final work, Exercitationes geometricae sex, since by 1647 Cavalieri's health had deteriorated to such an extent that he was unable to carry out the work himself. Angeli also corresponded with a number of other mathematicians including Torricelli and Viviani. After Cavalieri's death, later in 1647, Angeli was offered his chair of mathematics at the University of Bologna but he was still too modest about his own mathematical achievements to accept the position. He moved to Rome where he devoted himself to both mathematics and religious studies. *SAU

1766 John Leslie (17 April 1766 in Largo, Fife, Scotland - 3 Nov 1832 in Coates (near Largo), Fife, Scotland) Leslie was a successful professor of mathematics, attracting large classes of students and publishing his lectures in popular textbooks such as the three part work Elements of Geometry​, Geometrical Analysis, and Plane Trigonometry (1809). He mixed classical mathematical teaching with some new continental approaches to analysis and algebra particularly in his advanced classes. Leslie became professor in Natural Philosophy in 1819 after the chair fell vacant on Playfair's death. This was not without a battle, for again the Church put up a candidate but, having won a victory in the earlier encounter, this time proved much more straightforward. He gave courses which were filled with experiments on specially made apparatus, for which Leslie himself had paid over half the cost from his own pocket. He soon discovered that one of the main problems of teaching university level physics was the lack of mathematical background of most of his students. He wanted to rectify this by teaching mathematics courses specially tailored for his physics students, but the University of Edinburgh senate prevented him from giving such courses since these topics were deemed the responsibility of the professor of mathematics. *SAU

1798 Étienne Bobillier (April 17, 1798 – March 22, 1840) was a French mathematician. At the age of 19 he was accepted into the École Polytechnique and studied there for a year. However, due to a shortage of money, in 1818 he became an instructor in mathematics at the École des Arts et Métiers in Châlons-sur-Marne. In 1829, he was sent to Angers to be director of studies. The following year he served in the national guard during the 1830 revolution. In 1832 he returned to Châlons after his post was abolished, and was promoted to professor.
In 1836 he began suffering from health problems, but continued teaching; declining to take a leave to recuperate. As a result he died in Châlons at the relatively early age of 41.
He is noted for his work on geometry, particularly the algebraic treatment of geometric surfaces and the polars of curves. He also worked on statics and the catenary. The crater Bobillier on the Moon is named after him.*Wik

1853 Arthur Moritz Schönflies (17 April 1853 in Landsberg an der Warthe, Germany (now Gorzów-Wielkopolski, Poland) - 27 May 1928 in Frankfurt am Main, Germany) worked first on geometry and kinematics but became best known for his work on set theory and crystallography. He classified the 230 space groups in 1891 He studied under Kummer and Weierstrass, and was influenced by Felix Klein.
The Schoenflies problem is to prove that an (n − 1)-sphere in Euclidean n-space bounds a topological ball, however embedded. This question is much more subtle than initially appears. *Wik *SAU

1863 Augustus Edward Hough Love (17 Apr 1863; 5 Jun 1940 at age 77) British geophysicist and mathematician who discovered a major type of earthquake wave that was subsequently named for him. Love assumed that the Earth consists of concentric layers that differ in density and postulated the occurrence of a seismic wave confined to the surface layer (crust) of the Earth which propagated between the crust and underlying mantle. His prediction was confirmed by recordings of the behaviour of waves in the surface layer of the Earth. He proposed a method, based on measurements of Love waves, to measure the thickness of the Earth's crust. In addition to his work on geophysical theory, Love studied elasticity and wrote A Treatise on the Mathematical Theory of Elasticity, 2 vol. (1892-93). *TIS (Hard to imagine the newsperson announcing that "Love waves caused the collapse of multiple buildings in San Francisco on this day in 1906.")

1918 Matteo Bottasso (17 April 1878 in Chiusa di Pesio (Cuneo), Italy - 4 Oct 1918 in Messina, ItalyMessina, Italy)was an Italian mathematician who used the vector calculus in studying problems in geometry, mechanics and physics. *SAU

485 Proclus Diadochus (8 Feb 411 in Constantinople (now Istanbul), Byzantium (now Turkey) - 17 April 485 in Athens, Greece) was a Greek philosopher who became head of Plato's Academy and is important mathematically for his commentaries on the work of other mathematicians. *SAU

1761 Thomas Bayes (1702, 17 Apr 1761) English theologian and mathematician who was the first to use probability inductively and who established a mathematical basis for probability inference (a means of calculating, from the frequency with which an event has occurred in prior trials, the probability that it will occur in future trials). This became the basis of a statistical technique, now called Bayesian estimation, for calculating the probability of the validity of a proposition on the basis of a prior estimate of its probability and new relevant evidence. Later statisticians cite disadvantages of the method that include the different ways of assigning prior distributions of parameters and the possible sensitivity of conclusions to the choice of distributions. *TIS British mathematician and Presbyterian minister, known for having formulated a special case of Bayes' theorem, which was published posthumously. Bayes died in Tunbridge Wells, Kent. He is interred in Bunhill Fields Cemetery in London where many Nonconformists are buried. Bayesian probability is the name given to several related interpretations of probability, which have in common the application of probability to any kind of statement, not just those involving random variables. "Bayesian" has been used in this sense since about 1950.

1787 Wenceslaus Johann Gustav Karsten (15 Dec 1732 in Neubrandenburg, Mecklenburg-Strelitz, Germany - 17 April 1787 in Halle, Germany) He wrote an important article in 1768 Von den Logarithmen vermeinter Grössen in which he discussed logarithms of negative and imaginary numbers, giving a geometric interpretation of logarithms of complex numbers as hyperbolic sectors, based on the similarity of the equations of the circle and of the equilateral hyperbola. *SAU

1790 Benjamin Franklin, (17 Jan 1706; 17 Apr 1790) American printer and publisher, author, inventor and scientist, and diplomat. He become widely known in European scientific circles for his reports of electrical experiments and theories. He invented a type of stove, still being manufactured, to give more warmth than open fireplaces and the lightning rod, bifocal eyeglasses also were his ideas. Grasping the fact that by united effort a community may have amenities which only the wealthy few can get for themselves, he helped establish institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (1751), and a hospital (1751). In some cases these foundations were the first of their kind in North America. *TIS When he observed a balloon launch by the Montgolfier brothers he was asked of what use it was. He replied: Of what use is a new born baby? *VFR
While traveling on a ship, Franklin had observed that the wake of a ship was diminished when the cooks scuttled their greasy water. He studied the effects at Clapham common on a large pond there. "I fetched out a cruet of oil and dropt a little of it on the water...though not more than a teaspoon full, produced an instant calm over a space of several yards square." He later used the trick to "calm the waters" by carrying "a little oil in the hollow joint of my cane." *W. Gratzer, Eurekas and Euphorias, pgs 80,81

1847 Francois-Joseph Servois (19 July 1768 in Mont-de-Laval (N of Morteau), Doubs, France - 17 April 1847 in Mont-de-Laval, Doubs, France) He worked in projective geometry, functional equations and complex numbers. He introduced the word pole in projective geometry. He also came close to discovering the quaternions before Hamilton.
Servois introduced the terms "commutative" and "distributive" in a paper describing properties of operators, and he also gave some examples of noncommutativity. Although he does not use the concept of a ring explicitly, he does verify that linear commutative operators satisfy the ring axioms. In doing so he showed why operators could be manipulated like algebraic magnitudes. This work initiates the algebraic theory of operators.
Servois was critical of Argand's geometric interpretation of the complex numbers. He wrote to Gergonne telling him so in November 1813 and Gergonne published the letter in the Annales de mathématiques in January 1814. Servois wrote:- I confess that I do not yet see in this notation anything but a geometric mask applied to analytic forms the direct use of which seems to me simple and more expeditious.
Considered as a leading expert by many mathematicians of his day, he was consulted on many occasions by Poncelet while he was writing his book on projective geometry Traité des propriétés projective. *SAU

1942 Jean-Baptiste Perrin (30 Sep 1870, 17 Apr 1942 at age 71) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids, verified Albert Einstein's explanation of this phenomenon and thereby confirmed the atomic nature of matter. Using a gamboge emulsion, Perrin was able to determine by a new method, one of the most important physical constants, Avogadro's number (the number of molecules of a substance in so many grams as indicated by the molecular weight, for example, the number of molecules in two grams of hydrogen). The value obtained corresponded, within the limits of error, to that given by the kinetic theory of gases. For this achievement he was honoured with the Nobel Prize for Physics in 1926. *TIS

1977 Richard Dagobert Brauer (10 Feb 1901; 17 Apr 1977 at age 76) German-American mathematician and educator, a pioneer in the development of algebra theory. He worked with Weyl on several projects including a famous joint paper on spinors (published in 1935 in the American Journal of Mathematics). This work provided a background for Paul Dirac's theory of the spinning electron within the framework of quantum mechanics. With Nesbitt, Brauer introduced the theory of blocks (1937). Brauer used this to obtain results on finite groups, particularly finite simple groups, and the theory of blocks would play a big part in much of Brauer's later work. Starting with his group-theoretical characterisation of the simple groups (1951), he spent the rest of his life formulating a method to classify all finite simple groups. *TIS

1996 Piet Hein (December 16, 1905 – April 17, 1996) was a Danish scientist, mathematician, inventor, designer, author, and poet, often writing under the Old Norse pseudonym "Kumbel" meaning "tombstone". His short poems, known as gruks or grooks (Danish: Gruk), first started to appear in the daily newspaper "Politiken" shortly after the Nazi occupation in April 1940 under the pseudonym "Kumbel Kumbell"
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube. The pieces can also be used to make a variety of other 3D shapes. Piet Hein created the superellipse which became the hallmark of modern Scandinavian architecture.
In addition to the thousands of grooks he wrote, Piet Hein devised the games of Hex, Tangloids, Morra, Tower, Polytaire, TacTix, Nimbi, Qrazy Qube, Pyramystery, and the Soma cube. He advocated the use of the superellipse curve in city planning, furniture making and other realms. He also invented a perpetual calendar called the Astro Calendar and marketed housewares based on the superellipse and Superegg. *Wik My Favorite of his grooks is this one:
Problems worthy
of attack
prove their worth
by hitting back.

2006 Gloria Olive (8 June 1923 in New York City, USA - 17 April 2006 in Dunedin, New Zealand) Much of Olive's research was on applications of generalised powers. She published papers such as Binomial functions and combinatorial mathematics (1979), A combinatorial approach to generalized powers (1980), Binomial functions with the Stirling property (1981), Some functions that count (1983), Taylor series revisited (1984), Catalan numbers revisited (1985), A special class of infinite matrices (1987), and The ballot problem revisited (1988). Some of her work on binomial functions overlaps that of Gian-Carlo Rota's "polynomials of binomial type". She has had a special interest in the polynomials which are generated by her generalised powers, and hopes that someone will prove or disprove her conjecture, now about 30 years old, that all their zeros lie on the unit circle. This conjecture has now been verified for infinitely many special cases. *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

Thursday, 16 April 2015

On This Day in Math - April 16

Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?
~Edward Lorenz
Title of paper presented at the 139th Annual Meeting of the American Association for the Advancement of Science (29 Dec 1979)*TIS

The 106th day of the year; The sum of the first 106 digits of pi is prime. Amazingly, I could use this same numerical idea for tomorrow.
106106-105105 (a number of 215 decimal digits)is prime.
There are 106 distinct mathematical trees with ten vertices.

1178BC Homer records the events of a solar eclipse. This may have marked the return of Odysseus, legendary King of Ithaca, to his kingdom after the Trojan War. The date is surmised from a passage in Homer's Odyssey, which reads, "The Sun has been obliterated from the sky, and an unlucky darkness invades the world." This happens in the context of a new moon and at noon, both necessary preconditions for a full solar eclipse. In 2008, to investigate, Dr Marcelo O. Magnasco, an astronomer at Rockefeller University, and Constantino Baikouzis, of the Observatorio Astrónomico de La Plata in Argentina, looked for more clues. Within the text, they interpreted three definitive astronomical events: there was a new moon on the day of the slaughter (as required for a solar eclipse); Venus was visible and high in the sky six days before; and the constellations Pleiades and Boötes were both visible at sunset 29 days before. Since these events recur at different intervals, this particular sequence should be unique: the doctors found only one occurrence of this sequence while searching between 1250 and 1115 BC, the 135-year spread around the putative date for the fall of Troy. It coincided with the eclipse of April 16, 1178 BC.*Wik

837 Comet Halley passed 3.2 million miles from Earth, About 13x the lunar distance. *David Dickinson ‏ @Astroguyz (This is the closest to Earth in history. It is recorded widely, and was almost certainly an event in every culture on the planet.)

1610 George Fugger in a letter to Kepler debunks Galileo's claim to inventing the telescope. Fugger, in Venice, a member of the famous banking family who worked as an ambassador for the Holy Roman Empire, wrote to his correspondent Johannes Kepler
in Prague, about Galilei’s eye catching demonstrations in Italy:
"The man [Galilei] [...] intends to be considered the inventor of that ingenious spy-
glass, despite the fact that some Dutchman, on a trip here through France, brought it
here first. It was shown to me and others, and after Galilei saw it, he made others in
imitation of it and, what is easy perhaps, made some improvements to what was already
invented." In his next paragraph Zuidervaart makes very clear that the accusation was false and that Galileo had not claimed the invention. *Huib J. Zuidervaart, The ‘true inventor’ of the telescope. A survey of
400 years of debate, Royal Netherlands Academy of Arts and Sciences, Amsterdam 201

1673 “I conjecture that Mr. Collins himself does not speak of these summations of infinite series because he brings forward the example of the series 1/2, 1/3, 1/4, 1/5, 1/6, ... which if it is continued to infinity cannot be summed because the sum is not finite, like the sum of the triangular numbers, but infinite. But now I am cramped by the space of my paper.” Leibniz to Oldenburg, indicating some hint of a distinction between convergent and divergent series. [The Correspondence of Henry Oldenburg, 9, pp. 599–600.] *VFR

1705 Newton knighted by Queen Anne at Trinity College. [DSB 10, 83] *VFR

1811 Wilhelmine Reichard launched to her first solo flight in a gas balloon, thus becoming Germany`s very first female balloonist. The first recorded manned flight was made in a hot air balloon built by the Montgolfier brothers on 21 November 1783, starting in Paris and reaching a height of almost 200 meters. The very first woman to fly in a ballon followed only 8 months after the first manned flight on June 4, 1784, when opera singer Élisabeth Thible took her place with Mr. Fleurant on board a hot air balloon christened La Gustave in honour of King Gustav III of Sweden. Another early woman balloonist was Jeanne Geneviève Labrosse, who became the first woman to ascend solo in 1798 and, on October 12, 1799, the first woman to make a parachute descent (in the gondola), from an altitude of 900 meters. But also disaster is not far ahead. Ballooning was a risky business for the pioneers. When Marie Madeleine Sopie Blanchard ascended in her hydrogen balloon to watch a firework on July 6, 1819, she should become the first woman to lose her life while flying. Her craft crashed on the roof of a house and she fell to her death. *yovisto.

1866 “At the meeting held April 16th, 1866, Prof. Cayley called attention to the theorem, that the difference between two consecutive prime numbers may exceed any given number N − 1 whatever. For if a, b, c, . . . k are the prime numbers not greater than N, then abc . . . k + 1, and abc . . . k +1+ N may be one or both of them prime, but all the intermediate numbers are composite; that is, the difference of the two successive primes is = N at least.” *Proc. London Math. Soc., vol. 2 (1866-69)

1938 The first William Lowell Putnam competition was held. It was won by the team of three from the University of Toronto. Irving Kaplansky was one of the team members. For the history of this now famous exam for undergraduates, see AMM, 72(1965), p. 474. *VFR

1959 "LISP" Language Unveiled:
The programming language that provided the basis for work in artificial intelligence, LISP, has its first public presentation. Created by John McCarthy, LISP offers programmers flexibility in organization and it or its descendants are still used in the AI development environment.*CHM

2014 Steve Colyer pointed out to me that every day this week when written in the conventional US mo/day/year is a palindrome. Today is 41614, etc. May of next year will have the same relation for a week

1495 Peter Apian (16 Apr 1495; 21 Apr 1552 at age 56)German astronomer and geographer, also known as Petrus Apianus, whose major work was Instrumentum sinuum sivi primi mobilis (1534), in which he gave tables of his calculations of sines for every minute, with a decimal division of the radius. *TIS Apian remained in Ingolstadt until his death. Although he neglected his teaching duties, the university evidently was proud to host such an esteemed scientist. Apian's work included in mathematics—in 1527 he published a variation of Pascal's triangle, and in 1534 a table of sines— as well as astronomy. In 1531, he observed a comet and discovered that a comet's tail always point away from the sun. (Girolamo Fracastoro also detected this in 1531, but Apian's publication was the first to also include graphics.) He designed sundials, published manuals for astronomical instruments and crafted volvelles ("Apian wheels"), measuring instruments useful for calculating time and distance for astronomical and astrological applications.*Wik

1753 Sir Hans Sloane (16 Apr 1660; 11 Jan 1753 at age 92) (Baronet) British physician and naturalist whose collection of books, manuscripts, and curiosities formed the basis for the British Museum in London. By the time he died, Sloane had amassed one of the world's largest and most varied collections of natural history specimens. His passion for the collection and his concern for its future upkeep after his death led him to write a will which clearly stated that it must "remain together and not be separated." He offered it to the British nation, requesting in return a sum of £20,000 for his heirs. Parliament accepted, and King George II gave his royal assent 7 Jun 1753. Thus the British Museum was created and eventually its sister institution, the British Museum of Natural History. *TIS He also invented Hot Chocolate. Sloane encountered cocoa while he was in Jamaica, where the locals drank it mixed with water, and he is reported to have found it nauseating. However, he devised a means of mixing it with milk to make it more pleasant. When he returned to England, he brought his chocolate recipe back with him. *Wik The myth that Sloan had invented the process of Hot Chocolate, which is still strongly promoted in the shops in Chelsea that feature this product, is a myth. See James Delbourgo's Article on Sloan and Cocoa here. Skipping to page 78 for details of the history of Chocolate in use around Europe in the 17th century. It had been used for much longer by the natives of South America with some apparent religious or spiritual relationship. A book of recipes was published in England for Hot Chocolate in 1662, when Sloane would have been not quite two years old.

1682 John Hadley (16 Apr 1682; 14 Feb 1744 at age 61) British mathematician and inventor who perfected methods for grinding and polishing telescope lenses. Hadley improved the reflecting telescope (first introduced by Newton in 1668) and produced the first of its kind having sufficient accuracy and power to be useful in astronomy. It had a 6 inch mirror. He is also known for the reflecting octant (1730) used at sea to measure the altitude of the Sun or a celestial body above the horizon to within one second of arc. It was the ancestor of the modern nautical sextant. He was a prominent member of the Royal Society, of which he was vice-president from 21 Feb 1728. John Hadley was the older brother of George Hadley.*TIS

1728 Joseph Black (16 Apr 1728; 6 Dec 1799 at age 71)Scottish chemist and physicist who experimented with "fixed air" (carbon dioxide), discovered bicarbonates and identified latent heat. He lectured in chemistry, anatomy at the University of Glasgow, while also a physician. From heated magnesia alba (magnesium carbonate), Black collected a gas, carbon dioxide, different from common air. He published Experiments Upon Magnesia Alba, Quicklime, and Some Other Alcaline Substances (1756). Carbon dioxide was also released by fermentation, respiration, and burning charcoal so he assumed it was in the atmosphere. He also observed that ice melts without change of temperature, due to heat that becomes "hidden" - latent heat - and determined "specific heat" for heated of materials.*TIS

1823 Ferdinand Gotthold Max Eisenstein (16 Apr 1823; 11 Oct 1852 at age 29)
German mathematician whose work covered a range of topics including the theory of elliptic functions, and quadratic and cubic forms, which led to cyclotomy, the reciprocity theorem for cubic residues, and also theorems for quadratic and biquadratic residues from partition of prime numbers. *TIS Gauss said of him, "There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein."

1894 Jerzy Neyman (16 Apr 1894; 5 Aug 1981 at age 87) Russian-American mathematician who was one of the principal architects of modern theoretical statistics. His papers on hypothesis testing (1928-33) helped establish the subject. During 1934-38, he gave a theory of confidence intervals (important in the analysis of data); extended statistical theory to contagious distributions, (for interpretation of biological data); wrote on sampling stratified populations (which led to such applications as the Gallup Poll); and developed the model for randomised experiments (widely relevant across the fields of science, including agriculture, biology, medicine, and physical sciences). His later research applied statistics to meteorology and medicine. In 1968 he was awarded the prestigious National Medal of Science.*TIS

1446 Sometimes given as the date of the Death of the architect Filippo Brunelleschi, who helped develop a systematic theory of mathematical perspective. He is especially noted for his design of the Duomo in Florence. More Commonly given date is the 15th

1756 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1788 Comte Georges-Louis Leclerc de Buffon (7 Sep 1707, 16 Apr 1788 at age 80) French naturalist who formulated a crude theory of evolution and was the first to suggest that the earth might be older than suggested by the Bible. In 1739 he was appointed keeper of the Jardin du Roi, a post he occupied until his death. There he worked on a comprehensive work on natural history, for which he is remembered, Histoire naturelle, générale et particulière. He began this work in 1749, and it dominated the rest of his life. It would eventually run to 44 volumes, including quadrupeds, birds, reptiles and minerals. He proposed (1778) that the Earth was hot at its creation and, from the rate of cooling, calculated its age to be 75,000 years, with life emerging some 40,000 years ago.*TIS He is remembered in mathematics for a question he asked more than any questions he answered. Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution, in the case where the needle length is not greater than the width of the strips, can be used to design a Monte Carlo-style method for approximating the number π. *Wik

1901 Henry Augustus Rowland (27 Nov 1848, 16 Apr 1901 at age 52) American physicist who invented the concave diffraction grating, which replaced prisms and plane gratings in many applications, and revolutionized spectrum analysis--the resolution of a beam of light into components that differ in wavelength. His first major research was an investigation of the magnetic permeability of iron, steel and nickel, work which won the praise of Maxwell. Another experiment was the first to conclusively demonstrate that the motion of charged bodies produced magnetic effects. In the late 1870s, he established an authoritative figure for the absolute value of the ohm, and redetermined the mechanical equivalent of heat in the early 1880s, demonstrating that the specific heat of water varied with temperature. *TIS

1914 George William Hill (3 Mar 1838, 16 Apr 1914 at age 76)U.S. mathematical astronomer considered by many of his peers to be the greatest master of celestial mechanics of his time. Hill joined the Nautical Almanac Office in 1861. He computed the orbit of the moon while making original contributions to the three body problem. He introduced infinite determinants, a concept which later found application in many fields of mathematics and physics. When Simon Newcomb took over the Nautical Almanac in 1877 and began a complete recomputation of all solar system motions, Hill was assigned the difficult problem of the orbits of Jupiter and Saturn. After completing the enormous labor in ten years, he returned to his farm, where he continued his research in celestial mechanics.*TIS

1958 Rosalind Elsie Franklin (25 Jul 1920, 16 Apr 1958 at age 37) was an English physical chemist and X-ray crystallographer who contributed to the discovery of the molecular structure of deoxyribonucleic acid (DNA), a constituent of chromosomes that serves to encode genetic information. Beginning in 1951, she made careful X-ray diffraction photographs of DNA, leading her to suspect the helical form of the molecule, at least under the conditions she had used. When James Watson saw her photographs, he had confirmation of the double-helix form that he and Francis Crick then published. She never received the recognition she deserved for her independent work, but had died of cancer four years before the Nobel Prize was awarded to Crick and Watson. *TIS

2008 Edward Lorenz (23 May 1917, 16 Apr 2008 at age 90)American mathematician and meteorologist known for pointing out the "butterfly effect" whereby chaos theory predicts that "slightly differing initial states can evolve into considerably different states." In his 1963 paper in the Journal of Atmospheric Sciences, he cited the flapping of a seagull's wings as changing the state of the atmosphere in even such a trivial way can result in huge changes in outcome in weather patterns. Thus very long range weather forecasting becomes almost impossible. He determined this unexpected result in 1961 while running a computer weather simulation that gave wildly different results from even tiny changes in the input data. *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