Tuesday, 27 September 2016

On This Day in Math - September 27





Algebra exists only for the elucidation of geometry.

~William Edge

The 271st day of the year; 271 is a prime number and is the sum of eleven consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43).

271 is also the difference of two consecutive cubes, 103 - 93. Such numbers are called Cuban Primes, and were named by the British mathematician Allan Joseph Champneys Cunningham in 1923.

Using the English alphabet code, a = 1, b = 2, etc, there are exactly 271 positive numbers that give larger numbers when you write out their English names and add the letters *primecurios



EVENTS


14 A.D.: A total lunar eclipse marked the death of Augustus: "The Moon in the midst of a clear sky became suddenly eclipsed; the soldiers who were ignorant of the cause took this for an omen referring to their present adventures: to their labors they compared the eclipse of the planet, and prophesied 'that if to the distressed goodness should be restored her wonted brightness and splendor, equally successful would be the issue of their struggle.' Hence they made a loud noise, by ringing upon brazen metal, and by blowing trumpets and cornets; as she appeared brighter or darker they exulted or lamented"
- Tacitus *NASA Lunar Eclipses

1830 American Statesman Charles Sumner (1811-1874) paid little attention as an undergraduate at Harvard, but a year after graduation he became convinced that mathematics was a necessary part of a complete education. To a classmate he wrote: “Just a week ago yesterday, I commenced Walker’s Geometry, and now have got nearly half through. All those problems, theorems, etc., which were such stumbling-blocks to my Freshman-year career, unfold themselves as easily as possible now. You will sooner have thought, I suppose, that fire and water would have embraced than mathematics and myself; but, strange to tell, we are close friends now. I really get geometry with some pleasure. I usually devote four hours in the forenoon to it.” Quoted from Florian Cajori’s Mathematics in Liberal Education (1928), p. 115. *VFR  (Sumner was nearly beaten to death by a South Carolina Congressional Representative after a vindictive speech attacking the Kansas-Nebraska act, and it's authors.  His speech included direct insults, sexual innuendo, and made fun of South Carolina Senator Andrew Butler, one of the authors, by imitating his stroke impaired speech and mannerisms.  Butler's Nephew,  Preston Brooks, having decided that a duel could not take place between a gentleman (himself) and a drunk-lout(Sumner) stopped by Sumner's desk to confront him and nearly beat him to death with his cane.  Sumner lost the fight, but the incident put his star on the rise in the Northern states.)

In 1831, the first annual meeting of the British Association for the Advancement of Science was held in York. The British Association had been established in the same year by Sir David Brewster, R.I. Murchison and others. One of the association's main objectives was to "promote the intercourse of those who cultivate science with each other." The second annual meeting was held at Oxford (1832), and in following years at Cambridge, Edinburgh, Dublin, Bristol, Liverpool, Newcastle, Birmingham, Glasgow, Plymouth, Manchester and Cork respectively, until returning to York in 1844. It is incorporated by Royal Charter dated 21 Apr 1928.*TIS

1905 E=mc2 the day that Einstein's paper outlining the significance of the equation arrived in the offices of the German journal Annalen der Physik.  "Does the inertia of a body depend on its energy content?" 

1919 Einstein writes to his ailing mother that "H. A. Lorentz has just telegraphed me that the British Expeditions have definitely confirmed the deflection of light by the sun." He adds consolation on her illness and wishes her "good days", and closes with "affectionately, Albert *Einstein Archives

In 1922, scientists at the Naval Aircraft Radio Laboratory near Washington, D.C., demonstrated that if a ship passed through a radio wave being broadcast between two stations, that ship could be detected, the essentials of radar. *TIS

1996 Kevin Mitnick, 33, was indicted on charges resulting from a 2 ½-year hacking spree. Police accused the hacker, who called himself "Condor," of stealing software worth millions of dollars from major computer corporations. The maximum possible sentence for his crimes was 200 years. *CHM    Mitnick served five years in prison — four and a half years pre-trial and eight months in solitary confinement — because, according to Mitnick, law enforcement officials convinced a judge that he had the ability to "start a nuclear war by whistling into a pay phone". He was released on January 21, 2000. During his supervised release, which ended on January 21, 2003, he was initially forbidden to use any communications technology other than a landline telephone. Mitnick fought this decision in court, eventually winning a ruling in his favor, allowing him to access the Internet. Under the plea deal, Mitnick was also prohibited from profiting from films or books based on his criminal activity for seven years. Mitnick now runs Mitnick Security Consulting​ LLC, a computer security consultancy. *Wik


BIRTHS


1677 Johann Doppelmayr was a German mathematician who wrote on astronomy, spherical trigonometry, sundials and mathematical instruments.*SAU

1719 Abraham Kästner was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. His work on the parallel postulate influenced Bolyai and Lobachevsky*SAU

1814  Daniel Kirkwood (27 Sep 1814; 11 Jun 1895) American mathematician and astronomer who noted in about 1860 that there were several zones of low density in the minor-planet population. These gaps in the distribution of asteroid distances from the Sun are now known as Kirkwood gaps. He explained the gaps as resulting from perturbations by Jupiter. An object that revolved in one of the gaps would be disturbed regularly by the planet's gravitational pull and eventually would be moved to another orbit. Thus gaps appeared in the distribution of asteroids where the orbital period of any small body present would be a simple fraction of that of Jupiter. Kirwood showed that a similar effect accounted for gaps in Saturns rings.*TIS  The asteroid 1951 AT was named 1578 Kirkwood in his honor and so was the lunar impact crater Kirkwood, as well as Indiana University's Kirkwood Observatory. He is buried in the Rose Hill Cemetery in Bloomington, Indiana, where Kirkwood Avenue is named for him. *Wik

1824 Benjamin Apthorp Gould (27 Sep 1824; 26 Nov 1896) American astronomer whose star catalogs helped fix the list of constellations of the Southern Hemisphere Gould's early work was done in Germany, observating the motion of comets and asteroids. In 1861 undertook the enormous task of preparing for publication the records of astronomical observations made at the US Naval Observatory since 1850. But Gould's greatest work was his mapping of the stars of the southern skies, begun in 1870. The four-year endeavor involved the use of the recently developed photometric method, and upon the publication of its results in 1879 it was received as a signicant contribution to science. He was highly active in securing the establishment of the National Academy of Sciences.*TIS

1876 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California.
Hedrick was born in Union City, Indiana. After undergraduate work at the University of Michigan, he obtained a Master of Arts from Harvard University. With a Parker fellowship, he went to Europe and obtained his PhD from Göttingen University in Germany under the supervision of David Hilbert in 1901. He then spent several months at the École Normale Supérieure in France, where he became acquainted with Édouard Goursat, Jacques Hadamard, Jules Tannery, Émile Picard and Paul Émile Appell, before becoming an instructor at Yale University. In 1903, he became professor at the University of Missouri.
He was involved in the creation of the Mathematical Association of America in 1916 and was its first president.
His work was on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.
He moved in 1920 to UCLA to become head of the department of mathematics. In 1933, he was giving the first graduate lecture on mathematics at UCLA. He became provost and vice-president of the University of California in 1937. He humorously called his appointment The Accident, and told jokingly after this event, "I no longer have any intellectual interests —I just sit and talk to people." He played in fact a very important role in making of the University of California a leading institution. He retired from the UCLA faculty in 1942 and accepted a visiting professorship at Brown University. Soon after the beginning of this new appointment, he suffered a lung infection. He died at the Rhode Island hospital in Providence, Rhode Island. Two UCLA residence halls are named after him: Hedrick Hall in 1963, and Hedrick Summit in 2005.
Earle Raymond Hedrick worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics. *Wik

1843 Gaston Tarry was a French combinatorialist whose best-known work is a method for solving mazes.*SAU

1855 Paul Appell (27 September 1855 – 24 October 1930), also known as Paul Émile Appel, was a French mathematician and Rector of the University of Paris. The concept of Appell polynomials is named after him, as is rue Paul Appell in the 14th arrondissement of Paris.*Wik

1876 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California. He worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.*Wik

1879 Hans Hahn was an Austrian mathematician who is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass. *SAU

1892 Mykhailo Pilipovich Krawtchouk (27 Sept 1892 in Chovnitsy, (now Kivertsi) Ukraine - 9 March 1942 in Kolyma, Siberia, USSR) In 1929 Krawtchouk published his most famous work, Sur une généralisation des polynômes d'Hermite. In this paper he introduced a new system of orthogonal polynomials now known as the Krawtchouk polynomials, which are polynomials associated with the binomial distribution.
However his mathematical work was very wide and, despite his early death, he was the author of around 180 articles on mathematics. He wrote papers on differential and integral equations, studying both their theory and applications. Other areas he wrote on included algebra (where among other topics he studied the theory of permutation matrices), geometry, mathematical and numerical analysis, probability theory and mathematical statistics. He was also interested in the philosophy of mathematics, the history of mathematics and mathematical education. Krawtchouk edited the first three-volume dictionary of Ukrainian mathematical terminology. *SAU

1918 Sir Martin Ryle (27 Sep 1918; 14 Oct 1984) British radio astronomer who developed revolutionary radio telescope systems and used them for accurate location of weak radio sources. Ryle helped develop radar for British defense during WW II. Afterward, he was a leader in the development of radio astronomy. With his aperture synthesis technique of interferometry he and his team located radio-emitting regions on the sun and pinpointed other radio sources so that they could be studied in visible light. Ryle's 1C - 5C Cambridge catalogues of radio sources led to the discovery of numerous radio galaxies and quasars. Using this technique, eventually radio astronomers surpassed optical astronomers in angular resolution. He observed the most distant known galaxies of the universe. For his aperture synthesis technique, Ryle shared the Nobel Prize for Physics in 1974 (with Antony Hewish), the first in recognition of astronomical research. He was the 12th Astronomer Royal (1972-82).*TIS

1919 James Hardy Wilkinson (27 September 1919 – 5 October 1986) was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.
He received the Turing Award in 1970 "for his research in numerical analysis to facilitate the use of the high-speed digital computer, having received special recognition for his work in computations in linear algebra and 'backward' error analysis." In the same year, he also gave the John von Neumann Lecture at the Society for Industrial and Applied Mathematics.   The J. H. Wilkinson Prize for Numerical Software is named in his honour.*Wik



DEATHS


1783 Étienne Bézout was a French mathematician who is best known for his theorem on the number of solutions of polynomial equations.*SAU Bézout's theorem for polynomials states that if P and Q are two polynomials with no roots in common, then there exist two other polynomials A and B such that AP+BQ=1. *Wik

1997 William Edge graduated from Cambridge and lectured at Edinburgh University. He wrote many papers in Geometry. He became President of the EMS in 1944 and an honorary member in 1983. *SAU 

2014 Jacqueline Anne ( Barton)Stedall (4 August 1950; Romford, Essex, U.K.–27 September 2014; Painswick, Gloucestershire) was a well-known historian of mathematics. Although her career as a researcher, scholar and university teacher lasted less than 14 years, it was greatly influential. Her nine books, more than 20 articles, input to the online edition of the manuscripts of Thomas Harriot, journal editorships and contributions to Melvyn Bragg’s Radio 4 programme In Our Time showed her exceptional breadth of scholarship.
Jackie Stedall came to Oxford in October 2000 as Clifford-Norton Student in the History of Science at Queen’s College. She held degrees of BA (later MA) in Mathematics from Cambridge University (1972), MSc in Statistics from the University of Kent (1973), and PhD in History of Mathematics from the Open University (2000). She also had a PGCE in Mathematics (Bristol Polytechnic 1991). In due course she became Senior Research Fellow in the Oxford Mathematical Institute and at Queen’s College, posts from which, knowing that she was suffering from incurable cancer, she took early retirement in December 2013.
This was her fifth career. Following her studies at Cambridge and Canterbury she had been three years a statistician, four years Overseas Programmes Administrator for War on Want, seven years a full-time parent, and eight years a schoolteacher before she became an academic. *Obituaries at The Guardian, Oxford Mathemtics, and 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


Monday, 26 September 2016

On This Day in Math - September 26



"mathematics is not yet ready for such problems"
~Paul Erdos in reference to Collatz's problem

The 270th day of the year; the harmonic mean of the factors of 270 is an integer. The first three numbers with this property are 1, 6, and 28.. what is the next one? These are sometimes called Ore numbers for Øystein Ore, who studied them.  Many of them also have the arithmetic mean of their divisors is an integer, but not all.

270 is the sum of eight consecutive primes, 270 = 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 ; and the sum of three cubes \(270 = 3^3+ 3^3 + 6^3 \).

10! = 3628800 has 270 factors. (A good high school student should be able to confirm this quickly.)


EVENTS
1679 On September 26, 1679, a fierce fire consumed the Stellaburgum — Europe’s finest observatory, built by the pioneering astronomer Johannes Hevelius in the city of Danzig, present-day Poland, decades before the famous Royal Greenwich Observatory and Paris Observatory existed. *Maria Popova at brainpickings.org

1775 John Adams writes to his wife to entreat her to teach his children geometry and... "I have seen the Utility of Geometry, Geography, and the Art of drawing so much of late, that I must intreat you, my dear, to teach the Elements of those Sciences to my little Girl and Boys. It is as pretty an Amusement, as Dancing or Skaiting, or Fencing, after they have once acquired a Taste for them. No doubt you are well qualified for a school Mistress in these Studies, for Stephen Collins tells me the English Gentleman, in Company with him, when he visited Braintree, pronounced you the most accomplished Lady, he had seen since he left England.—You see a Quaker can flatter, but dont you be proud. *Natl. Archives


1874 James Clerk Maxwell in a letter to Professor Lewis Campbell describes Galton, "Francis Galton, whose mission it seems to be to ride other men's hobbies to death, has invented the felicitous expression 'structureless germs'. " *Lewis Campbell and William Garnett (eds.), The Life of James Clerk Maxwell (1884), 299.

1991 The first two year closed mission of Biosphere 2 began just outside Tucson, Arizona. *David Dickinson ‏@Astroguyz

1999 The Kobe meteorite fell on September 26 (local time 20:23), 1999, in Kita-ku in the north of Kobe city, Japan. The meteorite fall was widely observed in Kobe and the surrounding area, and was photographed by an amateur photographer in Imabari city, 200 km southwest of Kobe. The meteorite struck a house with an explosive sound but otherwise caused only minor property damage. The approximately 20 fragments of the meteorite had a total mass of 136 g. *terrapub.co.jp



 2011 Astronauts had this view of the aurora on September 26, 2011. Credit: NASA

We’ve had some great views of the aurora submitted by readers this week, but this one taken from the International Space Station especially highlights the red color seen by many Earth-bound skywatchers, too. Karen Fox from the Goddard Space Flight Center says the colors of the aurora depend on which atoms are being excited by the solar storm. In most cases, the light comes when a charged particle sweeps in from the solar wind and collides with an oxygen atom in Earth’s atmosphere. This produces a green photon, so most aurora appear green. However, lower-energy oxygen collisions as well as collisions with nitrogen atoms can produce red photons — so sometimes aurora also show a red band as seen here. *Universe Today



BIRTHS

1688 Willem 'sGravesande (26 September 1688 – 28 February 1742)was a Dutch mathematician who expounded Newton's philosophy in Europe. In 1717 he became professor in physics and astronomy in Leiden, and introduced the works of his friend Newton in the Netherlands.
His main work is Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam or Mathematical Elements of Natural Philosophy, Confirm'd by Experiments (Leiden 1720), in which he laid the foundations for teaching physics. Voltaire and Albrecht von Haller were in his audience, Frederic the Great invited him in 1737 to come to Berlin.
His chief contribution to physics involved an experiment in which brass balls were dropped with varying velocity onto a soft clay surface. His results were that a ball with twice the velocity of another would leave an indentation four times as deep, that three times the velocity yielded nine times the depth, and so on. He shared these results with Émilie du Châtelet, who subsequently corrected Newton's formula E = mv to E = mv2. (Note that though we now add a factor of 1/2 to this formula to make it work with coherent systems of units, the formula as expressed is correct if you choose units to fit it.) *Wik

1754 Joseph-Louis Proust (26 Sep 1754; 5 Jul 1826) French chemist who proved (1808) that the relative quantities of any given pure chemical compound's constituent elements remain invariant, regardless of the compound's source, and thus provided crucial evidence in support of John Dalton's “law of definite proportions,” which holds that elements in any compound are present in fixed proportion to each other. *TIS

1784 Christopher Hansteen (26 Sep 1784; 15 Apr 1873) Norwegian astronomer and physicist noted for his research in geomagnetism. In 1701 Halley had already published a map of magnetic declinations, and the subject was studied by Humboldt, de Borda, and Gay-Lussac, among others. Hansteen collected available data and also mounted an expedition to Siberia, where he took many measurements for an atlas of magnetic strength and declination.*TIS

1854 Percy Alexander MacMahon (26 Sept 1854 , 25 Dec 1929) His study of symmetric functions led MacMahon to study partitions and Latin squares, and for many years he was considered the leading worker in this area. His published values of the number of unrestricted partitions of the first 200 integers which proved extremely useful to Hardy and Littlewood in their own work on partitions. He gave a Presidential Address to the London Mathematical Society on combinatorial analysis in 1894. MacMahon wrote a two volume treatise Combinatory analysis (volume one in 1915 and the second volume in the following year) which has become a classic. He wrote An introduction to combinatory analysis in 1920. In 1921 he wrote New Mathematical Pastimes, a book on mathematical recreations. *SAU

1887 Sir Barnes (Neville) Wallis (26 Sep 1887; 30 Oct 1979) was an English aeronautical designer and military engineer whose famous 9000-lb bouncing "dambuster" bombs of WW II destroyed the German Möhne and Eder dams on 16 May 1943. He designed the R100 airship, and the Vickers Wellesley and Wellington bombers. The specially-formed RAF 617 Squadron precisely delivered his innovative cylindrical bombs which were released from low altitude, rotating backwards at high speed that caused them to skip along the surface of the water, right up to the base of the dam. He later designed the 5-ton Tallboy and 10-ton Grand Slam earthquake bombs (which used on many enemy targets in the later years of the war). Postwar, he developed ideas for swing-wing aircraft. *TIS (His courtship with his wife has been written by his daughter, Mary Stopes-Roe from the actual courtship in the entertaining, but perhaps overpriced book, Mathematics With Love: The Courtship Correspondence of Barnes Wallis, Inventor of the Bouncing Bomb.)

1891 Hans Reichenbach (September 26, 1891, April 9, 1953) was a leading philosopher of science, educator and proponent of logical empiricism. Reichenbach is best known for founding the Berlin Circle, and as the author of The Rise of Scientific Philosophy.*Wik

1924 Jean Hoerni, a pioneer of the transistor, is born in Switzerland. A physicist, Hoerni in 1959 invented the planar process, which, combined with Robert Noyce's technique for placing a layer of silicon dioxide on a transistor, led to the creation of the modern integrated circuit. Hoerni's planar process allowed the placement of complex electronic circuits on a single chip. *CHM

1926 Colin Brian Haselgrove (26 September 1926 , 27 May 1964) was an English mathematician who is best known for his disproof of the Pólya conjecture in 1958. the Pólya conjecture stated that 'most' (i.e. more than 50%) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was posited by the Hungarian mathematician George Pólya in 1919.. The size of the smallest counter-example is often used to show how a conjecture can be true for many numbers, and still be false. *Wik

1927 Brian Griffiths (26 Sept 1927 , 4 June 2008) He was deeply involved in the 'School Mathematics Project', he served as chairman of the 'Joint Mathematical Council', and chaired the steering group for the 'Low Attainers Mathematics Project' from 1983 to 1986. This project became the 'Raising Achievement in Mathematics Project' in 1986 and he chaired this from its foundation to 1989. *SAU



DEATHS

1766 Giulio Carlo Fagnano dei Toschi died. He is important for the identity
\pi = 2i\log{1 - i \over 1 +i}
and for his rectification of the lemmiscate. *VFR An Italian mathematician who worked in both complex numbers and on the geometry of triangles.*SAU
The lemniscate is of particular interest because, even if it has little relevance today, it
was
the catalyst for immeasurably important mathematical development in the 18th and 19th centuries. The figure 8-shaped curve first entered the minds of mathematicians in 1680, when Giovanni Cassini presented his work on curves of the form, appropriately known as the ovals of Cassini. Only 14 years later, while deriving the arc length of the lemniscate, Jacob Bernoulli became the first mathematician in history to define arc length in terms of polar coordinates.
The first major result of work on the lemniscate came in 1753, when, after reading Giulio Carlo di Fagnano’s papers on dividing the lemniscate using straightedge and compass, Leonhard Euler proved that:

Jacobi called December 23,1751 "the birthday of elliptic functions", as this was the day that Euler began reviewing the papers of Fagnanao who was being considered for membership in the Berlin Academy. *Raymond Ayoub, The lemniscate and Fagnano's contributions to elliptic integrals

1802 Jurij Vega (23 Mar 1754, 26 Sept 1802) wrote about artillery but he is best remembered for his tables of logarithms and trigonometric functions. Vega calculated π to 140 places, a record which stood for over 50 years. This appears in a paper which he published in 1789.
In September 1802 Jurij Vega was reported missing. A search was unsuccessful until his body was found in the Danube near Vienna. The official cause of death was an accident but many suspect that he was murdered. *SAU

1867 James Ferguson (31 Aug 1797, 26 Sep 1867) Scottish-American astronomer who discovered the first previously unknown asteroid to be detected from North America. He recorded it on 1 Sep 1854 at the U.S. Naval Observatory, where he worked 1848-67. This was the thirty-first of the series and is now known as 31 Euphrosyne, named after one of the Charites in Greek mythology. It is one of the largest of the main belt asteroids, between Mars and Jupiter. He was involved in some of the earliest work in micrometry was done at the old U.S. Naval Observatory at Foggy Bottom in the midst of the Civil War using a 9.6 inch refractor. He also contributed to double star astronomy. Earlier in his life he was a civil engineer, member of the Northwest Boundary Survey, and an assistant in the U.S. Coast Survey *TIS

1868 August Ferdinand Mobius died. He discovered his famous strip in September 1858. Johann Benedict Listing discovered the same surface two months earlier.*VFR (It is somewhat amazing that we call it after Mobius when Listing discovered it first and published, and it seems, Mobius did not. However Mobius did seem to have thought on the four color theorem before Guthrie, or anyone else to my knowledge.)

1877 Hermann Günther Grassmann (15 Apr 1809, 26 Sep 1877) German mathematician chiefly remembered for his development of a general calculus of vectors in Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844; "The Theory of Linear Extension, a New Branch of Mathematics"). *TIS

1910 Thorvald Nicolai Thiele (24 Dec 1838, 26 Sept 1910) He is remembered for having an interpolation formula named after him, the formula being used to obtain a rational function which agrees with a given function at any number of given points. He published this in 1909 in his book which made a major contribution to numerical analysis. He introduced cumulants (under the name of "half-invariants") in 1889, 1897, 1899, about 30 years before their rediscovery and exploitation by R A Fisher. *SAU

1976 Paul (Pál) Turán (18 August 1910, 26 September 1976) was a Hungarian mathematician who worked primarily in number theory. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers. *SAU

1978 Karl Manne Georg Siegbahn (3 Dec 1886, 26 Sep 1978) Swedish physicist who was awarded the Nobel Prize for Physics in 1924 for his discoveries and investigations in X-ray spectroscopy. In 1914 he began his studies in the new science of x-ray spectroscopy which had already established from x-ray spectra that there were two distinct 'shells' of electrons within atoms, each giving rise to groups of spectral lines, labeled 'K' and 'L'. In 1916, Siegbahn discovered a third, or 'M', series. (More were to be found later in heavier elements.) Refining his x-ray equipment and technique, he was able to significantly increase the accuracy of his determinations of spectral lines. This allowed him to make corrections to Bragg's equation for x-ray diffraction to allow for the finer details of crystal diffraction. *TIS

1990 Lothar Collatz​ (July 6, 1910, , September 26, 1990) was a German mathematician. In 1937 he posed the famous Collatz conjecture, which remains unsolved. The Collatz-Wielandt formula for positive matrices important in the Perron–Frobenius theorem is named after him. *Wik The Collatz conjeture is an iteration problem that deals with the following algorithm..
If a number n is odd, then f(n)= 3n+1
if n is even, then f(n) = 1/2 (n)
Each answer then becomes the new value to input into the function. The problem, or should I say problems, resolve around what happens to the sequence of outcomes when we keep putting the answer back into the function. For example if we begin with 15 we get the following sequence, also called the orbit of the number:
15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1...
One of the unproven conjectures is that for any number n, the sequence will always end in the number 1. This has been shown to be true for all numbers up to just beyond 1016. A second interesting question is how long it takes for a number to return to the value of 1. For the example above, the number 15 took 17 steps to get back to the unit value. Questions such as which three (or other n) digit number has the longest orbit. There are many vairations of the problem, but if you are interested in a good introduction, check this link from Simon Fraser University"
Collatz's Problem is often also called the Syracuse Algorithm, Hasse's problem, Thwaite's problem, and Ulam's problem after people who have worked and written on the problem. It is unclear where the problem originated, as it seems to have had a long history of being passed by word of mouth before it was ever written down. It is often attributed to Lothar Collatz from the University of Hamburg who wrote about the problem as early as 1932. The name "Syracuse Problem" was applied by after H. Hasse, an associate of Collatz, visited and discussed the problem at Syracuse University in the 1950's. During the 1960's Stan Ulam circulated the problem at Los Alamos laboratory. One famous quote about the problem is from Paul Erdos who stated, "mathematics is not yet ready for such problems". *Personal notes


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

Sunday, 25 September 2016

On This Day in Math - September 25


I am undecided whether or not the Milky Way​ is but one of countless others all of which form an entire system. Perhaps the light from these infinitely distant galaxies is so faint that we cannot see them.

~ Johann H Lambert



This is the 269th day of the year, (on non-leap years, the 269th day is Sep 26, and the date is written 26/9 in much of Europe. This is the only day of the year which presents itself in this way. (Are there any days that work using month/day?)

269 is a regular prime, an Eisenstein prime with no imaginary part, a long prime, a Chen prime, a Pillai prime, a Pythagorean prime, a twin prime, a sexy prime, a Higgs prime, a strong prime, and a highly cototient number. So many new terms to look up... Well? Look them up.

269 is the smallest natural number that cannot be represented as the determinant of a 10 × 10 (0,1)-matrix


EVENTS

1493 Columbus set sail on his second voyage to America.

1513 Balboa discovered the Pacific.

1608 The oldest written mention of the telescope: In a letter of introduction from the Council of Zeeland to Zeeland’s Delegates to the States General (the Netherlands parliament) in Den Haag asking them to organise an audience with Prince Maurice of Nassau for a spectacle maker from Middelburg who had invented a “…certain device by means of which all things at a very great distance can be seen as if they were nearby, by looking through glasses…”; the oldest written mention of the telescope. On an unknown day between 25th and 29th September: Hans Lipperhey (1570 – 1619) the spectacle maker from Middelburg (who was actually a German from Wesel) demonstrates his new invention at the court of Prince Maurice, where a peace conference in the Dutch-Spanish War is taking place along with the first visit to Europe of the Ambassador of Siam. Lipperhey’s demonstration is described in detail in a French flyer describing the Ambassadors visit and the news of the new invention is thus spread rapidly throughout Europe. *Renaissance Mathematicus,

1654 Fermat writes to Pascal defending his combinatorial method that Pascal had previously regarded as incorrect.*VFR

1820 Arago announces electromagnetism ... Francois Arago announced that a copper wire between the poles of a voltaic cell, could laterally attract iron filings to itself (Ann. de Chim. et de Physique., xv. p.93). His discovery came in the same year that Oersted discovered that an electric current flowing in a wire would deflect a neighbouring compass needle. Arago in the same publication described how he had successfully succeeded in causing permanent magnetism in steel needles laid at right angles to the copper wire. Arago and André-Marie Ampère, discussed and experimented with forming the copper wire into a helix to intensify the magnetizing action. However, it was not until 1825 that the electromagnet in its familiar form was invented by William Sturgeon. *TIS

1944 Denmark issued a stamp commemorating the 300th anniversary of the birth of Ole Roemer,*VFR

1989 IBM announces plans to develop a new design for transmitting information within a computer, called Micro Channel Architecture, which it said could transfer data at 160 million bytes per second or eight times faster than the fastest speed at the time. Although IBM was hoping to make its system the industry standard, manufacturers of IBM-compatible computers largely chose other methods. *CHM


BIRTHS

1644 Olaus Roemer, Danish astronomer, born. He was the first to measure the speed of light. *VFR (25 Sep 1644;23 Sep 1710) Astronomer who demonstrated conclusively that light travels at a finite speed. He measured the speed by precisely measuring the length of time between eclipses of Jupiter by one of its moons. This observation produces different results depending on the position of the earth in its orbit around the sun. He reasoned that meant light took longer to travel the greater distance when earth was traveling in its orbit away from Jupiter.*TIS "Ole Rømer took part in several other achievements considering measurement. He developed a temperature scale that is now famous as the Fahrenheit scale. Fahrenheit improved and distributed his ideas after visiting Rømer. In his last years, he was even given the position as second Chief of the Copenhagen Police and invented the first street oil lamps in the city of Copenhagen.
Further achievements and inventions may be added to Rømer's biography, like his innovative water supply system and his urban planning concept. " *Yovista.blogspot

1819 George Salmon (25 September 1819 – 22 January 1904) made many discoveries about ruled surfaces and other surfaces. *SAU His publications in algebraic geometry were widely read in the second half of the 19th century. A Treatise on Conic Sections remained in print for over fifty years, going though five updated editions in English, and was translated into German, French and Italian. *Wik

1825 Carl Harald Cramer,(25 September 1893 ,5 October 1985) was a Swedish mathematical statisticians and is one of the prominent figures in the statistical theory. He was once described by John Kingman as "one of the giants of statistical theory". 
In number theory, Cramér's conjecture,in 1936 states that
p_{n+1}-p_n=O((\log p_n)^2),\
where pn denotes the nth prime number, O is big O notation, and "log" is the natural logarithm. Intuitively, this means the gaps between consecutive primes are always small, and it quantifies asymptotically just how small they can be. This conjecture has not been proven or disproven.
*Wik

1846 Wladimir (Peter) Köppen (25 Sep 1846; 22 Jun 1940) German meteorologist and climatologist best known for his delineation and mapping of the climatic regions of the world. He played a major role in the advancement of climatology and meteorology for more than 70 years. The climate classification system he developed remains popular because it uses easily obtained data (monthly mean temperatures and precipitation) and straightforward, objective criteria. He recognized five principal climate groups: (A) Humid tropical -winterless climates; (B) Dry - evaporation constantly exceed precipitation; (C) humid mid-latitude, mild winters; (D) humid mid-latitude, severe winters; and (E) Polar - summerless climates. *TIS

1888 Stefan Mazurkiewicz (25 Sept 1888 , 19 June 1945) His main work was in topology and the theory of probability. His notion of dimension of a compact set preceded that of Menger and Urysohn by seven years. Mazurkiewicz applied topological methods to the theory of functions, obtaining powerful results. His theory gave particularly strong results when applied to the Euclidean plane, giving deep knowledge of its topological structure. *SAU



DEATHS

1777 Johann Heinrich Lambert (26 Aug 1728, 25 Sep 1777) Swiss-German mathematician, astronomer, physicist, and philosopher who provided the first rigorous proof that pi ( the ratio of a circle's circumference to its diameter) is irrational, meaning it cannot be expressed as the quotient of two integers. He also devised a method of measuring light intensity. *TIS In 1766 Lambert wrote Theorie der Parallellinien which was a study of the parallel postulate. By assuming that the parallel postulate was false, he managed to deduce a large number of non-euclidean results. He noticed that in this new geometry the sum of the angles of a triangle increases as its area decreases. *SAU

1852 Christoph Gudermann (March 25, 1798, September 25, 1852) was born in Vienenburg. He was the son of a school teacher and became a teacher himself after studying at the University of Göttingen, where his advisor was Karl Friedrich Gauss. He began his teaching career in Kleve and then transferred to a school in Münster.
He is most known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions, 1839–1840, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.
Gudermann originated the concept of uniform convergence, in an 1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and applied uniform convergence.
His researches into spherical geometry and special functions focused on particular cases, so that he did not receive the credit given to those who published more general works. The Gudermannian function, or hyperbolic amplitude, is named after him.Gudermann died in Münster. *Wik

1877 Urbain-Jean-Joseph Le Verrier (11 May 1811, 25 Sep 1877) French astronomer who predicted the position of a previously unknown planet, Neptune, by the disturbance it caused in the orbit of Uranus. In 1856, the German astronomer Johan G. Galle discovered Neptune after only an hour of searching, within one degree of the position that had been computed by Le Verrier, who had asked him to look for it there. In this way Le Verrier gave the most striking confirmation of the theory of gravitation propounded by Newton. Le Verrier also initiated the meteorological service for France, especially the weather warnings for seaports. *TIS (He died the day after the anniversary of the sighting of his most famous prediction. Between that moment of fame in 1846 and his death, he mistakenly attributed the variability of Mercury's orbit to another small planet he named "Vulcan". It took the theory of General Relativity to explain the variations. He was buried in Montparnasse cemetery in Paris. A large globe sits atop grave. Arago described him as, "the man who discovered a planet with the point of his pen."

1933 Paul Ehrenfest (January 18, 1880, September 25, 1933) was an Austrian and Dutch physicist and mathematician, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. *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, 24 September 2016

On This Day in Math - September 24


Scipio Ferro of Bologna well-nigh thirty years ago discovered this rule and handed it on to Antonio Maria Fior of Venice, whose contest with Niccolo Tartaglia of Brescia gave Niccolo occasion to discover it. He [Tartaglia] gave it to me in response to my entreaties, though withholding the demonstration. Armed with this assistance, I sought out its demonstration in [various] forms. This was very difficult.
~Girolamo Cardano


This is the 268th day of the year, 268 is the smallest number whose product of digits is 6 times the sum of its digits. (A good classroom exploration might be to find numbers in which the product of the digits is n x the sum of the digits for various values of n.. more generally, for what percentage of numbers is the sum a factor of the product at all?)

268 is the sum of two consecutive primes, 268 = 131 + 137


EVENTS

1846 Neptune First observed… “It was on that date, back in 1846, that German Astronomer Johann Galle, assisted by graduate student Heinrich Louis d’Arrest, trained the 24 centimeter (9 inch) Fraunhofer Refractor of the Berlin Observatory on a patch of sky near the Aquarius-Capricorn border (see illustration below) and observed the small, blue disk of Neptune. On July 12th, 2011 Neptune completed exactly one orbit since its discovery. One hundred and sixty five years ago a series of events played out in France, England and Germany that would culminate in a watershed moment in the history science and astronomy, a discovery that would prove to be unique and unrepeatable. These events were rife with centuries-old rivalries, political conspiracy and intrigue, all mixed together with good mathematics, some good science, some bad science, some luck and much mayhem.” more of this interesting story from Tom Madigan’s website.

1852 The steam powered airship was made by Baptiste Jules Henri Jacques Giffard His airship, powered with a steam engine, and weighing over 180 kg (400 lb), it was the world's first passenger-carrying airship (then known as a dirigible, which was French ). Both practical and steerable, the hydrogen-filled airship was equipped with a 3 hp steam engine that drove a propeller. The engine was fitted with a downward-pointing funnel. The exhaust steam was mixed in with the combustion gases and it was hoped by these means to stop sparks rising up to the gas bag; he also installed a vertical rudder.
On 24 September 1852 Giffard made the first powered and controlled flight traveling 27 km from Paris to Élancourt. The wind was too strong to allow him to make way against it, so he was unable to return to the start. However, he was able to make turns and circles,[citation needed] proving that a powered airship could be steered and controlled. *Wik



1940 Westinghouse patent application for the Nimatron, a machine to play the game of Nim, is approved. Created by Eduard Condon, Edgewood Tawney, Gerald Tawney, and Willard Dorr, the machine would be featured in the Westinghouse exhibit at the 1940 World's Fair. The machine played 100,000 games at the fair, winning about 90,000. Most of its defeats were apparently administered by attendants to demonstrate that possibility. When the machine did lose it would "present its opponent with a token coin stamped with the words 'Nim Champ'" *historyofinformation.com







BIRTHS

1501 Girolamo Cardano (24 Sep 1501; 21 Sep 1576) Famous for his Ars magna of 1545, which contained detailed and systematics algebraic solutions to cubic and quartic equations. He was one of the most colorful figures in the whole history of mathematics, as is well illustrated in his autobiography, The Book of My Life. *VFR
Italian physician, mathematician, and astrologer who was the first to give a clinical description of typhus fever. His book, Ars magna ("Great Art," 1545) was one of the great achievements in the history of algebra, in which he published the solutions to the cubic and quartic equations. His mechanical inventions included the combination lock, the compass gimbal consisting of three concentric rings, and the universal joint to transmit rotary motion at various angles (as used in present-day vehicles). He contributed to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science and introduced the Cardan grille, a cryptographic tool (1550). *TIS
His gambling led him to formulate elementary rules in probability, making him one of the founders of the field.
One story says that it was by his own hand so as to fulfill his earlier astrological prediction of of his death on this date. *H. Eves, Introduction to the History of Mathematics, Pg 221...


1625 Jan de Witt born. This statesman for the Netherlands wrote, before 1650, one of the first systematic developments of the analytic geometry of the straight line and conics. It was printed in Van Schooten’s second Latin edition of Descartes’ geometry (1659–1661).*VFR A nice short article about his unusual death, and life are at this blog by The Renaissance Mathematicus

1844 Max Noether born (24 September 1844 – 13 December 1921) . One of the leaders of nineteenth century algebraic geometry. Although himself a very distinguished mathematician, his daughter Emmy Noether was to bring greater innovation to mathematics than did her father. *SAU

1870 Georges Claude (24 Sep 1870; 23 May 1960) The French engineer, chemist, and inventor of the neon light, Georges Claude, was born in Paris. He invented the neon light, which was the forerunner of the fluorescent light. Claude was the first to apply an electrical discharge to a sealed tube of neon gas, around 1902 and make a neon lamp ("Neon" from Greek "neos," meaning "new gas.") He first publicly displayed the neon lamp on 11 Dec 1910 in Paris. His French company Claude Neon, introduced neon signs to the U.S. with two "Packard" signs for a Packard car dealership in Los Angeles, purchased by Earle C. Anthony for $24,000. *TIS

1891 William F. Friedman (24 Sep 1891; 12 Nov 1969) one of the world's greatest cryptologists, who helped decipher enemy codes from World War I to World War II. He was born as Wolfe Friedman.in Kishinev, Russia. He emigrated to the U.S. in 1893. Originally trained as an agricultural geneticist, he had become interested in cryptology. During World War I, with his wife Elizebeth, he set up a cryptology school for military personnel, which led to appointment by the U.S. as head of the Signal Intelligence Service (1930). He broke the Japanese "Purple" code (1937-40), thus allowing Americans to read much of Japan's secret messages during World War II. *TIS There is a bust of him at the National Cryptologic Museum in Fort Meade Maryland on which he is identified as the "Dean of American Cryptology". There is an interesting biography here .

1896 Tadeusz Ważewski (24 September 1896 – 5 September 1972) was a Polish mathematician.
Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. He is most famous for applying the topological concept of retract, introduced by Karol Borsuk to the study of the solutions of differential equations. *Wik
Ważewski studied at the Jagiellonian University in 1914–1920. He started from physics but very quickly turned to mathematics. Ważewski was a pupil of Zaremba.
He spent three years in Paris and got a doctoral diploma from Sorbona.
Ważewski’s research started from topology. In his doctoral dissertation he obtained interesting results on dendrites (locally connected continua not containing simple closed curves). *Ciesielski & Pogoda, EMS Newsletter December 2012

1898 Charlotte Moore Sitterly (24 Sep 1898; 3 Mar 1990) astrophysicist who organized, analyzed, and published definitive books on the solar spectrum and spectral line multiplets. From 1945 to age 90, she conducted this work at the U.S. National Bureau of Standards and the Naval Research Laboratory. She detected that technetium, an unstable element (previously known only as a result of laboratory experiments with nuclear reactions) exists in nature. She made major contributions to the compilation of tables for atomic-energy levels associated with optical spectra, which are now standard reference material. As instruments carried in space rockets provided new data in the ultraviolet, she extended these tables beyond the optical range. She was awarded the Bruce Medal in 1990.*TIS

1904 Evan T Davies graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations.*SAU

1906 Pol(idore) Swings, (24 Sep 1906; 1983) Belgian astrophysicist, made spectroscopic studies to identify elements and structure of stars and comets. He discovered the first interstellar molecule, the CH radical (1937). In comet atmospheres he studied the "Swings bands" - certain carbon emission lines. In 1941, with a slit spectrograph he identified a "Swings effect" in the violet CN bands (3875 A) - a fluorescence partly due to solar radiation that shows emmission line excitation differences dependant on the Doppler shift caused by a comet's motion relative to the Sun. He co-authored an Atlas of Cometary Spectra with Leo Haser in 1956. *TIS

1923 Raoul Bott,(September 24, 1923 – December 20, 2005)[1] was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. *Wik

1930 John Watts Young (24 Sep 1930, ) astronaut who was the commander of the first ever Space Shuttle mission (STS-1, 12 Apr 1981), walked on the Moon during the Apollo 16 mission (21 Apr 1972), made the first manned flight of the Gemini spacecraft with Virgil Grissom. *TIS

1945 Ian Nicholas Stewart FRS (24 September, 1945 - ) is an Emeritus Professor of Mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer.
While in the sixth form at school, Stewart came to the attention of the mathematics teacher. The teacher had Stewart sit mock A-level examinations without any preparation along with the upper-sixth students; Stewart placed first in the examination. This teacher arranged for Stewart to be admitted to Cambridge on a scholarship to Churchill College, where he obtained a BA in mathematics. Stewart then went to the University of Warwick for his doctorate, on completion of which in 1969 he was offered an academic position at Warwick, where he presently professes mathematics. He is well known for his popular expositions of mathematics and his contributions to catastrophe theory.
While at Warwick he edited the mathematical magazine Manifold. He also wrote a column called "Mathematical Recreations" for Scientific American magazine for several years.
Stewart has held visiting academic positions in Germany (1974), New Zealand (1976), and the U.S. (University of Connecticut 1977–78, University of Houston 1983–84). *Wik




DEATHS

1054 Hermann of Reichenau (1013 July 18 – 1054 September 24), was a German mathematician who important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe. Hermann introduced three important instruments into central Europe, knowledge of which came from Arabic Spain. He introduced the astrolabe, a portable sundial and a quadrant with a cursor.
His works include De Mensura Astrolabii and De Utilitatibus Astrolabii (some parts of these works may not have been written by Hermann).
Hermann's contributions to mathematics include a treatise dealing with multiplication and division, although this book is written entirely with Roman numerals. He also wrote on a complicated game based on Pythagorean number theory which was derived from Boethius. *SAU

1651 Etienne Pascal died (Clermont, May 2, 1588 - Paris, September 24, 1651). The Pascal limacon is named after him, and not after his famous son who later came blazing on the scene. *VFR Étienne is famed as the discoverer of the curve the Limaçon of Pascal. The curve, so named by Roberval, can be used to trisect an angle. He discovered the curve in around 1637. (Limacon is from the Latin word for a snail the curve is a roulette formed when a circle rolls around the outside of another circle.) In a letter (see Lettre d'Étienne Pascal et Roberval à Fermat, samedi 16 août 1636) he actively argued in favour of Fermat's De maximis et minimis in opposition to Descartes who viewed the work in a very negative light. *SAU

1938 Lew Genrichowitsch Schnirelmann (2 January(15January 1905greg.) in Gomel; 24 September 1938 in Moscaw) . He was a Belarussian mathematician who made important contributions to the Goldbach conjecture. Using these ideas of compactness of a sequence of natural numbers he was able to prove a weak form of the Goldbach conjecture showing that every number is the sum of ≤ 20 primes.*SAU

1945 Hans (Wilhelm) Geiger (30 Sep 1882, 24 Sep  1945) was a German physicist who introduced the Geiger counter, the first successful detector of individual alpha particles and other ionizing radiations. After earning his Ph.D. at the University of Erlangen in 1906, he collaborated at the University of Manchester with Ernest Rutherford. He used the first version of his particle counter, and other detectors, in experiments that led to the identification of the alpha particle as the nucleus of the helium atom and to Rutherford's statement (1912) that the nucleus occupies a very small volume in the atom. Geiger returned to Germany in 1912 and continued to investigate cosmic rays, artificial radioactivity, and nuclear fission. *TIS

1999 Anneli Cahn Lax (23 Feb 1922 in Katowice, Poland - 24 Sept 1999 in New York City, New York, USA) Anneli Cahn was born in Katowice, then a German city, but now part of Poland, on February 23, 1922. Her family fled Hitler’s regime in 1935 and settled in New York. She married Peter Lax, a fellow mathematician,
in 1948. Their lives together included a shared love for mathematics. Perhaps her most important contribution to mathematics was as editor of the New Mathematics Library. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt on every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. Out of this endeavor grew the New Mathematical Library. The notion was to make accessible to interested high school students, and to a more general public, deep results in mathematics
described by research mathematicians. (This sort of work had long been going on in Eastern Europe.) Lax was asked to take over as general editor for this series, and under her guidance it grew to be the foremost mathematical expository
series in the language. Upon her death it was renamed in her honor. *Mark Saul, Obituary for the AMS VOl 47,#7


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