## Thursday, 30 June 2011

### On This Day in Math -June 30

You know we all became mathematicians for the same reason:
we were lazy.
Max Rosenlicht

EVENTS
1737 John Harrison, after positive results on the test of his first sea-clock, receives the first money awarded by the Board of Longitude (23 years after the Act to create the Board). Harrison received 500 Pounds, 250 Pounds to be paid immediately, and another 250 Pounds after completing a second clock that passes testing at sea. *Derek Howse, Britain's Board of Longitude: The Finances 1714-1828
1742 Euler replied (see June 7 post) in a letter dated 30 June 1742, and reminded Goldbach of an earlier conversation they had ("...so Ew vormals mit mir communicirt haben.."), in which Goldbach remarked his original (and not marginal) conjecture followed from the following statement, “Every even integer greater than 2 can be written as the sum of two primes,” which is thus also a conjecture of Goldbach. In the letter dated 30 June 1742, Euler stated:“Dass ... ein jeder numerus par eine summa duorum primorum sey, halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe necht demonstriren kann.” ("every even integer is a sum of two primes. I regard this as a completely certain theorem, although I cannot prove it.")*Wik
As of this date, no one else has proved it either. It is one of the oldest open questions in mathematics.

1812 Congress authorized the President of the US to issue interest bearing Treasury Notes for the first time in history.  The interest was fixed at "five and two-fifths per centum a year."  *Kane, Famous First Facts (students might calculate the present value of a $10 investment on that date compounded to the present) 1808 Humphry Davy announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days ealier, on 21 Jun 1808*TIS The 1860 Oxford evolution debate took place at the Oxford University Museum on 30 June 1860, seven months after the publication of Charles Darwin's On the Origin of Species. Several prominent British scientists and philosophers participated, including Thomas Henry Huxley, Bishop Samuel Wilberforce, Benjamin Brodie, Joseph Dalton Hooker and Robert FitzRoy. The debate is best remembered today for a heated exchange in which Wilberforce supposedly asked Huxley whether it was through his grandfather or his grandmother that he claimed his descent from a monkey. Huxley is said to have replied that he would not be ashamed to have a monkey for his ancestor, but he would be ashamed to be connected with a man who used his great gifts to obscure the truth *Wik 1894 ==In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS 1908 Comet(?) explodes above Tunguska, Siberia. *VFR In 1908, at around 7:15 am, northwest of Lake Baikal, Russia, a huge fireball nearly as bright as the Sun was seen crossing the sky. Minutes later, there was a huge flash and a shock wave felt up to 650 km (400 mi) away. Over Tunguska, a meteorite over 50-m diameter, travelling at over 25 km per second (60,000 mph) penetrated Earth's atmosphere, heated to about 10,000 ºC and detonated 6 to10 km above the ground. The blast released the energy of 10-50 Megatons of TNT, destroying 2,200 sq km of forest leaving no trace of life. The Tunguska rock came out of the Taurid Meteor storm that crosses Earth's orbit twice a year. The first scientific expedition for which records survive was made by Russian mineralogist Leonid Kulik in 1927. *TIS 1946 ENIAC formally accepted by the government. See 2 October 1955*VFR In 1948, the transistor was demonstrated by its inventors, John Bardeen and Walter Brattain, scientists at the Bell Telephone Laboratory in Murray Hill, NJ.* It was a simple, tiny device utilizing the electronic semiconducting properties of a germanium wafer. The transistor represented a significant advance in technology. As it was developed over the next few years, it was incorporated into electronic equipment as a functional replacment for the vacuum tube. Such use of transistors provided great savings in space and electrical power consumption. This made possible the small portable, battery-powered transistor radios which were sold to the public by late 1954.*TIS 1955 Sperry Rand formed. BIRTHS 1748 Dominique Cassini was a French mathematician and surveyor who worked on his father's map of France. He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later. He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy’s watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father’s map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments. Cassini’s Mémoires pour servir à l’histoire de l’observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik 1791 Félix Savart (June 30, 1791, Charleville-Mézières, Ardennes – March 16, 1841, Paris) became a professor at Collège de France in 1836 and was the co-originator of the Biot-Savart Law, along with Jean-Baptiste Biot. Together, they worked on the theory of magnetism and electrical currents. Their law was developed about 1820. The Biot-Savart Law relates magnetic fields to the currents which are their sources. Félix Savart also studied acoustics. He developed the Savart wheel which produces sound at specific graduated frequencies using rotating disks. Félix Savart is the namesake of the unit of measurement for musical intervals, the savart, though it was actually invented by Joseph Sauveur.*Wik 1856 Cargill Knott born. He graduated from Edinburgh University and was then an assistant in the Physics department. With Barclay and Fraser he was one of the writers who originally proposed the founding of the EMS. He went to the Imperial University in Tokyo as Professor. He returned to a lectureship in Edinburgh and eventually became a Reader in Applied Mathematics. He became Secretary and Treasurer of the EMS in 1883 and President in 1893 and 1918.*SAU 1880 Birthdate of Rudolf Fueter who worked with functions with non-commutative variables and also in number theory. *SAU DEATHS 1660 William Oughtred, inventor of the slide rule (1621) and a staunch royalist, died in a transport of joy on hearing the news of the restoration of Charles II. Augustus De Morgan later remarked, “It should be added, by way of excuse, that he was eighty-six years old.” *VFR an Episcopal minister who invented the earliest form of the slide rule, two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner rule with tongue-in-groove linear construction came later. He introduced the familiar multiplication sign x in a 1631 textbook, along with the first use of the abbreviations sin, cos and tan.*TIS 1919 John William Strutt, 3rd Baron of Rayleigh (of Terling Place) was an English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his investigations into the densities of the most important gases and his successful isolation of argon, an inert atmospheric gas.*TIS 2010 Vladimir Arnold won a Wolf prize for his work on dynamical systems, differential equations, and singularity theory.*SAU Credits: *VFR = V Frederick Rickey, USMA *TIS= Today in Science History *Wik = Wikipedia *SAU=St Andrews Univ. Math History ## Wednesday, 29 June 2011 ### On This Day in Math - June 29 Jeannie, You'll always be beautiful to me! EVENTS In 3123 BC, a Sumerian astronomer saw a devastating asteroid, perhaps a half-mile wide, according to an interpretation of a clay tablet, made by researchers from Bristol University, reported in The Times on 31 Mar 2008. The ancient date was indicated by a computer recreation of the night sky using symbols on the tablet recording the positions of constellations The Planiform tablet found by Henry Layard at Nineveh, likely a 700 BC copy of the astronomer's notes, described in cuneiform a "white stone bowl approaching" that "vigorously swept along." The asteroid probably crashed into the Austrian Alps, leaving a swath of cataclysmic damage such as, for example, the Genesis destruction of Sodom and Gomorrah.*TIS 1877 After proving that the points in a square can be put in one-to-one correspondence with the points on a line segment Cantor wrote his friend Dedekind “Je le vois, mais je ne le crois pas.” (I see it, but I don’t believe it.) [Dauben, Georg Cantor, p. 55]*VFR In 1954, the Atomic Energy Commission, by a vote of 4 to1 decided against reinstating Dr. J. Robert Oppenheimer's access to classified information. The Atomic Energy Act of 1946 required consideration of "the character, associations, and loyalty" of the individuals engaged in the work of the Commission. Substantial defects of character and imprudent and dangerous associations, particularly with known subversives who place the interests of foreign powers above those of the United States, were considered reasons for disqualification. The Commission regarded his associations with persons known to him to be Communists exceeded tolerable limits of prudence and self-restraint, and lasted too long to be justified as merely the intermittent and accidental revival of earlier friendships.*TIS 1956 The interstate highway system was signed into law by President Eisenhower. Even (odd) num­bered roads run East–West (North–South) with the numbers increasing from South to North (West to East). Roads with three digit numbers are loops around cities (when the ﬁrst digit is even) or spurs (ﬁrst digit odd); In either case the last two digits are the main road number. *VFR In 1956, the Act that made possible the modern interstate highway system in the U.S. was signed by President Dwight D. Eisenhower. Eisenhower had seen the speed and efficiency in moving troops and equipment on the four-lane autobahns in Germany during WW II. The idea of federal support of interstate limited-access routes in the U.S. had begun with a study under the Federal-Aid Highway Act of 1938. Little progress was made on building these roads while federal funding was low. When the Federal-Aid Highway Act of 1956 committed federal funds to the States for 90% of the cost, construction began in earnest for the System of Interstate and Defense Highways having at least four lanes with no at-grade railroad crossings. *TIS 2011 - My Jeannie is celebrating her birthday today, and I'm celebrating having her in my life... all the good I ever do is a reflection of a single sun. BIRTHS 1818 Pietro Angelo Secchi Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall. *TIS 1869 George Ellery Hale born. American astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200" reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him - the Hale telescope.*TIS 1893 Eduard Cech, Czech topologist. Czech mathematician born in Stračov, Bohemia (then Austria-Hungary, now Czech Republic). His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik 1904 Topologist Witold Hurewicz born. Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative...". *Wik 1942 K. Jon Barwise. an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.*Wik DEATHS 1895 T(homas) H(enry) Huxley was an English biologist whose promotion of Darwinism led him to an advocacy of agnosticism (a word he coined). At the age of 12 he was reading advanced works on geology, and by early adolescence he recorded the results of simple self-conducted experiments. As a ship's assistant surgeon on HMS Rattlesnake he studied marine specimens by microscope. During the 1850's he published papers on animal individuality, the cephalous mollusks (ex. squids), the methods of paleontology, and the methods and principles of science and science education. *TIS 1924 Robert Simpson Woodward was an American physicist and mathematician, born at Rochester, Michigan. He graduated C.E. at the University of Michigan in 1872 and was appointed assistant engineer on the United States Lake Survey. In 1882 he became assistant astronomer for the United States Transit of Venus Commission. In 1884 he became astronomer to the United States Geological Survey, serving until 1890, when he became assistant in the United States Coast and Geodetic Survey. In 1893 he was called to Columbia as professor of mechanics and subsequently became professor of mathematical physics as well. He was dean of the faculty of pure science at Columbia from 1895 to 1905, when he became president of the Carnegie Institution of Washington, whose reputation and usefulness as a means of furthering scientific research was widely extended under his direction. He was elected to the National Academy of Sciences in 1896. In 1898-1900 he was president of the American Mathematical Society, and in 1900 president of the American Association for the Advancement of Science. In 1915 he was appointed to the Naval Consulting Board. He died in 1924 in Washington, D.C.*Wik Credits: *VFR = V Frederick Rickey, USMA *TIS= Today in Science History *Wik = Wikipedia *SAU=St Andrews Univ. Math History ## Tuesday, 28 June 2011 ### On This Day in Math - June 28 In my opinion, a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy -- an opinion, moreover, which has been expressed by many philosophers. Henri Lebesgue EVENTS 1751 The ﬁrst volume of Diderot’s and d’Alembert’s Encyclopedie appeared. See Hawkins, Jean d’Alembert, p. 69.*VFR 1751 The ﬁrst volume of Diderot’s and d’Alembert’s Encyclopedie appeared. See Hawkins, Jean d’Alembert, p. 69. *VFR 1832, the first American case of a cholera epidemic was reported in New York City. Previously, Europe and the Americas were unaffected by the First Cholera Pandemic of 1817 when cholera, long endemic to the Indian subcontinent, spread to Arabia, Syria, and southern Russia. This abated in the early 1820's, but a new cholera cycle began in 1826. It invaded the British Isles in Oct 1831. Canada was struck shortly before cholera reached New York. Cholera was a horrible disease, spread through fouled water. Its victims died after hours of cramps, diarrhea, and vomiting. Crowded into unsanitary slums, the poor suffered most. Many of the city's elite fled to the countryside. In America, the disease's hold broke by Dec 1832.*TIS 1884 Sonya Kovalevskaya ocially appointed extraordinary professor at Stockholm University. [The Mathematical Intelligencer, vol. 6, no. 1, p. 29; *VFR In 1958, the Mackinac Bridge, the world longest suspension bridge, was dedicated. Ceremonies began on 24 Jun with the first "Governor's Walk" across the bridge. (It had opened to traffic on 1 Nov 1957.) This bridge joins the upper and lower peninsulas of the state of Michigan, reducing the crossing time, from a couple of hours, to just 10 minutes. Ceremonial groundbreaking took place at the St. Ignace end of the bridge on 7 May 1954, and on the opposite shore at Mackinaw City the next day. Meanwhile caissons and superstructures were assembled as far away as Indiana, Pennsylvania and Ohio. Including approaches, the total length is 26,444-ft, needing 34 bridge support foundations. The main span is 3,800-ft long. *TIS 2011 6-28 has become popular as Tau day with many people who think 2 pi (or 6.28...) is more appropriate, or just a nice addition to Pi-day, on March 14 (or 3.14... ) . BIRTHS 1768 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church. 1875 Henri Lebesgue He introduced the concept of Lebesgue Measure, a device for measuring the ‘length’ of complicated sets of points on the line, and so is known as the father of modern integration theory. *VFR French mathematician whose generalization of the Riemann integral revolutionized the field of integration. He was maître de conférences (lecture master) at the University of Rennes until 1906, when he went to Poitiers, first as chargé de cours (assistant lecturer) of the faculty of sciences and later as...*TIS 1894 Einar Hille born. In the preface of his Analytic Function Theory (1959) he wrote “It is my hope that students of this book may come to respect the historical continuity of the subject.” More authors should include historical footnotes as good as those in this book.*VFR 1920 Nicolaas Hendrik "Nico" Kuiper was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem. Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude. He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985.*Wik DEATHS 1889 Maria Mitchell First American professional woman astronomer, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Sciences. She died at age 70 in Lynn, Mass. 1930 William J Greenstreet graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette 1956 Functional analyst Friedrich Riesz died.*VFR One of the most significant personalities among Hungarian mathematicians. At the beginning he studied engineering at the Technical University of Zurich, but he soon realised that he was much more interested in mathematics than in technical subjects. So he continued to study at the Royal Hungarian University of Sciences in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he learnt for a year in Göttingen and attended the lectures of David Hilbert and . He obtained his PhD degree and diploma of secondary school teacher of mathematics and physics in Budapest. 1952 William Watson graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh.*SAU 1984 Claude Chevalley had a major influence on the development of several areas of mathematics including Ring Theory and Group Theory *SAU 1974 Vannever Bush American electrical engineer and administrator who and oversaw government mobilization of scientific research during World War II. At the age of 35, in 1925, he developed the differential analyzer, the world's first analog computer. It was capable of solving differential equations. He put into concrete form that which began 50 years earlier with the incomplete efforts of Babbage, and the theoretical details developed by Kelvin. This machine filled a 20 x 30 foot room. He innovated one of the largest growing media in our time, namely hypermedia as fulfilled in the Internet with hypertext links *TIS Credits: *VFR = V Frederick Rickey, USMA *TIS= Today in Science History *Wik = Wikipedia *SAU=St Andrews Univ. Math History ## Monday, 27 June 2011 ### On This Day in Math - June 27 Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols. Augustus de Morgan EVENTS 432 B.C. Meton observed the summer solstice and began his cycle. Meton was one of the first Greek astronomers to make accurate astronomical observations. It is widely believed that, working with Euctemon, he observed the summer solstice, which marked the Athenian New Year, in 432 BC. The Metonic cycle appears in the oldest known astronomical device, the Antikythera Mechanism (2nd century BC) together with its multiple the Callippus cycle of 76 years. The foundations of Meton's observatory in Athens are still visible just behind the podium of the Pnyx, the ancient parliament. Meton found the dates of equinoxes and solstices by observing sunrise from his observatory. The bisectrice of the observatory lies in an easterly direction, between the Acropolis and the Lycabetus hill.*Wik In 1847, New York and Boston were linked by telegraph wires. This enabled the New York newspapers to receive foreign news brought by Cunard's steamers to the Boston port about 190 miles away. When the Cambria next arrived in Boston, three New York Newspapers on 18 Jul 1846 carried identical brief first-day telegraphic summaries of the Cambia's news*. This telegraph link opened three years after the first U.S. telegraph line was opened on 24 May 1844 with a message sent by Samuel Morse 80 miles from Washington D.C. and Baltimore, Md.*TIS 1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat’s great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth$50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik

1967 The first ATM in England that was put into use was by Barclays Bank in Enfield Town in North London, United Kingdom, on 27 June 1967. This machine was the first in the UK and was used by English comedy actor Reg Varney, at the time so as to ensure maximum publicity for the machines that were to become mainstream in the UK. This instance of the invention has been credited to John Shepherd-Barron of printing firm De La Rue, who was awarded an OBE in the 2005 New Year's Honours List. His design used special cheques that were matched with a personal identification number, as plastic bank cards had not yet been invented. *Wik (The plaque posted at the sight makes the claim to be the first cash machine in the world, but cash dispensing machines had been installed in Tokyo and another shortly after in Upsalla.)

1977 Italy issued a postage stamp honoring Filippo Brunelleschi (1377–1446). [Scott #1266]. *VFR

1980 Creighton Carvello recited 20,013 digits of π from memory in nine hours and one minute. *VFR

BIRTHS

1767 Alexis Bouvard French astronomer and director of the Paris Observatory, who is noted for discovering eight comets and writing Tables astronomiques of Jupiter and Saturn (1808) and of Uranus (1821). Bouvard's tables accurately predicted orbital locations of Jupiter and Saturn, but his tables for Uranus failed, leading him to hypothesize that irregularities were caused by an unknown perturbing body. This spurred observations leading to the discovery of Neptune by Adams and Leverrier.*TIS

1806 Augustus de Morgan born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his ﬁrst book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR
In formal logic, De Morgan's laws are rules relating the logical operators "and" and "or" in terms of each other via negation. With two operands A and B:
$\overline{A \cdot B} = \overline A + \overline B$
$\overline{A + B} = \overline {A} \cdot \overline {B}$
In another form:
NOT (P AND Q) = (NOT P) OR (NOT Q)
NOT (P OR Q) = (NOT P) AND (NOT Q)
The rules can be expressed in English as:
"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
*Wik When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS  A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.

1850 Jorgen Pedersen Gram. Danish mathematician. Today he is best known for his criterion of linear independence of functions. The Gram-Schmidt Orthonormal Basis Theorem in Linear Algebra was ﬁrst published by him in 1883.
1940 Daniel G. Quillen bon in Orange, New Jersey. In 1978 he won a Fields Medal as the “prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particu¬larly ring theory and module theory.” *VFR French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc, she corresponded with Lagrange who recognised her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer. TIS

DEATHS
1829 James Smithson English scientist who provided funds in his will for the founding of the Smithsonian Institution, Washington, D.C. "for the increase and diffusion of knowledge." He had inherited his fortune chiefly through his mother's family. He was a chemist and minerologist who published 27 scientific papers. The mineral smithsonite (carbonate of zinc) was named for him.*TIS

1831 Sophie Germain died before she could receive the honorary doctorate Gauss had persuaded the University of Gottingen to give her. *VFR

1880 Carl Borchardt was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1952 Max Dehn died. He solved Hilbert’s third problem in 1900 (shortly after receiving his Ph.D. un¬der Hilbert on another topic in the foundations of geometry): a tetrahedron cannot be cut up into ﬁnitely many pieces and reassembled into a cube of equal volume. Thus Dehn became the ﬁrst mathematician to join “the honors class” of mathematicians who had solved one of the twenty-three problems Hilbert posed in Paris in 1900.

1975 Sir Geoffrey Ingram Taylor OM (7 March 1886 – 27 June 1975) was a British physicist, mathematician and expert on fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century". His final research paper was published in 1969, when he was 83. In it he resumed his interest in electrical activity in thunderstorms, as jets of conducting liquid motivated by electrical fields. The cone from which such jets are observed is called the Taylor cone for his namesake. In the same year Taylor was appointed to the Order of Merit. He suffered a stroke in 1972 which effectively put an end to his work; he died in Cambridge in 1975.*Wik

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

## Sunday, 26 June 2011

### On This Day in Math - June 26

When you measure what you are speaking about and express it in numbers,
but when you cannot express it in numbers
William Thompson, Lord Kelvin

EVENTS
1614   The first lottery of significance in the new world was held on this date by the Virginia Company.  The first Great Prize was 4,500 Crowns. *JN Kane, Famous First Facts (I have seen the date of this lottery also given as 1612)

In 1819, The first US patent for a velocipede, a predecessor of the bicycle, was issued to William K. Clarkson Jr. of New York. Little information remains available, however, because a fire at the Patent Office in 1836 destroyed the patent record, and it was not restored. The photo shows the Draisine design of the period (Europe, 1816). Bicycles were introduced to the US also in 1819 and were manufactured by David and Rogers in Troy, NY*TIS

In 1974, at 8:01 a.m., a package of Wrigley's chewing gum with a bar code printed on it passed over a scanner at the Marsh Supermarket, Troy, Ohio, and became the first product ever logged under the new Universal Product Code (UPC) computerized recognition system. Invented by IBM, and approved for use in 1973, the UPC is a 12-number bar code representing the manufacturer's identity and an assigned product number. Within nanoseconds, this information is read with a laser beam moving at around 10,000 inches per second and transfers it to the store's database computer for price lookup and inventory management*TIS

In 1984, the National Maritime Museum, of which the Royal Observatory, Greenwich is a part, encouraged people up and down the Line to organise events in order to mark the so-called ‘centenary’ of the Prime Meridian. Although the International Meridian conference took place in October 1884, the Museum designated Tuesday 26 June as ‘Meridian Day’, on the grounds that any outdoor events would be less likely to be affected by the weather.
Commemorative six-inch diameter plastic plaques were offered to any individual who could show that the Meridian passed through the curtilage of their property. Potential claimants were required to write to their regional office of the Ordnance Survey to verify their claim and send this as proof of authenticity to the English Tourist Board who were distributing them. No records of how many were issued can be traced. The locations of just four are known, along with the existence of a fifth.
The National Maritime Museum also arranged for the Enfield Foundry to cast a bronze plaque as a more enduring alternative. At the time, it was stated that they would only be produced if 20 or more orders were received. How many were made is unknown, the Foundry’s records having been destroyed. Only three have been located to date.

In 2000, the completion of a working draft reference DNA sequence of the human genome was announced at the White House by President Bill Clinton, and representatives from the Human Genome Project (HGP) and the private company Celera Genomics. Clinton stated that even greater discoveries would follow from the working draft. As a draft, it contained some gaps and errors, but represented about 95% of all genes. HGP expected to use it as a scaffold for generating the high-quality reference genome sequence within three years. This provides knowledge to link genes with particular diseases, of the influence of genetics and to help discover new treatments.
*TIS

BIRTHS
1730 Charles Messier French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.

1824 Lord Kelvin.. Born as William Thomson, he became an influential physicist, mathematician and engineer who has been described as a Newton of his era. At Glasgow University, Scotland, he was a professor for over half a century. The name he made for himself was more than just a temperature scale. His activities ranged from being the brains behind the laying of a transatlantic telephone cable, to attempting to calculate the age of the earth from its rate of cooling. In 1892, when raised to the peerage as Baron Kelvin of Largs, he had chosen the name from the Kelvin River, near Glasgow.*TIS

1878 Leopold Löwenheim was a German mathematician who worked on mathematical logic and is best-known for the Löwenheim-Skolem paradox.*SAU

DEATHS
1274 Nasir al-Tusi was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.*SAU

1796 David Rittenhouse American astronomer, instrument maker and inventor who was an early observer of the atmosphere of Venus. For observations for the transit of Venus on 3 Jun 1769, he constructed a high precision pendulum clock, an astronomical quadrant, an equal altitude instrument, and an astronomical transit. He was the first one in America to put spider web as cross-hairs in the focus of his telescope. He is generally credited with inventing the vernier compass and possibly the automatic needle lifter. He was professor of astronomy at the University of Pennsylvania. Benjamin Franklin consulted him on various occasions. For Thomas Jefferson he standardized the foot by pendulum measurements in a project to establish a decimal system of weights and measures.*TIS

1810 Joseph Montgolfier French ballooning pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world. *TIS

1951 George Udny Yule graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU

1967 H T H Piaggio graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations. *SAU

1990 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to forsee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*Wik

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

## Saturday, 25 June 2011

### On This Day in Math - June 25

Astronomy was the cradle of the natural sciences and the starting point of geometrical theories.
~Cornelius Lanczos

EVENTS

1641 John Pell begins the work of expanding Walter Warner's table of anti-logarithms from 10,000 to 100,000 entries. Warner felt he was too old to complete the laborious task he had set for  himself, and offered Pell 40 GBPounds (appx. worth 5,000 pounds today) to complete the tables and make them ready for printing.  *Thomas Harriot's Doctrine of Triangular Numbers, Beery &Stedall, pg 39

1665  René Descartes died on 11 February 1650 in Stockholm, Sweden, where he had been invited as a teacher for Queen Christina of Sweden. The cause of death was said to be pneumonia—accustomed to working in bed until noon, he may have suffered a detrimental effect on his health due to Christina's demands for early morning study (the lack of sleep could have severely compromised his immune system). Others believe that Descartes may have contracted pneumonia as a result of nursing a French ambassador, Dejion A. Nopeleen, ill with the aforementioned disease, back to health. In his recent book, Der rätselhafte Tod des René Descartes (The Mysterious Death of René Descartes), the German philosopher Theodor Ebert asserts that Descartes died not through natural causes, but from an arsenic-laced communion wafer given to him by a Catholic priest. He believes that Jacques Viogué, a missionary working in Stockholm, administered the poison because he feared Descartes's radical theological ideas would derail an expected conversion to Roman Catholicism by the monarch of Protestant Lutheran Sweden.*Wik
After his death in Stockholm, his body was returned to Paris, arriving on 25 Jun 1665 , though the coffin had been looted by his followers for relics in Stockholm.  Supposedly, the coffin was shipped overland from Copenhagen to avoid piracy by English admirers!  The remains were in Ste. Geneviève, then in Lenoir's Museum of French Monuments, and then finally moved to St‑Germain-des-Prés in 1819. His headstone (or gravestone) is in St‑Germain‑des‑Prés, in the second chapel on the right of the apse.   Stephen Jay Gould says the (purported) skull of Descartes is in the Musée de l'Homme, apparently on display.  Arjen Dijksman recently advised me that the Musee de l'Homme is closed for another year, and there has been efforts to move the skull to the Pantheon
Église St-Germain-des-Prés, at 3 Place St-Germain-des-Prés, is the oldest church in Paris. Part of it dates to the 6th century, when a Benedictine abbey was founded on the site by King Childebert, son of Clovis. The church was originally built to house a relic of the True Cross brought from Spain in 542. The Normans destroyed the abbey on multiple occasions and only the marble columns in the triforium remain from the original structure. The carved capitals on the pillars are copies of the originals, which are kept in the Musée National du Moyen-Age. The church was enlarged and reconsecrated by Pope Alexander III in 1163. The abbey was completely destroyed during the Revolution, but the church was spared. The present building is a fine example of Romanesque architecture, with gothic interior elements. The square tower, dating from the early 11th century, is topped by a landmark spire, which dates to the 19th century.  For a time, the abbey served as a pantheon for Merovingian kings. The Chapelle Saint Symphorien, built during the Middle Ages and restored in 1981, served as the necropolis mérovingienne (crypt of the Merovingians). This is the presumed site of first tomb of Saint Germain, Bishop of Paris, who died in 576. Among the others interred here are King Jean-Casimir of Poland.

1712 Brook Taylor suggested that if two glass plates which are clamped together into a “V” are placed into a pan of water then capillary action will draw water up into the shape of a rectangular hyperbola with asymptotes the surface of the water and the point of the “V.” This and several similar experiments performed by Francis Hauksbee before the Royal Society caused Newton to rethink his ideas on capillary force. *VFR

1783  Antonie Lavoisier announced to the French Academy of Sciences that water was the product formed by the combination of hydrogen and oxygen. However, this discovery had been made earlier by the English chemist Henry Cavendish. *TIS

1795 Founding of the Bureau of Longitude in Paris. *VFR

BIRTHS
1864 Walther Hermann Nernst German who was one of the founders of modern physical chemistry. In 1889, he devised his theory of electric potential and conduction of electrolytic solutions (the Nernst Equation) and introduced the solubility product to explain precipitation reactions. In 1906, Nernst showed that it is possible to determine the equilibrium constant for a chemical reaction from thermal data, and in so doing he formulated what he himself called the third law of thermodynamics. This states that the entropy, (a thermodynamic measure of disorder in a system), approaches zero as the temperature goes towards absolute zero. For this, he was awarded the 1920 Nobel Prize in Chemistry. In 1918, he explained the H2-Cl2 explosion on exposure to light as an atom chain reaction. *TIS

1879  Sir William Fothergill Cooke English inventor who worked with Charles Wheatstone in developing electric telegraphy. Of the pair, Cooke contributed a superior business ability, whereas Wheatstone is generally considered the more important of the two in the history of the telegraph. After Cooke attended a demonstration of the use of wire in transmitting messages, he began his own experiments with telegraphy (1836) and formed a partnership with Wheatstone. Their first patent (1837) was impractical because of cost. They demonstrated their five-needle telegraph on 24 July 1837 when they ran a telegraph line along the railway track from Euston to Camden Town able to transmit and successfully receive a message. In 1845, they patented a single-needle electric telegraph. *TIS

DEATHS
1671 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

1941 Alfred Pringsheim died. His work in Fourier series, analytic function theory, and continued fractions was a model of the Weierstrassian approach, although he was not a student of Weier­strass. *VFR

1960 Walter Baade (24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

1974 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU

1978 Hsien Chung Wang 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

1997 Jacques-Yves Cousteau French naval officer, oceanographer, marine biologist and ocean explorer, known for his extensive underseas investigations. He was co-inventor of the aqualung which made SCUBA diving possible (1943). Cousteau the developed the Conshelf series of manned habitats, the Diving Saucer, a process of underwater television and numerous other platforms and specialized instruments of ocean science. In 1945 he founded the French Navy's Undersea Research Group. He modified a WWII wooden hull minesweeper into the research vessel Calypso, in 1950. An observation dome added to the foot of Calypso's bow was found to increase the ship's stability, speed and fuel efficiency. *TIS2006

2006  Irving "Kap" Kaplansky was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D  from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to
group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of
pi
.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act.
He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

## Friday, 24 June 2011

### On This Day in Math - June 24

For example is not a proof.
Jewish proverb

EVENTS
1634 Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Coll`ege Royal in Paris. Thereafter, he kept his mathematical discoveries secret so that he could continue to win the competition and keep the chair. As a consequence he lost credit for many of his discoveries. *VFR
He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented.
Another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines."

1644 In a letter to Torricelli, Fr. Marin Mersenne gives a method to find a number with any number of factors. He explained; since 60 = 2*2*3*5 subtract one from each factor (1,1,2, 4) and make them the exponents of any primes.. he used 24*32*5*7= 5040.. Of course Plato knew much earlier that 5040 had sixty factors.In Laws, Plato suggests that 5040 is the optimal number of citizens in a state because a) It is the product of 12, 20, and 21; b) the 12th part of it can still be divided by 12; and c) it has 59 proper divisors, including all numbers for 1 to 12 except 11, and 5038--which is very close to 5040--is divisible by 11.

1687 In a letter to Huygens, Fatio de Dullier used an integrating factor to solve the diﬀerential equation 3x dy − 2y dx = 0. No earlier instance of an integrating factor is known. The fundamental conception of integrating factors was due to Euler (1734) and further developed by Clairaut (1739). *VFR

In 1778, David Rittenhouse observed a total solar eclipse in Philadelphia. In a letter to him, dated 17 Jul 1778, Thomas Jefferson wrote that "We were much disappointed in Virginia generally on the day of the great eclipse, which proved to be cloudy." Rittenhouse (1732-1796) was not only an American astronomer, but also a mathematician and public official. He is reputed to have built the first American-made telescope and was the first director of the U.S. Mint (1792-1795).*TIS  Jefferson was an excellent applied mathematician and had contacted Rittenhouse on another occasion.  Travelling through France ten years later, " in 1788, he noticed peasants near Nancy ploughing, and fell to wondering about the design of the moldboard, that is, the surface which turns the earth: he spent the next ten years working on this, on and off, wondering how to achieve the most efficient design, both offering least frictional resistance, and which also would be easy for farmers out in the frontiers to construct, far from technical help. He consulted the Pennsylvania mathematician Robert Patterson (born in Ireland in 1743), and consulted also another Philadelphia luminary, the self-taught astronomer and mathematical instrument-maker David Rittenhouse (1732-1796)."   Jefferson also communicated with Thomas Paine about bridge design, suggesting the use of catenary arches.  Jefferson is believed to be the first person ever to use the term "catenary" in English.

1847 The first observation with the Great Refractor at Harvard was of the Moon on the afternoon of June 24, 1847. A number of significant achievements quickly followed. The eighth satellite of Saturn was discovered in 1848 by W.C. Bond and his son, George P. Bond, who was to succeed his father as Director in 1859. In 1850, Saturn's crape, or inner, ring was first observed, again by the Bonds. That same year, the first daguerreotype ever made of a star, the bright Vega, was taken by J.A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes. One of the earliest photographs of a double star, Mizar and Alcor in the handle of the Big Dipper, was achieved in 1857, using the wet-plate collodion process. *Observatory web page...  The 15 inch Great Refractor was "once the biggest and best telescope in the United States, perhaps the world."  *Frederik Pohl, Chasing Science, pg 42.

In 1898, a U.S. commemorative stamp was first used that carried the design of a major engineering construction project, the Mississippi River Bridge, a triple-arch steel bridge between East St. Louis, Illinois and St. Louis,
Missouri. Each span was roughly 500 feet and rested on piers resting on bedrock some 100 feet beneath the river bottom. Opened on 4 Jul 1874, the bridge was named after its designer, the self-trained engineer, James Eads. The upper level road also carried streetcars, which are seen in the stamp design along with steam ships on the river below. The trains that ran on its lower level are hidden from view at this angle. (Although still in use, the bridge no longer carries rail traffic.) The design was reissued in 1998.*TIS

In 1975, a moon tremour, caused by a strike of Taurid meteors, was detected by the seismometer network left on the Moon's surface by American astronauts. The major series of lunar impacts between 22 - 26 Jun 1975 represented 5% of the total number of impacts detected during the eight years of the network's operation, and included numerous 1-ton meteorites. The impacts were detected only when the nearside of the Moon (where the astronauts landed) was facing the Beta Taurid radiant. At the same time, there was a lot of activity detected in Earth's ionosphere, which has been linked with meteor activity. The Taurid meteor storm crosses the Earth orbit twice a year, during the period 24 Jun to 6 Jul and the period 3 Nov to 15 Nov.*TIS

BIRTHS
1880 Oswald Veblen,  American mathematician, born in Decorah, Iowa, who made important contributions to differential geometry and early topology. Many of his contributions found application to atomic physics and relativity. Along with his interest in the foundations of geometry he developed an interest in algebraic topology, or analysis situs as it was then called and by 1912 was writing papers on this subject. Gradually he became more interested in differential geometry. From l922 onward most of his papers were in this area and in its connections with relativity. His work on axioms for differentiable manifolds and differential geometry contributed directly to the field.*TIS
1909 William Penney (24 Jun 1909, 3 Mar 1991 at age 81)(Baron Penney of East Hendred) British nuclear physicist who led Britain's development of the atomic bomb. Penney was to Britain as Robert Oppenheimer was to the U.S. He was a prominent part of the British Mission at Los Alamos during WW II, where his principal assignment was studying the damage effects from the blast wave of the atomic bomb, but he became involved in implosion studies as well. Penney's combination of expertise, analytical skill, effective communication, and the ability to translate them into practical application soon made him one of the five members of the Los Alamos “brain trust” that made key decisions. He was the only Briton to be part of the ten man Target Committee that drew up the list of targets for the atomic bombing of Japan. *TIS
1915 Sir Fred Hoyle English mathematician and astronomer, best known as the foremost proponent and defender of the steady-state theory of the universe. This theory holds both that the universe is expanding and that matter is being continuously created to keep the mean density of matter in space constant. He became Britain's best-known astronomer in 1950 with his broadcast lectures on The Nature of the Universe, and he recalled coining the term "Big Bang" in the last of those talks. Although over time, belief in a "steady state" universe as Hoyle had proposed was shared by fewer and fewer scientists because of new discoveries, Hoyle never accepted the now most popular "Big Bang" theory for the origin of the universe.

DEATHS
1832 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

1880 Jules Lissajous was a French mathematician best known for the Lissajous figures produced from a pair of sine waves. *SAU  The curves are also called Bowditch curves for the early American mathematician, Nathanial Bowditch,  who worked with them earlier.  In general, a parametric curve with equations x= A sin(k t ); y= B sin(m t), the curves can describe things as simple as a circle or ellipse to more complex open and closed curves.  If the ratio of k/m is rational, the curve will eventually close.
Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

### On This Day in Math - June 23

We can only see a short distance ahead,
but we can see plenty there that needs to be done.

Alan Turing, From his paper on the Turing test

EVENTS
1585 Thomas Harriot arrived oﬀ the coast of Virginia (actually Cape Lookout, NC). He was the ﬁrst substantial mathematician to visit North America. [John W. Shirley in Thomas Harriot: A Biography, 1983, p. 129; Thanks to Kullman] *VFR Thomas Harriot's name was once synonymous with a common method of solving quadratics taught in nearly every high school. Once commonly called Harriot's Method, today it is simply referred to as factoring.
And how did he come to be in the exploration of Virginia?? Here is the story from Encyclopedia Virginia, 2010:

Thomas Hariot (often spelled Harriot) was an English mathematician, astronomer, linguist, and experimental scientist. During the 1580s, he served as Sir Walter Raleigh's primary assistant in planning and attempting to establish the English colonies on Roanoke Island off the coast of present-day North Carolina. He taught Raleigh's sea captains to sail the Atlantic Ocean using sophisticated navigational methods not well understood in England at the time. He also learned the Algonquian language from two Virginia Indians, Wanchese and Manteo. In 1585, Hariot joined the expedition to Roanoke, which failed and returned to England the next year. During his stay in America, Hariot helped to explore the present-day Outer Banks region and, farther north, the Chesapeake Bay. He also collaborated with the artist John White in producing several maps notable at the time for their accuracy. Although Hariot left extensive papers, the only work published during his lifetime was "A Briefe and True Report of the New Found Land of Virginia", which evaluated the economic potential of Virginia. The report appeared most impressively in Theodor de Bry's 1590 edition that included etchings based on the White-Hariot maps and White's watercolors of Indian life. After a brief imprisonment in connection to the Gunpowder Plot (1605), Hariot calculated the orbit of Halley's Comet, sketched and mapped the moon, and observed sunspots. He died in 1621.

1676 Newton, via Oldenburg, sent his famous Epistola prior to Leibniz. It contained the ﬁrst use of fractional exponents as well as the newly discovered binomial theorem.*VFR

In 1775, the first American-made book was advertised in Philadelphia, Penn. Titled Impenetrable Secret, the book was printed and sold by Story and Humphreys. Their advertisement in the Pennsylvania Mercury announced it was "printed with types, paper and ink manufactured in this Province."*TIS

1835 Mobius receives a letter from Bellavitis with a method for adding and subtracting non-collinear vectors. (A history of vector analysis: the evolution of the idea of a vectorial system By Michael J. Crowe) A geometrical work by Bellavitis was published in 1832 which also contains vector type quantities. His basic objects are line segments AB and he considers AB and BA as two distinct objects. He defines two line segments as 'equipollent' if they are equal and parallel, so, in modern notation, two line segments are equipollent if they represent the same vector. Bellavitis then defines the 'equipollent sum of line segments' and obtains an 'equipollent calculus' which is essentially a vector space. *SAU

1993 Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards. After announcing his results, (Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

BIRTHS
1775 Étienne-Louis Malus (23 Jun 1775, 24 Feb 1812 at age 36)French physicist who discovered that light, when reflected, becomes partially plane polarized; i.e., its rays vibrate in the same plane. He served in Napoleon's corps of engineers, fought in Egypt, and contracted the plague during Napoleon's aborted campaign in Palestine. Posted to Europe after 1801, he began research in optics. In 1808, he discovered that light rays may be polarized by reflection, while looking through a crystal of Iceland spar at the windows of a building reflecting the rays of the Sun. He noticed that on rotating the crystal the light was extinguished in certain positions. Applying corpuscular theory, he argued that light particles have sides or poles and coined the word "polarization." *TIS

1902 Dr. Howard T. Engstrom American computer designer who promoted the first commercially available digital computer, the Univac. As a Yale professor he had written a paper on the mathematical basis for cryptanalysis techniques. During WW II he was called to the Navy and placed in command of the OP-20-G automated machines "Research Section" for message decryption. After the war, he was a co-founder of Engineering Research Associates, a private company to work on electronic digital circuit technology for the Navy on a contract basis, with former Navy researchers. ERA delivered its first Atlas computer to the National Security Agency in Dec 1950. As vice president for research, Engstrom took the initiative to make a commercial version, renamed Univac.*TIS

1912 Alan Mathison Turing born. This British mathematician was one of the founders of recursion theory, invented the Turing machine (an abstract model of a computer), did important work in cryptography, and invented the computer. *Alan Turing. The Enigma by Andrew Hodges, 1983.

DEATHS
1891 Wilhelm Eduard Weber German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

1891 Norman Robert Pogson (23 Mar 1829; 23 Jun 1891 at age 62) English astronomer who devised the magnitude scale of the brightness of stars (1850) now in use. He divided the classical scale in which a first magnitude star is one hundred times brighter than a sixth magnitude star using five integer steps. Each step represents a fifth-root of 100 (about 2.512) increase in brightness. The Sun's magnitude on this scale is -26.91, whereby negative numbers denote objects brighter than first magnitude. Sirius is magnitude -1.58, Aldebaran is 1 and the faintest star detected is 30. His interest in astronomy began in his youth; by age 18 he had calculated orbits for two comets. He discovered 8 asteroids, 21 new variable stars and compiled a massive star catalogue. In 1860 he moved to India for the remainder of his life's work.*TIS

1892 Pierre Ossian Bonnet died. He worked on minimal surfaces, geodesics, and integral geometry. *VFR  Bonnet made major contributions introducing the notion of geodesic curvature. A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss-Bonnet theorem. Gauss published a special case.

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History