Friday, 21 July 2017

On This Day in Math - July 21

The saddest aspect of life right now is that
science gathers knowledge faster than society gathers wisdom.

-Isaac Asimov

Today is the 202nd day of the year; in an alphabetical listing of the first one-thousand numbers, 202 is last.

202293 begins with the digits 293 and 293202 begins with the digits 202. *jim wilder ‏@wilderlab

There are 46 palindromes in the 365 (ir 366) days of the year, 202 is the 30th of these.


1807 Gauss, in a letter to his friend Olbers, praised the mathematical ability of Sophie Germain. *VFR Although Gauss thought well of Germain, his replies to her letters were often delayed, and he generally did not review her work. Eventually his interests turned away from number theory, and in 1809 the letters ceased. Despite the friendship of Germain and Gauss, they never met.*Wik

1820 Oersted announced his discovery of electromagnetism. *VFR The actual discovery of electromagnetism was made during a lecture demonstration that Oersted was conducting for advanced students during the spring of 1820. It is perhaps the only case known in the history of science when a major scientific discovery was mate in front of a classroom of students.

1814 Joseph von Fraunhofer was the eleventh child of an indigent glazier he was orphaned and apprenticed to Philipp Weichselberger. It may seem strange to say that he was lucky to have the dilapidated building which was the house and shop of Weichselberger collapse on top of him. But being the only survivor made him newsworthy, and when he was visited by Maximilian Joseph, the Bavarian Elector, he was given a sum of eighteen ducats with which he bought a glass making machine, books, and his freedom from his apprenticeship. Ahead in his brief life, he would discover the spectral lines which still carry his name. *Timothy Ferris, Coming of Age in the Milky Way

These dark fixed lines were later shown to be atomic absorption lines, as explained by Kirchhoff and Bunsen in 1859. These lines are still called Fraunhofer lines in his honor - although they had previously been noted by Wollaston in 1802.

1925 John Scopes is found guilty of teaching evolution in violation of Tennessee's Butler Act.
"After eight days of trial, it took the jury only nine minutes to deliberate. Scopes was found guilty on July 21 and ordered to pay a US$100 fine (approximately $1,345 in present day terms when adjusted from 1925 for inflation).[35] Raulston imposed the fine before Scopes was given an opportunity to say anything about why the court should not impose punishment upon him and after Neal brought the error to the judge's attention the defendant spoke for the first and only time in court:

Your honor, I feel that I have been convicted of violating an unjust statute. I will continue in the future, as I have in the past, to oppose this law in any way I can. Any other action would be in violation of my ideal of academic freedom—that is, to teach the truth as guaranteed in our constitution, of personal and religious freedom. I think the fine is unjust. (World's Most Famous Court Trial, p. 313.)

1959 The first “International Mathematical Olympiad” began in Brasov, Romania. It lasted until 31 July and involved 52 competitors on teams from seven Eastern European countries. The Romanian Team won the team event, and the individual Gold Medal went to Bohuslav Diviš from Czechoslovakia. *IMO Website

1961 popularization of the term "Big Science" is usually attributed to an article by Alvin M. Weinberg, then director of Oak Ridge National Laboratory, published in Science #OTD

1967 Brazil (Scott #1053) issued a stamp to commemorate the 6th Brazilian Mathematical Congress. It depicted, in bright blue and black, a M¨obius strip—the first time that this famous shape has been shown on either stamp or coin. [Journal of Recreational Mathematics, 1(1968), 44] *VFR

In 1970, the Aswan High Dam in Egypt was completed after 18 years of work. It is a huge rockfill dam that lies just north of the border between Egypt and Sudan. It captures the world's longest river, the Nile, in the world's third largest reservoir, Lake Nasser. Built with Soviet aid at a cost of $1 billion, it now produces hydroelectricity meeting 50% of Egypt's power needs. It holds several years of irrigation reserves, assists multi-cropping, has increased productivity 20-50%, enormously increased Egypt's arable land, and overall, increased Egypt's agricultural income by 200%. The embankment is 111 metres high, with a width of near 1,000 metres. Lake Nasser is 480 long and up to 16 km wide. *TIS

In 1982, the first look at the Three Mile Island Unit 2 partial core meltdown was recorded by a mini-TV camera. This was the first inspection of the core made since the nuclear power plant in Harrisburg, Pennsylvania, first experienced a serious accident on 28 Mar 1979, due to a loss of water coolant. With the camera nothing was seen until five feet down - signifying that five feet of the core was gone. Many fuel rods had melted causing the tubes to break, spilling uranium to the bottom of the pressure vessel. Thus out of reach of the control rods, the uranium fission continued. Fifty percent of the core was destroyed or molten and an estimated twenty tons of uranium pellets had travelled to the bottom of the pressure vessel. *TIS

1990 Meteorologist Joe Rao was able to coerce American Trans-Air Airlines to alter the course of one of their regularly scheduled flights in order to be in the right position to experience the total phase of the July 22-21, 1990 total solar eclipse. The
eclipse began on Sunday, July 22, with the path of totality passing over Helsinki, Finland. The shadow path then moved across northernmost sections of Russia, then crossed the International Date Line, causing the eclipse date to change to Saturday, July 21.
The totality track swept southeast over Alaska's Aleutian Island chain, before reaching its end at a point midway between Honolulu, Hawaii and San Francisco, California. American Trans-Air Flight 403 normally flies from Hawaii to San Francisco on Saturday afternoons. A few weeks in advance of the eclipse, Rao informed the airline that by delaying the flight by 41 minutes out of Honolulu, that Flight 403 would likely be in position to catch the total phase. The airline agreed to make the attempt, allowing most of the 360 persons on board their Lockheed L-1011 jet the opportunity to witness totality. Rao, his wife Renate, and two friends, flew out of New York's JFK airport late on Friday night, July 20 . . . arrived in San Francisco early on Saturday morning for a few hours of sleep, before boarding ATA Flight 402 to Hawaii. They were in Honolulu for 45 minutes before turning around and heading back for San Francisco (encountering the eclipse along the way). After spending the night in San Francisco, they returned to New York the next day, having traveled over 11,000 miles in 46 hours just to see 73 seconds of a total eclipse!*NSEC

1620 Jean Picard (July 21, 1620 – July 12, 1682) Astronomer, born La Flêche, France. Picard is regarded as the founder of modern astronomy in France. He introduced new methods, improved the old instruments, and added new devices, such as Huygens' pendulum clock to record times and time intervals. Jean Picard was the first to put the telescope to use for the accurate measurement of small angles, making use of Gascoigne's micrometer. His most important work was the first measurement of the circumference of the earth. He used the method of Eratosthenes, but with greater accuracy. The concept behind neon signs began in 1675, when astronomer Jean Picard observed a glow in a barometer.*TIS (Dates of Birth and death are only 9 days apart)

1810 Henri-Victor Regnault (21 July 1810 – 19 January 1878) French chemist and physicist noted for his work on the properties of gases. His invaluable work was done as a skilful, thorough, patient experimenter in determining the specific heat of solids, liquids, gases, and the vapour-tensions of water and other volatile liquids, as well as their latent heat at different temperatures. He corrected Mariotte's law of gases concerning the variation of the density with the pressure, determined the coefficients of expansion of air and other gases, devised new methods of investigation and invented accurate instruments. Two laws governing the specific heat of gases are named after him.*TIS

1849 Robert Simpson Woodward (July 21, 1849–June 29, 1924) 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.
Professor Woodward carried on researches and published papers in many departments of astronomy, geodesy, and mechanics. In the course of his work with the United States Coast and Geodetic Survey he devised and constructed the "iced bar and long tape base apparatus," which enables a base line to be measured with greater accuracy and with less expense than by methods previously employed. His work on the composition and structure of the earth and the variation of latitude found expression in a number of valuable papers. *Wik (Calendar Dates of birth and death less than one month apart)

1861 Herbert Ellsworth Slaught born.(21 July 1861 in Seneca Lake, Watkins, New York, USA - 21 May 1937 in Chicago, Illinois, USA)*VFR During 1902-3 Slaught travelled in Europe attending lectures by the leading mathematicians. Perhaps he felt that he could never achieve the depth of research he was exposed to at this time for, after a worrying time of indecision, he decided that he was not cut out for a research career but could give most to the world of mathematics by concentrating on teaching.
After seeking Dickson's advice on the best way to serve the mathematical community, he accepted Dickson's suggesting of becoming co-editor of the American Mathematical Monthly. He also became active in the organisation of the Mathematical Association of America, the National Council of Teachers of Mathematics, and the Chicago section of the American Mathematical Society. He served as secretary of the last named Society from 1906 to 1916.
Bliss describes Slaught as:-... one of the men most widely known by teachers and students of mathematics... His lifelong devotion to... the promotion of the study of mathematics, his skill as a teacher, his effective leadership in the mathematical organizations which he sponsored, and his influence with teachers of mathematics the country over, were remarkable. *Wik

1880 Milan (Rastislav) Stefánik (July 21, 1880 – May 4, 1919) Slovakian astronomer and general who, with Tomás Masaryk and Edvard Benes, from abroad, helped found the new nation of Czechoslovakia by winning much-needed support from the Allied powers for its creation as a post-WWI republic, (1918-19). Before the war, the famous observatory in Meudon near Paris sent a scientific expedition to the 4810m high Mont Blanc. He joined the expedition, which was paid for by the French government to go to the roof of Europe.*TIS

1926 John Leech (July 21, 1926 in Weybridge, Surrey – 28 September 1992 in Scotland) is best known for the Leech lattice which is important in the theory of finite simple groups.*SAU  He also discovered Ta(3) in 1957. (In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways. The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, and was made famous in the early 20th century by a story involving Srinivasa Ramanujan.
\begin{matrix}\operatorname{Ta}(3)&=&87539319&=&167^3 &+& 436^3 \\&&&=&228^3 &+& 423^3 \\&&&=&255^3 &+& 414^3\end{matrix}

1725  Johann Philipp von Wurzelbau (28 September 1651 in Nürnberg; 21 July 1725 Nürnberg )was a German astronomer.
A native of Nuremberg, Wurzelbauer was a merchant who became an astronomer. As a youth, he was keenly interested in mathematics and astronomy but had been forced to earn his living as a merchant. He married twice: his first marriage was to Maria Magdalena Petz (1656–1713), his second to Sabina Dorothea Kress (1658–1733). Petz bore him six children.
He first published a work concerning his observations on the great comet of 1680, and initially began his work at a private castle-observatory on Spitzenberg 4 owned by Georg Christoph Eimmart (completely destroyed during World War II), the director of Nuremberg's painters' academy. Wurzelbauer was 64 when he began this second career, but proved himself to be an able assistant to Eimmart. A large quadrant from his days at Eimmart's observatory still survives.
After 1682, Wurzelbauer owned his own astronomical observatory and instruments, and observed the transit of Mercury, solar eclipses, and worked out the geographical latitude of his native city. After 1683, he had withdrawn himself completely from business life to dedicate himself to astronomy.
By 1700, Wurzelbauer had become the most well-known astronomer in Nuremberg. For his services to the field of astronomy, he was ennobled in 1692 by Leopold I, Holy Roman Emperor and added the von to his name. He was a member of the French and the Prussian academies of the sciences.
The crater Wurzelbauer on the Moon is named after him. *Wik

1873 Delfino Codazzi (March 7, 1824 – July 21, 1873) was an Italian mathematician who worked in differential geometry.*SAU He made some important contributions to the differential geometry of surfaces, such as the Gauss–Codazzi–Mainardi equations. *Wik

1925 Giovanni Frattini (January 8, 1852 Rome – July 21, 1925, Rome) was an Italian mathematician, noted for his contributions to group theory.  In 1885 he published a paper where he defined a certain subgroup of a finite group. This subgroup, now known as the Frattini subgroup, is the subgroup Φ(G) generated by all the non-generators of the group G. He showed that Φ(G) is nilpotent and, in so doing, developed a method of proof known today as Frattini's argument.*TIS
He entered the University of Rome in 1869, where he studied mathematics with Giuseppe Battaglini, Eugenio Beltrami, and Luigi Cremona, obtaining his PhD. in 1875.*Wik

1926 Washington Roebling U.S. civil engineer under whose direction the Brooklyn Bridge, New York City, was completed in 1883. The bridge was designed by Roebling with his father, John Augustus Roebling, from whom he had gained experience building wire-rope suspension bridges. Upon his father's death, he superintended the building of the Brooklyn Bridge (1869-83). He was disabled by decompression sickness after entering a caisson in 1872. He was brought out nearly insensible and his life was saved with difficulty. Because of resulting poor health, he directed operations from his home in Brooklyn overlooking the site. Though he continued to head the family's wire-rope manufacturing business for several years, medical problems forced retirement (1888).

1937 Edwin Bailey Elliott (1 June 1851, Oxford, England - 21 July 1937 in Oxford, England)After outstanding achievements at university, Elliott became a Fellow and Mathematical Tutor of Queen's College, Oxford, in 1874.
In addition to his Fellowship at Queen's College, Elliott was appointed a lecturer in mathematics at Corpus Christi College in Oxford in 1884. These appointments came to an end in 1892 when Elliott became the first Waynflete professor of Pure Mathematics. This chair was named after William of Waynflete, the English lord chancellor and bishop of Winchester who founded Magdalen College in the 15th century. The Waynflete chair came with a Fellowship at Magdalen College so Elliott was again attached to his old College. One year after being appointed to the Waynflete Chair of Pure Mathematics, Elliot married Charlotte Amelia Mawer.
Elliott held the Waynflete chair for 29 years until his retirement in 1921. During this time he was much involved with the London Mathematical Society, being President of the Society from 1896 to 1898. A few years before this, in 1891, he had been honoured by being elected a Fellow of the Royal Society. As Chaundy writes-
Elliott's mathematical life circulated round the twin foci of Oxford and London. Besides his work in formal teaching and lecturing at Oxford, he was one of the founders (1888) of the Oxford Mathematical Society, its first secretary, and later its president.
His mathematical work included algebra, algebraic geometry, synthetic geometry, elliptic functions and the theory of convergence. However his most important contribution was the book An introduction to the algebra of quantics which was first published in 1895. This work was a major contribution to invariant theory. *SAU

1966 Francesco Cantelli (20 December 1875, Palermo – 21 July 1966, Rome) was an Italian mathematician who made contributions to the theory of probability.*SAU  He was the founder of the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics.
His early papers were on problems in astronomy and celestial mechanics.
The later work was all on probability and it is in this field where his name graces the Borel–Cantelli lemma and the Glivenko–Cantelli theorem.  *Wik

1966 Philipp Frank (March 20, 1884, Vienna, Austria - July 21, 1966, Cambridge, Massachusetts, USA) was a physicist, mathematician and also an influential philosopher during the first half of the 20th century. He was a logical-positivist, and a member of the Vienna Circle.He was born on 20 March 1884 in Vienna, Austria, and died on 21 July 1966 in Cambridge, Massachusetts, USA. He studied physics at the University of Vienna and graduated in 1907 with a thesis in theoretical physics under the supervision of Ludwig Boltzmann. Albert Einstein recommended him as his successor for a professorship at the German Charles-Ferdinand University of Prague, a position which he held from 1912 until 1938. He then emigrated to the United States, where he became a lecturer of physics and mathematics at Harvard University.
Astronomer Halton Arp described Frank's Philosophy of Science class at Harvard as being his favorite elective.
He was a colleague and admirer of both Mach and Einstein. In lectures given during World War II at Harvard, Frank attributed to Mach himself the following graphic expression of "Mach's Principle":"When the subway jerks, it's the fixed stars that throw you down."
In commenting on this formulation of the principle, Frank pointed out that Mach chose the subway for his example because it shows that inertial effects are not shielded (by the mass of the earth): The action of distant masses on the subway-rider's mass is direct and instantaneous. It is apparent why Mach's Principle, stated in this fashion, does not fit with Einstein's conception of the retardation of all distant action.*Wik

1971 Yrjo Vaisala (6 September 1891 – 21 July 1971) Finnish meteorologist and astronomer regarded as the "father of space research in Finland," As early as 1946, he had suggested that geodetic triangulation at that time being done with rockets or balloons with onboard flashes could better be accomplished by artificial satellites. By the next year he was talking about artificial satellites being used for solar system exploration. In the 1950's he founded Tuorla Observatory and went on to build a tunnel under the hill at Tuorla Observatory to enable making interference measurements to accurately define the length standard for geodesy. He was outstanding in his ability to produce excellent optics for telescopes. Vaisala, together with Liisa Oterman at Tuorla, outpaced the rest of the world in their discovery of minor planets*TIS

1993 Edwin James George Pitman was born in Melbourne on 29 October 1897 and died at Kingston near Hobart on 21 July 1993.
In 1920 he completed the degree course and graduated B.A. (1921), B.Sc. (1922) and M.A. (1923). In the meantime he was appointed Acting Professor of Mathematics at Canterbury College, University of New Zealand (1922-23). He returned to Australia when appointed Tutor in Mathematics and Physics at Trinity and Ormond Colleges and Part-time Lecturer in Physics at the University of Melbourne (1924-25). In 1926 Pitman was appointed Professor of Mathematics at the University of Tasmania, a position he held until his retirement in 1962.
Pitman described himself as 'a mathematician who strayed into Statistics'; nevertheless, his contributions to statistical and probability theory were substantial.
Pitman was active in the formation of the Australian Mathematical Society in 1956. He also took an active part in the Summer Research Institutes organized by the Mathematical Society, and used them as a sounding board for his research on statistical inference.
He was a renowned member of the Statistical Society of Australia, attending its biennial conferences. In 1978 the Statistical society established the Pitman Medal.
Pitman presented the first systematic account of non-parametric inference and lectured extensively on the subject, both in Australia and in the United States. The kernel of the subject, as described by him, is 'Suppose that the sum of two samples A, B is the sample C. Then A, B are discordant if A is an unlikely sample from C.' Again, he writes, 'The approach to the subject, starting from the sample and working towards the population instead of the reverse, may be a bit of a novelty'; and later, 'the essential point of the method is that we do not have to worry about the populations which we do not know, but only about the sample values which we do know'.
The notes of the 'Lectures on Non-parametric Inference' given in the United States, though never published, have been widely circulated and have had a major impact on the development of the subject. Among the new concepts introduced in these Lectures are asymptotic power, efficacy, and asymptotic relative efficiency.
A major contribution to probability theory is his elegant treatment of the behavior of the characteristic function in the neighborhood of the origin, in three papers. This governs such properties as the existence of moments. There are also interesting properties of the Cauchy distribution, and of subexponential distributions.
On his death, on 21 July 1993, Edwin was buried at the Hobart Regional Cemetery in Kingston. He lives on in the memory of many of us who are grateful for his life and legacy.
*Evan J. Williams, Australian Academy of Science

1998 Alan (Bartlett) Shepard, Jr. (November 18, 1923 – July 21, 1998) was America's first man in space and one of only 12 humans who walked on the Moon. Named as one of the nation's original seven Mercury astronauts in 1959, Shepard became the first American into space on 5 May 1961, riding a Redstone rocket on a 15-minute suborbital flight that took him and his Freedom 7 Mercury capsule 115 miles in altitude and 302 miles downrange from Cape Canaveral, FL. (His flight came three weeks after the launch of Soviet cosmonaut Yuri Gagarin, who on 12 Apr 1961, became the first human space traveler on a one-orbit flight lasting 108 minutes.) Although the flight of Freedom 7 was brief, it was a major step for the U.S. in a race with the USSR.*TIS

2011 Franz Leopold Alt (November 30, 1910 – July 21, 2011) was an Austrian-born American mathematician who made major contributions to computer science in its early days. He was best known as one of the founders of the Association for Computing Machinery, and served as its president from 1950 to 1952. *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

Thursday, 20 July 2017

On This Day in Math - July 20

The greatest discoveries of science have always been
those that forced us to rethink our beliefs
about the universe and our place in it.

-Robert L. Park

The 201st day of the year; 201 is a harshad number... A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997. (Can you find the string of three consecutive Harshad numbers smaller than 201?)

201 is also a lucky number, a number that survives from the sieve process created about 1955 by Stanislaw Ulam, the great Polish mathematician who coinvented the H-bomb and was the father of cellular automata theory. Students who are familiar with the way the Sieve of Erathosthenes produces the primes may wish to compare the lucky numbers produced by this sieve. "Start wtih the odd numbers.The first odd number >1 is 3, so strike out every third number from the list (crossing out the 5, 11,17 etc): 1, 3, 7, 9, 13, 15, 19, .... The first odd number greater than 3 in the list is 7, so strike out every seventh number: 1, 3, 7, 9, 13, 15, 21, 25, 31, .... The numbers that remain are the so called "lucky numbers". Look for similarities to the primes. *Martin Gardner, Mathworld


1632 Pierre de Carcavi became a member of the parliament of Toulouse. His friendship with Fermat dates from this time.*VFR

1714 Just twelve days before her death, Queen Anne signs "An Act for Providing a Publick Reward for such Person or Persons as shall Discover the Longitude at Sea". *Derek Howse, Britain's Board of Longitude:the Finances 1714-1828

1795 James Woodhouse was elected professor of "Chymistry" at the University of Pennsylvania.
The American Chemist founded the Chemical Society of Philadelphia and authored numerous works on chemistry, including the first book of directed chemical experiments.*

1798 The Battle of the Pyramids during Napoleon’s Egyptian campaign. It is a myth that his troops damaged the Sphinx by using it for target practice. *VFR (I'm afraid it is a myth I have shared, sorry kids!)

The Meteor of 1860 by Frederic Church
1860 Great Meteor Procession of 1860 occurred on the evening of July 20. Unlike early morning meteors that are more frequent and run into the Earth head-on as it plows along in its orbit, evening meteors are rarer and have to approach the Earth from behind. In contrast, these often leave slow and stately trains as they move across the evening sky, struggling to keep up with the Earth. *David Dickinson, Universe Today

1925 Clarence Darrow calls William Jennings Bryan, counsel for the prosecution, to the stand as a witness for the defense in the Scopes Trial on the teaching of Evolution in Dayton, Tennessee, USA. Bryan testified to his literal interpretation of the Bible. He called the questioning a ridiculing of god. *Des Moines Register, July 21, 1925

1959 The first “International Mathematical Olympiad” began in Brasov, Romania. It lasted until 30 July and involved teams from seven Eastern Euroean countries. [The College Mathematics Journal, 16 (1985), p. 333] *VFR A comment from J. points out that the IMO site gives dates one day later for start and finish, "first IMO was organised between 21,July to 31,July." Thanks

1969 Neil Armstrong, now of Lebanon, OH, was the first man on the moon; Edwin Aldrin was a close second. Armstrong all but quoted what D. T. Whiteside wrote two years earlier about Isaac Newton: “May this present edition be a small step towards that long-overdue monument to a man who in so many areas of human thought himself took a giant’s leap.” See The Mathematical Papers of Isaac Newton, I, xxxvi and VIII, xxix. *VFR In 1969, Apollo XI astronauts Neil Armstrong and Edwin "Buzz" Aldrin became the first men to walk on the moon, after their lunar module separated from the command module and landed on the lunar surface at 09:18 GMT/4:18 EDT on the Sea of Tranquillity. Neil Armstrong and Edwin Aldrin establish Tranquility Base while Michael Collins orbited above. Armstrong stepped on the lunar surface at 10:56 ET and proclaimed, "That's one small step for a man, one giant leap for mankind." Internationally, nearly 700 million television viewers witnessed the event live as it happened.*TIS

1969 The mineral armalcolite was found on the moon, before it was known to exist on the earth. Named for the first letters of the Apollo 11 astronauts who found it, ARMstrong, COLlins, and ALDrin, the mineral was later found in Montana, South Africa, Greenland, and the Ukraine. *FFF pg 220

1805 Ormbsy MacKnight Mitchel (July 20, 1805 – October 30, 1862) American astronomer and major general in the American Civil War.
A multi-talented man, he was also an attorney, surveyor, and publisher. He is notable for publishing the first magazine in the United States devoted to astronomy. Known in the Union Army as "Old Stars", he is best known for ordering the raid that became famous as the Great Locomotive Chase during the Civil War. He was a classmate of Robert E. Lee and Joseph E. Johnston at West Point where he stayed as assistant professor of mathematics for three years after graduation.
The U.S. communities of Mitchell, Indiana, Mitchelville, South Carolina, and Fort Mitchell, Kentucky were named for him. A persistently bright region near the Mars south pole that was first observed by Mitchel in 1846 is also named in his honor. *TIA

1806 Alexander (Dallas) Bache (July 19, 1806 – February 17, 1867) was Ben Franklin's great grandson. A West Point trained physicist, Bache became the second Superintendent of the Coast Survey (1844-65). He made an ingenious estimate of ocean depth in 1856. He studied records of a tidal wave that had taken 12 hours to cross the Pacific. Knowing that wave speeds depend on depth, he calculated a 2 1/5-mile average depth for the Pacific (within 15% of the right value). Bache created the National Academy of Sciences, securing greater government involvement in science. Through the Franklin Institute he instituted boiler tests to promote safety for steamboats.*TIS

1873 Alberto Santos-Dumont (July 20, 1873 – July 23, 1932) was a Brazilian aviation pioneer, deemed the Father of Aviation by his countrymen. At the age of 18, Santos-Dumont was sent by his father to Paris where he devoted his time to the study of chemistry, physics, astronomy and mechanics. His first spherical balloon made its first ascension in Paris on 4 July 1898. He developed steering capabilities, and in his sixth dirigible on 19 Oct 1901 won the "Deutsch Prize," awarded to the balloonist who circumnavigated the Eiffel Tower. He turned to heavier-than-air flight, and on 12 Nov 1906 his 14-BIS airplane flew a distance of 220 meters, height of 6 m. and speed of 37 km/h. to win the "Archdecon Prize." In 1909, he produced his famous "Demoiselle" or "Grasshopper" monoplanes, the forerunners of the modern light plane. *TIS

1894 Georges Henri Joseph Édouard Lemaître (17 July 1894 – 20 June 1966) was a Belgian priest, astronomer and professor of physics at the Catholic University of Leuven. He proposed the theory of the expansion of the universe, widely misattributed to Edwin Hubble. He was the first to derive what is now known as Hubble's law and made the first estimation of what is now called the Hubble constant, which he published in 1927, two years before Hubble's article. Lemaître also proposed what became known as the Big Bang theory of the origin of the universe, which he called his "hypothesis of the primeval atom" or the "Cosmic Egg" *Wik

1894 Errett Lobban Cord (20 July 1894 – 2 January 1974) U.S. automobile manufacturer, advocate of front-wheel-drive vehicles. Cord, still in his twenties when he arrived at the Auburn Automobile Company, had a talent for seeking and hiring young, innovative minds, full of drive and ambition. Cord was a brilliant, complex industrialist who helped personal and public transportation come of age. He is best known today for Auburn, Cord and Duesenberg automobiles, Cord's greatest talent may have been his unparalleled ability to construct an automotive empire durable enough to thrive during the darkest years of the Great Depression. Photo: 1929 Cord L-29 Sedan, America's first front-drive production car. Built by the Auburn Automobile Company, Auburn, Indiana. *TIS

1924 Robert D. Maurer (born July 20, 1924, ) was born. Maurer is an American physicist who co-invented the optical fiber with Donald Keck and Peter Schultz . Optical fiber is a fiber made of glass or plastic that can carry light along its length. They are used in telecommunications and information technology or even illumination. They work as a waveguide because the core keeps the light by total internal reflection. The light bounces off the edges and is reflected back into the fiber without any loss out the side.*Today in History

1947 Gerd Binnig (20 July 1947, ) German-born physicist who co-invented the scanning tunneling microscope with Heinrich Rohrer. They shared the 1986 Nobel Prize for Physics with Ernst Ruska, who designed the first electron microscope. This instrument is not a true microscope ( i.e. an instrument that gives a direct image of an object) since it is based on the principle that the structure of a surface can be studied using a stylus that scans the surface at a fixed distance from it. Vertical adjustment of the stylus is controlled by means of what is termed the tunnel effect - hence the name of the instrument.*TIS

1819 John Playfair (10 March 1748 – 20 July 1819) Scottish mathematician, physicist, and geologist who is remembered for his axiom that two intersecting straight lines cannot both be parallel to a third straight line. His Illustrations of the Huttonian Theory of the Earth (1802) gave strong support to James Hutton's principle of uniformitarianism, essential to a proper understanding of geology. Playfair was the first scientist to recognise that a river cuts its own valley, and he cited British examples of the gradual, fluvial origins of valleys, to challenge the catastrophic theory (based on the Biblical Flood in Genesis) that was still widely accepted. He was also the first to link the relocation of loose rocks to the movement of glaciers. Playfair published texts on geometry, physics, and astronomy. *TIS

1866 Georg Friedrich Bernhard Riemann died in Bolzano, Italy, at age 39 (September 17, 1826 – July 20, 1866). The inscription on his tombstone (translated from the German) reads: “All things work together for good to them that love the Lord.” *VFR Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics.
Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier series—a first step in generalized function theory—and studied the Riemann–Liouville differintegral.
He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he introduced the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.
He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities.*Wik

1937 Guglielmo Marconi (25 April 1874 – 20 July 1937)Italian inventor, born in Bologna. He was a physicist, who invented the wireless telegraph in 1935 known today as radio. Nobel laureate (1909). In 1894, Marconi began experimenting on the "Hertzian Waves" (the radio waves Hertz first produced in his laboratory a few years earlier). Lacking support from the Italian Ministry of Posts and Telegraphs, Marconi turned to the British Post Office. Encouraging demonstrations in London and on Salisbury Plain followed. Marconi obtained the world's first patent for a system of wireless telegraphy, in 1897, and opened the world's first radio factory at Chelmsford, England in 1898. In 1900 he took out his famous patent No. 7777 for "tuned or syntonic telegraphy."*TIS

1922 Andrey Andreyevich Markov (14 June 1856 N.S. – 20 July 1922) Russian mathematician who helped to develop the theory of stochastic processes, especially those called Markov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors. (For example, the probability of winning at the game of Monopoly can be determined using Markov chains.) His work based on the study of the probability of mutually dependent events has been developed and widely applied to the biological and social sciences.*TIS - Simple Markov chain problem for students, The probability of Events A, B and C are 1/2, 1/3, and 1/6 respectively.  If one of these events occurs on each trial, what is the probability that it takes six or less trials to get all three outcomes?

1997 Eric Charles Milner, FRSC (May 17, 1928–July 20, 1997) was a mathematician who worked mainly in combinatorial set theory.
A former London street urchin, Milner attended King's College London starting in 1946, where he competed as a featherweight boxer. He graduated in 1949 as the best mathematics student in his year, and received a masters degree in 1950 under the supervision of Richard Rado and Charles Coulson. Partial deafness prevented him from joining the Navy, and instead, in 1951, he took a position with the Straits Trading Company in Singapore assaying tin. Soon thereafter he joined the mathematics faculty at the University of Malaya in Singapore, where Alexander Oppenheim and Richard K. Guy were already working. In 1958, Milner took a sabbatical at the University of Reading, and in 1961 he took a lecturership there and began his doctoral studies; he obtained a Ph.D. from the University of London in 1963. He joined his former Singapore colleagues Guy and Peter Lancaster as a professor at the University of Calgary in 1967, where he was head of the mathematics department from 1976 to 1980. In 1973, he became Canadian citizen, and in 1976 he became a fellow of the Royal Society of Canada.
In 1954, while in Singapore, Milner married Esther Stella (Estelle) Lawton, whom he had known as a London student; they had four children. Estelle died of cancer in 1975, and in 1979 Milner remarried Elizabeth Forsyth Borthwick, with whom he had another son.
Milner's interest in set theory was sparked by visits of Paul Erdős to Singapore and by meeting András Hajnal while on sabbatical in Reading. He generalized Chang's ordinal partition theorem for arbitrary finite k. He is also known for the Milner–Rado paradox. *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

Wednesday, 19 July 2017

On This Day in Math - July 19

[The infinitesimals] neither have nor can have theory; in practise it is a dangerous instrument in the hands of beginners ... anticipating, for my part, the judgement of posterity, I would predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.
~Francois Servois

The 200th day of the year; 200 is the smallest unprimeable number - it can not be turned into a prime number by changing just one of its digits to any other digit. (What would be the next one? What is the smallest odd unprimeable number?)
Sum of first 200 primes divides product of first 200 primes. (How often is this property true of integers?) *Math Year-Round ‏@MathYearRound

418 First report of a comet discovered during a solar eclipse, seen by the historian Philostorgius in Asia Minor. Many chronicles do mention this observation (12 western, 3 Byzantine). Philostorgius mentions that the sun was eclipsed at the 8th hour of the day. In his sketch there is a comet. This Total Solar Eclipse was from the Caribbean, Bay of Bengal, north Spain, central Italy, little Asia and ends in the north of India. *NSEC

1595 “God in creating the universe and regulating the order of the cosmos had in view the five regular bodies of geometry as known since the days of Pythagoras and Plato.” So did Kepler record his discovery that the universe was based on the Platonic solids, a conjecture he published in 1596. *VFR "as I was showing in my class how the great conjunctions [of Saturn and Jupiter] occur successively eight zodiacal signs later, and how they gradually pass from one trine to another, that I inscribed within a circle many triangles, or quasi-triangles such that the end of one was the beginning of the next. In this manner a smaller circle was outlined by the points where the line of the triangles crossed each other.
The proportion between the circles struck Kepler’s eye as almost identical with that between Saturn and Jupiter, and he immediately initiated a vain search for similar geometrical relations.
And then again it struck me: why have plane figures among three-dimensional orbits? Behold, reader, the invention and whole substance of this little book! In memory of the event, I am writing down for you the sentence in the words from that moment of conception: The earth’s orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing this will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe within the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of planets.
Kepler of course based his argument on the fact that there are five and only five regular polyhedrons. *

1676 Flamsteed began living at the Observatory with his two servants on July 10. On 19 July, his long series of Greenwich observations began? *Rebekah Higgitt, Teleskopos

1799 The Rosetta stone was found by Napoleon’s troops in the Nile delta. It attracted the interest of the learned men with Napoleon, which included several mathematicians, and copies were circulated to scholars. The text is in Greek, hieroglyphics and demotic Egyptian scripts and was deciphered by Thomas Young and Fran¸cois Champollion. The cartouches on the stone, which contained royal names, were the key to decipherment. It is now a prized possession of the British Museum.*VFR

1819 Poisson submitted a paper on the solution of the wave equation. He used the method of power series, but the techniques advocated by Cauchy and Fourier using complex variables and “Fourier analysis” won out. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, pp. 682, 687ff, 1393] *VFR

1895 George Cantor, first uses Aleph-null in a letter to Felix Klein. Prior to this he had use aleph-one for the first infinite cardinal. The first part of his Bietrage was already in print, so his letter to Klein is added, almost verbatim, to explain the changes with the publication date still showing March of that year. *From the Calculus to Set Theory, 1630-1910: An Introductory History, By I. Grattan-Guinness

1983 The first three-dimensional reconstruction of a human head via computed tomography (CT) is published. Michael W. Vannier (Mallinckrodt Institute of Radiology, St. Louis) and his co-workers J. Marsh (Cleft Palate and Craniofacial Deformities Institute, St. Louis Children's Hospital) and J. Warren (McDonnell Aircraft Company) published the first three-dimensional reconstruction of single computed tomography (CT) slices of the human head. Computer-aided aircraft design techniques were adapted to make the cranial imaging possible. Since then, CT imaging has become a cornerstone of the medical profession.*CHM

1767 Francois-Joseph Servois born (19 July 1768 in Mont-de-Laval (N of Morteau), Doubs, France - 17 April 1847 in Mont-de-Laval, Doubs, France). He worked in projective geometry, functional equations and complex numbers. He introduced the word pole in projective geometry. He also came close to discovering the quaternions before Hamilton.
Servois introduced the terms "commutative" and "distributive" in a paper describing properties of operators, and he also gave some examples of noncommutativity. Although he does not use the concept of a ring explicitly, he does verify that linear commutative operators satisfy the ring axioms. In doing so he showed why operators could be manipulated like algebraic magnitudes. This work initiates the algebraic theory of operators.
Servois was critical of Argand's geometric interpretation of the complex numbers. He wrote to Gergonne telling him so in November 1813 and Gergonne published the letter in the Annales de mathématiques in January 1814. Servois wrote:- I confess that I do not yet see in this notation anything but a geometric mask applied to analytic forms the direct use of which seems to me simple and more expeditious.
Considered as a leading expert by many mathematicians of his day, he was consulted on many occasions by Poncelet while he was writing his book on projective geometry Traité des propriétés projective. *SAU

1817 Charles Auguste Briot (July 19, 1817 - September 20, 1882) undertook research on analysis, heat, light and electricity. His first major work on analysis was Recherches sur la théorie des fonctions which he published in the Journal of the École Polytechnique in 1859, and he also published this work as a treatise in the same year. His researches on heat, light and electricity was all based on his theories of the aether. He was strongly influenced in developing these theories by Louis Pasteur, the famous chemist. Of course Pasteur was a great scientist, but Briot had an additional reason to hold him in high esteem for, like himself and his friend Bouquet, Pasteur was brought up in the Doubs region of France.
In 1859 Briot and Bouquet published their important two volume treatise on doubly periodic functions. They published another joint effort in 1875 when their treatise on elliptic functions appeared. In this same year they published a second edition to their two volume work of 1859. In 1879 Briot, this time in a single author work, produced his treatise on abelian functions. The physical motivation for the mathematical theories which gave rise to this work in analysis was published by Briot in 1864 when he published his work on light, Essai sur la théorie mathématique de la lumière and five years later when he published his work on heat, Théorie mécanique de la chaleur.
We noted above that Briot was a dedicated teacher and as such he wrote a great number of textbooks for his students. This was certainly a tradition in France at this time and it was natural for a teacher of Briot's quality to write up his courses as textbooks. He wrote textbooks which covered most of the topics from a mathematics course: arithmetic, algebra, calculus, geometry, analytic geometry, and mechanics. For his outstanding contributions to mathematics the Académie des Sciences in Paris awarded Briot their Poncelet Prize in 1882 shortly before he died. *SAU

1846 Edward Charles Pickering, (July 19, 1846–February 3, 1919)was born Boston, Mass., U.S. physicist and astronomer. After graduating from Harvard, he taught physics for ten years at MIT where he built the first instructional physics laboratory in the United States. At age 30, he directed the Harvard College Observatory for 42 years. His observations were assisted by a staff of women, including Annie Jump Cannon. He introduced the use of the meridian photometer to measure the magnitude of stars, and established the Harvard Photometry (1884), the first great photometric catalog. By establishing a station in Peru (1891) to make the southern photographs, he published the first all-sky photographic map (1903).*TIS

1894 Aleksandr Yakovlevich Khinchin July 19, 1894 – November 18, 1959) was a Russian mathematician who contributed to many fields including number theory and probability.Khinchin's book Mathematical Foundations of Information Theory, translated into English from the original Russian in 1957, is important. It consists of English translations of two articles: The entropy concept in probability theory and On the basic theorems of information theory which were both published earlier in Russian. The second of these articles provides a refinement of Shannon's concepts of the capacity of a noisy channel and the entropy of a source. Khinchin generalised some of Shannon's results in this book which was written in an elementary style yet gave a comprehensive account with full details of all the results.*SAU

1913 Mary Cannell (19 July 1913 in Liverpool, England - 18 April 2000) It was the work which she undertook after she retired which earns her a place as a highly respected historian of mathematics. Her work stemmed from the fact that George Green had worked as a miller near Nottingham. Green was a mathematician who was well known to almost all students of mathematics around the world, yet little was known of his life. Flauvel writes:- ... widespread knowledge of Green himself dates only from the 1970s when Cannell and other Nottingham colleagues worked to restore his windmill and his memory...When I first visited Green's windmill in Nottingham the booklet which I purchased was George Green Miller and Mathematician written in 1988 by Mary Cannell. She produced a major biography of Green, George Green : Mathematician and Physicist 1793-1841 : The Background to His Life and Work in 1993. In addition she wrote research articles on Green's life and work bringing to the world of mathematics an understanding of Green's remarkable life.
Flauvel writes:- She charmed audiences on several continents, promoting interest in Green and early 19th-century mathematical physics, in the clear tones and pure vowels of pre-war English, somewhere between Miss Marple and Dame Peggy Ashcroft. ... Mary Cannell was working on projects of one sort or another - the Green website, the revised edition of the biography, research papers, the catalogue in the university of Nottingham library - right to the end, in days filled with her characteristic energy and enthusiasm. *SAU

1878 Egor Ivanovich Zolotarev (March 31, 1847, Saint Petersburg – July 19, 1878, Saint Petersburg) produced fundamental work on analysis and number theory. *SAU

1947 John Clark graduated from Edinburgh University and became a teacher at George Heriot's School in Edinburgh. He went on to become Rector of this school. He became Secretary of the EMS in 1891 and President in 1897. *SAU

Hugh Everett III (November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.
Discouraged by the scorn of other physicists for MWI, Everett ended his physics career after completing his Ph.D. Afterwards, he developed the use of generalized Lagrange multipliers for operations research and applied this commercially as a defense analyst and a consultant. He was married to Nancy Everett née Gore. They had two children: Elizabeth Everett and Mark Oliver Everett, who became frontman of the musical band Eels.

1992 Allen Newell (March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *Wik

*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

Tuesday, 18 July 2017

On This Day in Math - July 18

Math is the only place where truth and beauty mean the same thing.

-Danica McKellar

(I can't believe I'm doing math quotes by "Winnie" from Wonder Years)
The 199th day of the year; 199 is prime (in fact, all three permutations of the number are prime) and is the sum of three consecutive primes: 61 + 67 + 71, and of five consecutive primes: 31 + 37 + 41 + 43 + 47. (Suddenly struck me I don't know what is the smallest prime that is the sum of consecutive primes in more than one way!)

199 is the smallest number with an additive persistence of 3. (iterate the sum of the digits. The number of additions required to obtain a single digit from a number n is called the additive persistence of n, and the digit obtained is called the digital root of n. ) 1+9+9 =19, 1+9=10, 1+0 = 1. so the additive persistence is 3 and the digital root is 1.

I like "almost constants". For the 199th day, \( ( \frac{\sqrt{5} +1}{2})^{11}= 199.0050249987406414902082… \)

1860 July 18, 1860 First wet plate photographs of an eclipse; they require 1/30 of the exposure time of a daguerreotype. *NSEC

1872 Weierstrass, in a lecture to the Berlin Academy, gave his classical example of a continuous nowhere differentiable function. See Big Kline, p. 956.*VFR

1898 Marie and Pierre Curie discover the previously unknown element Polonium which she named for her home country, Poland. *Brody & Brody, The Science Class You Wished You Had

1979 Great Britain issued a stamp honoring Alice’s Adventures in Wonderland. *VFR

1962 Hearings on Mercury 13 Women suspended. The first potential US women in space, often called the Mercury 13 in comparison to the original Mercury 7 astronauts, had a hearing in congress beginning July 17th. The house convened public hearings before a special Subcommittee on Science and Astronautics. Significantly, the hearings investigated the possibility of gender discrimination two full years before the Civil Rights Act of 1964 made that illegal, making these hearings a marker of how ideas about women's rights permeated political discourse even before they were enshrined in law. The hearings would abruptly be terminated at lunch on the 18th. In less than a year, Soviet cosmonaut Valentina Tereshkova became the first woman in space on June 16, 1963. In response, Clare Boothe Luce published an article in Life criticizing NASA and American decision makers. By including photographs of all thirteen Lovelace finalists, she made the names of all thirteen women public for the first time. (The Time issue is available at Google Books here. Astronaut Sally Ride became the first American woman in space in 1983 on STS-7. *Wik

2014 first "Sun-spotless day" on the Earthward side of sun since 2011, *David Dickinson ‏@Astroguyz


1013 Hermann of Reichenau (July 18, 1013 – September 24, 1054), was a German mathematician who was important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe.*SAU

1635 Robert Hooke ( 18 July[NS 28 July] 1635 – 3 March 1703) born.English natural philosopher, architect and polymath. His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but eventually becoming ill and party to jealous intellectual disputes. These issues may have contributed to his relative historical obscurity.
He was at one time simultaneously the curator of experiments of the Royal Society and a member of its council, Gresham Professor of Geometry and a Surveyor to the City of London after the Great Fire of London , in which capacity he appears to have performed more than half of all the surveys after the fire. He was also an important architect of his time, though few of his buildings now survive and some of those are generally misattributed, and was instrumental in devising a set of planning controls for London whose influence remains today. Allan Chapman has characterised him as "England's Leonardo" *wik
He was born in Freshwater, Isle of Wight, and discovered the law of elasticity, known as Hooke's law, and invented the balance spring for clocks. He was a virtuoso scientist whose scope of research ranged widely, including physics, astronomy, chemistry, biology, geology, architecture and naval technology. On 5 Nov 1662, Hooke was appointed the Curator of Experiments at the Royal Society, London. After the Great Fire of London (1666), he served as Chief Surveyor and helped rebuild the city. He also invented or improved meteorological instruments such as the barometer, anemometer, and hygrometer. Hooke authored the influential Micrographia (1665)*TIS

1689 Samuel Molyneux (16 July 1689 – 13 April 1728), British astronomer (Royal Observatory at Kew) and politician. Together with assistant James Bradley, he made measurements of abberation - the diversion of light from stars. They made observations of the star  Draconis with a vertical telescope. Starting in 1725 they had the proof of the movement of the earth giving support to the Copernican model of the earth revolving around the sun. The star oscillated with an excursion of 39 arcsecs between its lowest declination in May and its the highest point of its oscillation in September. He was unfortunate to fall ill in 1728 and into the care of the Anatomist to the Royal Family, Dr Nathaniel St Andre, whose qualifications were as a dancing master. Molyneux died shortly thereafter.*TIS

1768 Jean Robert Argand born (July 18, 1768 – August 13, 1822). His single original contribution to mathematics was the invention and elaboration of a geometric representation of complex numbers and operations on them. In this he was preceded by Wessel and followed by Gauss.*VFR Swiss mathematician who was one of the earliest to use complex numbers, which he applied to show that all algebraic equations have roots. He invented the Argand diagram - a geometrical representation of complex numbers as a point with the real portion of the number on the x axis and the imaginary part on the y axis.*Wik

1813 Pierre Laurent (July 18, 1813 – September 2, 1854) was a French mathematician best-known for his study of the so-called Laurent Series in Complex analysis. *SAU

1853 Antoon Lorentz (18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the transformation equations subsequently used by Albert Einstein to describe space and time. *Wik
Lorentz is best known for his work on electromagnetic radiation and the FitzGerald-Lorentz contraction. He developed the mathematical theory of the electron.*SAU

1856 Giacinto Morera (Novara, 18 July 1856 – Turin, 8 February 1909), was an Italian engineer and mathematician. He is remembered for Morera's theorem in the theory of functions of a complex variables and for his work in the theory of linear elasticity. *Wik

1899 Robert Schlapp (18 July 1899 in Edinburgh, Scotland - 31 May 1991 in Ashford, Kent, England)studied at Edinburgh and Cambridge universities. He spent his whole career at Edinburgh University teaching mathematics and Physics. He was also interested in the History of Mathematics. He became President of the EMS in 1942 and 1943. *SAU

1922 Thomas S(amuel) Kuhn (July 18, 1922 – June 17, 1996) was an American historian of science, MIT professor, noted for The Structure of Scientific Revolutions (1962), one of the most influential works of history and philosophy written in the 20th century. His thesis was that science was not a steady, cumulative acquisition of knowledge, but it is "a series of peaceful interludes punctuated by intellectually violent revolutions." Then appears a Lavoisier or an Einstein, often a young scientist not indoctrinated in the accepted theories, to sweep the old paradigm away. Such revolutions, he said, came only after long periods of tradition-bound normal science. "Frameworks must be lived with and explored before they can be broken," *TIS This was the first modern use of the term "paradigm" in this way.


1650 Christoph Scheiner SJ (25 July 1573 (or 1575) – 18 July 1650) was a Jesuit priest, physicist and astronomer in Ingolstadt. In 1603, Scheiner invented the pantograph, an instrument which could duplicate plans and drawings to an adjustable scale. Later in life he would invent a sunspot viewing appartus. In 1611, Scheiner observed sunspots; in 1612 he published the "Apelles letters" in Augsburg. Marcus Welser had the first three Apelles letters printed in Augsburg on January 5, 1612. They provided one of many reasons for the subsequent unpleasant argument between Scheiner and Galileo Galilei. *Wik Thus, in 1614, Galileo found himself in an unresoved dispute over priority with a mean and determined Jesuit. The fight was to grow meaner in subsequent years. It would play a major role in Galileo's Inquisitional trial eighteen years later. *James Reston, Jr., Galileo: A Life

1742 Abraham Sharp (1653– 18 July 1742) was an English mathematician who worked with Flamsteed. He calculated π to 72 places (using an arcsine sequence, briefly holding the record until John Machin calculated 100 digits in 1706).*SAU

1807 Thomas Jones (23 June 1756 – 18 July 1807) was Head Tutor at Trinity College, Cambridge for twenty years and an outstanding teacher of mathematics. He is notable as a mentor of Adam Sedgwick.
He was born at Berriew, Montgomeryshire, in Wales. On completing his studies at Shrewsbury School, Jones was admitted to St John's College, Cambridge on 28 May 1774, as a 'pensioner' (i.e. a fee-paying student, as opposed to a scholar or sizar). He was believed to be an illegitimate son of Mr Owen Owen, of Tyncoed, and his housekeeper, who afterwards married a Mr Jones, of Traffin, County Kerry, Thomas then being brought up as his son.
On 27 June 1776, Jones migrated from St John's College to Trinity College. He became a scholar in 1777 and obtained his BA in 1779, winning the First Smith's Prize and becoming Senior Wrangler. In 1782, he obtained his MA and became a Fellow of Trinity College in 1781. He became a Junior Dean, 1787–1789 and a Tutor, 1787-1807. He was ordained a deacon at the Peterborough parish on 18 June 1780. Then he was ordained priest, at the Ely parish on 6 June 1784, canon of Fen Ditton, Cambridgeshire, in 1784, and then canon of Swaffham Prior, also 1784. On 11 December 1791, he preached before the University, at Great St Mary's, a sermon against duelling (from Exodus XX. 13), which was prompted by a duel that had lately taken place near Newmarket between Henry Applewhaite and Richard Ryecroft, undergraduates of Pembroke, in which the latter was fatally wounded. Jones died on 18 July 1807, in lodgings in Edgware Road, London. He is buried in the cemetery of Dulwich College. A bust and a memorial tablet are in the ante-chapel of Trinity College. *Wik

1930 Karl Emmanuel Robert Fricke (September 24, 1861 in Helmstedt, Germany ; July 18, 1930 in Bad Harzburg, Germany) was a German mathematician, known for his work in function theory, especially on elliptic, modular and automorphic functions. He was one of the main collaborators of Felix Klein, with whom he produced two classic two volume monographs on elliptic modular functions and automorphic functions.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Monday, 17 July 2017

On This Day in Math - July 17

Science is built up with facts, as a house is with stones. 
But a collection of facts is no more a science
than a heap of stones is a house.
~Henri Poincaré

The 198th day of the year; 198 is a Harshad number, divisible by the sum of its digits. A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997.
(Students might try to find a pair of consecutive numbers greater than 10 which are harshad numbers)

198 nines followed by a one is prime 9999...... 91.  *Derek Orr@Derektionary

198 is between the twin primes 197 and 199.  If you multiply 198 by its reversal, 891, you get 176,418 which is between the twin primes 176,417 and 176,419. Is there another example of this curiosity?

In 709 BC, the earliest record of a confirmed total solar eclipse was written in China. From: Ch'un-ch'iu, book I: "Duke Huan, 3rd year, 7th month, day jen-ch'en, the first day (of the month). The Sun was eclipsed and it was total." This is the earliest direct allusion to a complete obscuration of the Sun in any civilisation. The recorded date, when reduced to the Julian calendar, agrees exactly with that of a computed solar eclipse. Reference to the same eclipse appears in the Han-shu ('History of the Former Han Dynasty') (Chinese, 1st century AD): "...the eclipse threaded centrally through the Sun; above and below it was yellow." Earlier Chinese writings that refer to an eclipse do so without noting totality.*TIS

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.

1850 Vega became the first star (other than the Sun) to be photographed, when it was imaged by William Bond and John Adams Whipple at the Harvard College Observatory. The photo was a daguerreotype. *Wik

1879 It was announced in Nature that Kempe had proved the four-color conjecture. A correct proof, based on Kempe’s ideas, had to wait another century. [N. L. Biggs, et al., Graph Theory 1736–1936, p. 94] *VFR

1935 The first problem was entered into the Scottish Book, a large bound notebook that Stefan Banach brought to the Scottish Cafe in LLw´ow for mathematicians to record research problems. Many of the problems offered prizes to the solver. They ranged from “2 small beers” to “100 grammes of caviar.” This book has been translated into English and edited by R. D. Mauldin. (below) *VFR ..(A PDF file of the book is now available, thanks to a tip from Robin Whitty at )in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and
topology. Stanislaw Ulam recounts that the tables of the café had marble tops, so they could write in pencil, directly on the table, during their discussions. To keep the results from being lost, and after becoming annoyed with their writing directly on the table tops, Stefan Banach's wife provided the mathematicians with a large notebook, which was used for writing the problems and answers and eventually became known as the Scottish Book. The book—a collection of solved, unsolved, and even probably unsolvable problems—could be borrowed by any of the guests of the café. For problem 153, which was later recognized as being closely related to Stefan Banach 's "basis problem", Stanislaw Mazur offered the prize of a live goose. This problem was solved only in 1972 by Per Enflo, who was presented with the live goose in a ceremony that was broadcast throughout Poland.
The café building now houses the Universal Bank at the street address of 27 Taras Shevchenko Prospekt.*Wik

1962 The first potential US women in space, often called the Mercury 13 in comparison to the original Mercury 7 astronauts would get a hearing in congress beginning on this day. The house convened public hearings before a special Subcommittee on Science and Astronautics. Significantly, the hearings investigated the possibility of gender discrimination a two full years before the Civil Rights Act of 1964 made that illegal, making these hearings a marker of how ideas about women's rights permeated political discourse even before they were enshrined in law. The hearings would abruptly be terminated at lunch the next day. In less than a year, Soviet cosmonaut Valentina Tereshkova became the first woman in space on June 16, 1963. In response, Clare Boothe Luce published an article in Life criticizing NASA and American decision makers. By including photographs of all thirteen Lovelace finalists, she made the names of all thirteen women public for the first time. (The Time issue is available at Google Books here. Astronaut Sally Ride became the first American woman in space in 1983 on STS-7. *Wik

1969 New York Times Apologizes for ridicule of Robert H. Goddard. and his report, “A Method of Reaching Extreme Altitudes,” published by the Smithsonian press in 1920.
In a famously nasty 1920 editorial, The New York Times ridiculed his ideas about rocketry, declaring that his claim that a rocket could fly in the vacuum of space would “deny a fundamental law of dynamics, and only Dr. Einstein and his chosen dozen, so few and fit, are licensed to do that.”

(On July 17, 1969, as Apollo 11 was racing moonward, the Times published a gently self-mocking correction: “Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th Century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error.”)

1997 "You DON'T have mail"... A programming error temporarily threw the Internet into disarray in a preview of the difficulties that inevitably accompany a world dependent on e-mail, the World Wide Web, and other electronic communications.
At 2:30 a.m. Eastern Daylight Time, a computer operator in Virginia ignored alarms on the computer that updated Internet address information, leading to problems at several other computers with similar responsibilities. The corruption meant most Internet addresses could not be accessed, resulting in millions of unsent e-mail message. *This Day in History, Computer History Museum

2011 NASA's Dawn Spacecraft Enters Orbit Around Vesta
NASA's Dawn spacecraft on Saturday became the first probe ever to enter orbit around an object in the main asteroid belt between Mars and Jupiter. *NASA


1698 Pierre Louis de Maupertuis, (Saint-Malo, 17 July 1698 – Basel, 27 July 1759) developer of the principle of least action. *VFR a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Berlin Academy of Science, at the invitation of Frederick the Great.
Maupertuis made an expedition to Lapland to determine the shape of the earth. He is often credited with having invented the principle of least action; a version is known as Maupertuis' principle – an integral equation that determines the path followed by a physical system. His work in natural history has its interesting points, since he touched on aspects of heredity and the struggle for life.*Wik (he died in the home of Johann II Bernoulli, whose death occurred on this same date, (see Deaths)
John S. Wilkins‏@john_s_wilkins pointed out in a tweet that "Maupertuis was the first scientific evolutionist, 7 years after first edition of Systema Naturae."

1752 Barnaba Oriani (July 17 1752 - November 12 1832) Italian geodesist, astronomer and scientist. After getting his elementary education in Carignano, he went on to study at the College of San Alessandro in Milan, under the tutelage and with the support of the Order of Barnabus, which he later joined. After completing his studies in the humanities, physical and mathematical sciences, philosophy, and theology, he was ordained as a priest in 1775.
Oriani was a devoted friend of the Theatine monk, Giuseppe Piazzi, the discoverer of Ceres. Oriani and Piazzi worked together for thirty-seven years, cooperating on many astronomical observations.For his work in astronomy, Oriani was honored by naming asteroid (4540) "Oriani". This asteroid had been discovered at the Osservatorio San Vittore in Bologna, Italy on November 6, 1988. *TIA

1831 Victor Mayer Amédée Mannheim (17 July 1831 – 11 December 1906) was the inventor of the modern slide rule. Around 1850, he introduced a new scale system that used a runner to perform calculations. This type of slide rule became known under the name of its inventor: the Mannheim.*Wik

1837 Wilhelm Lexis (July 17, 1837, Eschweiler – October 25, 1914, Göttingen), studied data presented as a series over time thus initiating the study of time series.*SAU  Although the author of an Allgemeine Volkswirtschaftslehre (general economics book) (1910) and certainly a distinguished economist, even a pioneer of Law and Economics thinking and of the study of consumption and crises, Lexis is today primarily known as a statistician, partially due to his creation of the Lexis ratio. His reputation as a demographer is underlined by the ubiquity of Lexis Diagrams, which are named for him, although primary credit for their invention belongs to Gustav Zeuner and O. Brasche (a notable example of Stigler's law of eponymy). He is also one of the founding fathers of the interdisciplinary, professional study of insurance. A Kathedersozialist, he was closely affiliated with academic policy makers in Prussia and one of Friedrich Althoff’s experts and the editor of important works on German higher education, most famously the six-volume Das Unterrichtswesen im Deutschen Reich, compiled for the St. Louis World's Fair of that year and still the key reference work for that time. *Wik

1863 Herbert Richmond (17 July 1863 in Tottenham, Middlesex, England - 22 April 1948 in Cambridge, England) studied at Cambridge and spent his whole career there, His main interest was in Algebraic Geometry. He became an honorary member of the EMS in 1930.*SAU

1868 Peter Comrie (17 July 1868 in Muthill, near Crieff, Perthshire, Scotland
Died: 20 Dec 1944 in Edinburgh, Scotland) graduated from St Andrews and after a series of teaching posts became Rector of Leith Academy. He was much involved in the EMS, becoming Secretary in 1911 and President in 1916 and 1917.*SAU

1894 Georges Henri Joseph Édouard Lemaître (17 July 1894 – 20 June 1966) was a Belgian priest, astronomer and professor of physics at the Catholic University of Louvain. He was the first person to propose the theory of the expansion of the Universe, widely misattributed to Edwin Hubble.[1][2] He was also the first to derive what is now known as the Hubble's law and made the first estimation of what is now called the Hubble constant, which he published in 1927, two years before Hubble's article.[3][4][5][6] Lemaître also proposed what became known as the Big Bang theory of the origin of the Universe, which he called his 'hypothesis of the primeval atom' *Wik

1909 Geoffrey Walker (17 July 1909 - 31 March 2001) studied at Oxford and Edinburgh. He taught at Imperial College London, Liverpool and Sheffield before returning to Liverpool as Professor of Pure Mathematics. He worked on Differential Geometry, Relativity and Cosmology.*SAU Walker was an accomplished geometer, but he is best remembered today for two important contributions to general relativity. Together with H. P. Robertson, the well known Robertson-Walker metric for the Friedmann-Lemaître-Robertson-Walker cosmological models, which are exact solutions of the Einstein field equation. Together with Enrico Fermi, he introduced the notion of Fermi-Walker differentiation.*Wik

1920 Gordon Gould (July 17, 1920 – September 16, 2005) American physicist who coined the word "laser" from the initial letters of "Light Amplification by Stimulated Emission of Radiation." Gould was inspired from his youth to be an inventor, wishing to emulate Marconi, Bell, and Edison. He contributed to the WWII Manhattan Project, working on the separation of uranium isotopes. On 9 Nov 1957, during a sleepless Saturday night, he had the inventor's inspiration and began to write down the principles of what he called a laser in his notebook Although Charles Townes and Arthur Schawlow, also successfully developed the laser, eventually Gould gained his long-denied patent rights. *TIS

1975 Terence "Terry" Chi-Shen Tao FAA FRS (17 July 1975, Adelaide - ), is an Australian mathematician working in harmonic analysis, partial differential equations, additive combinatorics, ergodic Ramsey theory, random matrix theory, and analytic number theory. He currently holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. In August 2006, at the 25th International Congress of Mathematicians in Madrid, he became one of the youngest persons, the first Australian, and the first UCLA faculty member ever to be awarded a Fields Medal. *Wik


1790 Johann II Bernoulli died (28 May 1710 in Basel, Switzerland - 17 July 1790 in Basel, Switzerland) Johann II Bernoulli (also known as Jean), the youngest of the three sons of Johann Bernoulli. He studied law and mathematics, and, after travelling in France, was for five years professor of eloquence in the university of his native city. In 1736 awarded the prize of the French Academy for his suggestive studies of Aether On the death of his father he succeeded him as professor of mathematics. He was thrice a successful competitor for the prizes of the Academy of Sciences of Paris. His prize subjects were, the capstan, the propagation of light, and the magnet. He enjoyed the friendship of P. L. M. de Maupertuis, who died under his roof (July 27, 1759) while on his way to Berlin. He himself died in 1790. His two sons, Johann and Jakob, are the last noted mathematicians of the Bernoulli family. *Wik

1912 Jules Henri Poincare (29 April 1854 – 17 July 1912) died very suddenly from an embolism while dressing, in his 59th year. *VFR French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity.
The Poincaré group used in physics and mathematics was named after him.*Wik
His Poincaré Conjecture holds that if any loop in a given three-dimensional space can be shrunk to a point, the space is equivalent to a sphere. Its proof remains an unsolved problem in topology.*TIS
His family gravestone at Cimetière de Montparnasse in Paris is covered with coins, flowers, and notes.  One telling him that "It has been proven."

1917 Giuseppe Veronese (7 May 1854 – 17 July 1917) Although his work was severely criticised as unsound by Peano, he is now recognised as having priority on many ideas that have since become parts of transfinite numbers and model theory, and as one of the respected authorities of the time, his work served to focus Peano and others on the need for greater rigor.
He is particularly noted for his hypothesis of relative continuity which was the foundation for his development of the first non-archimedean linear continuum.*SAU

1944 William James Sidis (April 1, 1898 – July 17, 1944) an American child prodigy with exceptional mathematical and linguistic abilities. He became famous first for his precocity, and later for his eccentricity and withdrawal from the public eye. He avoided mathematics entirely in later life, writing on other subjects under a number of pseudonyms. The difficulties Sidis encountered in dealing with the social structure of a collegiate setting may have shaped opinion against allowing such children to rapidly advance through higher education in his day.*Wik

1963 Bevan Braithwaite Baker (1890 in Edinburgh, Scotland - 1 July 1963 in Edinburgh, Scotland) graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London.*SAU

1998 Sir Michael James Lighthill (23 January 1924 – 17 July 1998) was a British mathematician who contributed to supersonic aerofoil theory and, aeroacoustics which became relevant in the design of the Concorde supersonic jet, and reduction of jet engine noise. Lighthill's eighth power law which states that the acoustic power radiated by a jet is proportional to the eighth power of the jet speed. His work in nonlinear acoutics found application in the lithotripsy machine used to break up kidney stones, the study of flood waves in rivers and road traffic flow. Lighthill also introduced the field of mathematical biofluiddynamics. Lighthill followed Paul Dirac as Lucasian professor of Mathematics (1969) and was succeeded by Stephen Hawking *TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell