Saturday, 22 July 2017

On This Day in Math - July 22

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.

~David van Dantzig

This is the 203rd day of the year; 203 is the 6th Bell number, i.e. it is the number of partitions of a set of size 6.

203^2 + 203^3 + 1 is prime.

203 is the number of nondegenerate triangles that can be made from rods of lengths 1,2,3,4,...,11

203 is the number of triangles pointing in opposite direction to largest triangle in triangular matchstick arrangement of side length 13

Saw a tweet about July 22 as "Casual Pi Day" at Rimwe@RimweLLC which he told me he found at page of GeorgeTakei.

The NCTM uses "Pi Approximation Day" for it's poster


1694 Johann Bernoulli sent “L’Hospital’s rule” to L’Hospital under the terms of their agreement of 17 March 1694. *VFR The agreement between them led to the first real calculus text in 1696.

1925 After Norbert Wiener suggested to his friend Phillip Franklin in a letter that they hang a sign outside their office at MIT reading “Wiener and Franklin. Wholesale and Retail Mathematicians and Exporters,” he wrote: “As to the state of the market: differential geometry seems rather quiet, and some of the principal operators have deserted it for other securities. Real and complex variables continue firm, without much change. Analysis situs has a bull market. Bull operators have been very active in differential equations, also. Quantum theory continues speculative, with chances of a very sharp rise, but the market contains a lot of wildcat stock. Hilbert, Brouwer, and Co. are doing well with mathematical logic.” From Science in America, ed. Nathan Reingold, p. 384.*VFR

1933 Wiley Post startled the world by completing the first solo airplane flight around the world. The 15,400 mile flight lasted seven days, 18 hours, 49 and 1/2 minutes. Two years later he was killed in an airplane crash with humorist, Will Rogers. [Scientific American, November 1933]*VFR   He had made an accompanied flight around the world in 1931. Born 22 Nov 1898, Wiley Post made his first solo flight in 1926, the year he got his flying license, signed by Orville Wright, despite wearing a patch over his left eye, lost in an oilfield accident. Post invented the first pressurized suit to wear when he flew around the world. Another credit was his research into the jet streams. He died with his passenger, humorist Will Rogers, 15 Aug 1935 in a plane crash in Alaska.*TIS

1976 “researchers from Univ of Illinois announced they had found an unavoidable set containing 1936 reducible configurations effectively proving the four color theorem.*VFR

1978 Roger Apéry gave a talk entitled "Sur l'irrationalité de ζ(3)." to outline proofs that ζ(3) and ζ(2) were irrational. Alfred J. Van der Poorten's reprint of the talk describes the less than hopeful anticipation of the audience.,
"The board of programme changes informed us that R. Apery (Caen) would speak Thursday, 14:00 ‘Sur l’irrationalit'e de ζ(3)’. Though there had been earlier rumours of his claiming a proof, scepticism was general. The lecture tended to strengthen this view to rank disbelief. Those who listened casually, or who were afflicted with being non-Francophone, appeared to hear only a sequence of unlikely assertions"
"I heard with some incredulity that, for one, Henri Cohen (then Bordeaux, now Grenoble) believed that these claims might well be valid. Very much intrigued, I joined Hendrik Lenstra (Amsterdam) and Cohen in an evening’s discussion in which Cohen explained and demonstrated most of the details of the proof. We came away convinced that Professeur Apery had indeed found a quite miraculous and magnificent demonstration of the irrationality of ζ(3)." *, Poorten, A PROOF THAT EULER MISSED , with special thanks to Tim Pentilla who helped me establish the date of the original address.

1983 Science reported that Gerd Faltings of Wuppertal University in Germany proved the sixty-year ­old Mordell conjecture: most equations of degree higher than three have only a finite number of rational solutions. In particular, this applies to Fermat’s Last Theorem. [Mathematics Magazine 57 (1984), p. 52].*VFR  In number theory, the Mordell conjecture is the conjecture made by Mordell (1922) that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points. The conjecture was later generalized by replacing Q by a finite extension. It was proved by Gerd Faltings (1983), and is now known as Faltings' theorem.

1997Apple Announces OS 8-Apple Computer Inc. announces a new operating system for its Macintosh computers, OS 8. An important move at a time when Apple's upper-level management and profits were experiencing significant problems, the new operating system offered new features such as easier integration of the Internet and a three-dimensional look. Immediately after the announcement, the software earned positive reviews from users, although it was not expected to end Apple's financial troubles as it faced growing competition from improvements in the Microsoft Windows operating system used on IBM-compatible PCs. *CHM

2009 A total solar eclipse the longest-lasting total eclipse of the 21st century – takes place. It lasted a maximum of 6 minutes and 39 seconds off the coast of Southeast Asia, causing tourist interest in eastern China, Japan, India, Nepal and Bangladesh. It will not be surpassed until 13 June 2132. *Wik

2381 The maximum theoretical length for a British total eclipse is 5.5 minutes. The eclipse of June 16, 885 lasted for almost 5 minutes and the same will be true for the Scottish total eclipse of 22 Jul, 2381. This TSE will be the first total solar eclipse
in Amsterdam since 17 June 1433. *NSEC


1784 Friedrich Wilhelm Bessel born (22 July 1784 – 17 March 1846). He is noted for the special class of functions that have become an indispensable tool in applied mathematics. This, like all of his mathematical work, was motivated by his work in astronomy. *VFR    In 1809, at the age of 26, Bessel was appointed director of Frederick William III of Prussia's new Königsberg Observatory and professor of astronomy, where he spent the rest of his career. His monumental task was determining the positions and proper motions for about 50,000 stars, which allowed the first accurate determination of interstellar distances. Bessel's work in determining the constants of precession, nutation and aberration won him further honors. Other than the sun, he was the first to measure the distance of a star, by parallax, of 61 Cygni (1838). In mathematical analysis, he is known for his Bessel function. *TIS

1795 Gabriel Lam´e (22 July 1795 – 1 May 1870) born in Tours, in today's département of Indre-et-Loire.
He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:
 \left|\,{x\over a}\,\right|^n + \left|\,{y\over b}\,\right|^n =1
where n is any positive real number.
He is also known for his running time analysis of the Euclidean algorithm. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digits of b. He also proved a special case of Fermat's last theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics. *Wik
Piet Hein's Super Ellipse is a Lame Curve

1822 Gregor Mendel (July 20, 1822 – January 6, 1884) (Original name (until 1843) Johann Mendel). Austrian pioneer in the study of heredity. He spent his adult life with the Augustinian monastery in Brunn, where as a geneticist, botanist and plant experimenter, he was the first to lay the mathematical foundation of the science of genetics, in what came to be called Mendelism. Over the period 1856-63, Mendel grew and analyzed over 28,000 pea plants. He carefully studied for each their plant height, pod shape, pod color, flower position, seed color, seed shape and flower color. He made two very important generalizations from his pea experiments, known today as the Laws of Heredity. Mendel coined the present day terms in genetics: recessiveness and dominance.

1882 Konrad Knopp (22 July 1882 – 20 April 1957) born. He is best known for comprehensive book on infinite series.*VFR

1887 - Gustav Hertz born (22 July 1887 – 30 October 1975) .Hertz was a German physicist who shares the 1925 Nobel Prize in Physics with James Franck for their Frank-Hertz experiment. The Frank-Hertz experiment shows that an atom absorbs energy in discrete amounts, confirming the quantum theory of atoms. This experiment was an important step confirming the Bohr model of the atom. *TIS

1902 Reinhold Baer (July 22, 1902 – October 22, 1979) Baer's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups.*SAU

1914 Edward (Rolke) Farber was an American who invented a portable, battery-operated stroboscopic flash unit for still cameras (1937) that effectively "stopped action." He began his career as a photojournalist on the staff of the Milwaukee Journal. After studying electrical engineering at Northwestern University, Farber went on to design flash equipment for the U.S. Army during World War II, and then established his own electronic-flash manufacturing firm. He was a good friend and collaborator of Harold Edgerton and developed the first practical portable strobe flash for news photographers. In 1942, the Milwaukee Journal became the first newspaper to furnish all of its photographers with the portable flash. Weighing only 13.5 pounds, it was a considerable improvement over the 90-pound units photographers used prior to Farber's invention. He sold his Strobe Research firm in 1954. He was a photographic adviser to the U.S. Government during its intercontinental ballistic missile testing program in the late 1950's.*TIS

1935 John Robert Stallings (July 22, 1935 – November 24, 2008) In 1968 Stallings published his most famous paper On torsion-free groups with infinitely many ends in the Annals of Mathematics. L Neuwirth explains what is contained in the paper:-
In this remarkable paper, the author, using very little besides his bare hands, proves the following theorem:
1. If G is a torsion-free, finitely presented group, with infinitely many ends, then G is a non-trivial free product.
This simple sounding theorem proves to be very powerful, implying
(with a little work) the following two theorems:
2. A torsion-free, finitely generated group, containing a free subgroup of finite index, is itself free.
3. A finitely generated group of cohomological dimension 1 is free.
This last theorem answers a question which had been unanswered for over ten years and which had received considerable attention over that period of time. Theorem
2 answers a question of J-P Serre, who proved an analogue of Theorem 2 for pro-p groups. The proof of Theorem 1 is both combinatorial and geometric in nature and, as suggested, is self-contained.
For this truly outstanding paper the American Mathematical Society awarded Stallings their Frank Nelson Cole Prize in Algebra in 1970. Also in 1970 he was invited to address the International Congress of Mathematicians in Nice, France. He gave a talk on Group theory and 3-manifolds. He had been honoured in the previous year when invited to give the James K Whittemore Lecture in Mathematics at Yale University in 1969. His topic was Group theory and three-dimensional manifolds. This lecture and his Nice address were both published in 1971.
Among the 50 or so papers Stalling published, we should highlight another two which have proved particularly important: Topology on finite graphs (1983) and Non-positively curved triangles of groups (1991). The first of these introduced the 'Stallings subgroup graph' as a method to describe subgroups of free groups. It also introduced a foldings technique now known as 'Stallings' foldings method' which has been the basis for much later work. The second of these two papers introduced the notion of a triangle of groups which became the basis for later work on the theory of complexes of groups.*SAU


1575  Francisco Maurolico (Messina, Sicily, 16 Sept 1494 - near Messina, Sicily, 21/22 July 1575) was an Italian Benedictine who wrote important books on Greek mathematics. He also worked on geometry, the theory of numbers, optics, conics and mechanics.*SAU

1826 Giuseppe Piazzi (July 16, 1746 – July 22, 1826) Italian astronomer and author, born in Valtellina, discovered the first asteroid - Ceres. He established an observatory at Palermo and mapped the positions of 7,646 stars. He also discovered that the star 61 Cygni had a large Proper Motion , which led Bessel to chose it as the object of his parallax studies. He discovered Ceres in 1801, but was able to make only three observations. Fortuitously, Gauss had recently developed mathematical techniques that allowed the orbit to be calculated. This was the first asteroid discovered. The thousandth Asteroid discovered was named Piazzia in his honor.*TIS  (His dates of birth and death are six days apart)

1869 John A. Roebling (June 12, 1806 – July 22, 1869) German-American engineer who pioneered the design and construction of suspension bridges. In 1831 he immigrated to Saxonburg, near Pittsburgh, Pa., and shortly thereafter was employed by the Pennsylvania Railroad Corp. to survey its route across the Allegheny Mountains. He then demonstrated the practicability of steel cables in bridge construction and in 1841 established at Saxonburg the first U.S. factory to manufacture steel-wire rope. Roebling utilized steel cables in the construction of numerous suspension bridges including a railroad suspension bridge over the Niagara River at Niagara Falls (1851-55). He designed the Brooklyn Bridge. He died from injuries while supervising preliminary construction operations.*TIS

1915 Sir Sandford Fleming (January 7, 1827 – July 22, 1915) Scottish surveyor and leading railway engineer who divided world into time zones. He emigrated at age 17 years to Quebec, Canada, on April 24, 1845, as a surveyor. Later became one of the foremost railway engineers of his time. While in charge of the initial survey for the Canadian Pacific Railway, the first Canadian railway to span the continent, he realized the problems of coordinating such a long railway. This lead him to the idea of time zones, which contribution to the adoption of the present system of time zones earned him the title of "Father of Standard Time." Fleming also designed the first Canadian postage stamp. Issued in 1851, it cost three pennies and depicted the beaver, now the national animal of Canada.*TIS

1932 Reginald Aubrey Fessenden (October 6, 1866 – July 22, 1932), was a Canadian inventor and engineer with 300 patents. He broadcast the first program of voice and music. In 1893, Fessenden moved to Pittsburgh as the head of electrical engineering at the university, Fessenden read of Marconi's work and began experimenting himself. Marconi could only transmit Morse code. But Fessenden's goal was to transmit the human voice and music. He invented the "continuous wave": sound superimposed onto a radio wave for transmission. A radio receiver extracts the signal so the listener with the original sound. Fessenden made the first long-range transmissions of voice on Christmas Eve 1906 from a station at Brant Rock, Massachusetts, heard hundreds of miles out in the Atlantic.*TIS

1938 Ernest (William) Brown (29 November 1866 – 22 July 1938) was a British astronomer who devoted his career to the theory of the Moon's motion and constructing accurate lunar tables. His theory took account of "the gravitational action of every particle of matter which can have a sensible effect on the Moon's motion," some 1500 terms. He then determined the numerical values of the constants by analyzing 150 years of Greenwich observations, and computed tables accurate to 0.01 arcsec. After 30 years of work, Brown published his lunar tables Tables of the Motion of the Moon in 1919. In 1926 Brown published a paper in which he ascribed fluctuations in the Moon's motion to irregular changes in the Earth's period of rotation, which has subsequently proved correct. *TIS

1943 William Fogg Osgood died (March 10, 1864, Boston - July 22, 1943, Belmont, Massachusetts). Although his nickname was “Foggy,” this was not an apt description of him as a teacher. He instilled the habit of careful thought in Harvard students for 43 years. His A First Course in Differential and Integral Calculus (1907) was revised once and reprinted 17 times.*VFR From 1899 to 1902, he served as editor of the Annals of Mathematics and in 1904–1905 was president of the American Mathematical Society, whose Transactions he edited in 1909–1910. In 1904, he was elected to the National Academy of Sciences.
The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations. He was invited by Felix Klein to write an article on complex analysis in the Enzyklopädie der mathematischen Wissenschaften which was later expanded in the book Lehrbuch der Funktionentheorie. Besides his research on analysis, Osgood was also interested in mathematical physics and wrote on the theory of the gyroscope. *Wik

1959 David van Dantzig (September 23, 1900, Amsterdam – July 22, 1959) was at secondary school when he wrote his first mathematics paper. He was only thirteen years old at the time. However, his main interest in secondary school was not mathematics, rather it was chemistry. After leaving school he continued with his studies of chemistry, but this he did not enjoy and when he was forced to give up his academic studies to help support his family van Dantzig took on a number of jobs purely to make money.
By now van Dantzig knew that mathematics was the subject which he really wanted to study but he was not in a position to do so, both because he had to earn money and also because he did not have the necessary school qualifications. He put in hours of work on mathematics in the evenings after finishing his money earning tasks for the day. He took the state mathematics examinations in 1921, at a higher level the following year and again in 1923 he passed at a higher level still. Entering the University of Amsterdam to study mathematics he soon passed examinations which took him essentially to Master's Degree level.
Van Dantzig became an assistant to Schouten in 1927 at Delft Technical University. Then, for a short time, he taught at a teacher training institution, but he returned to Delft as a lecturer in 1932. This was the year in which he received his doctorate from Gröningen for a thesis which he submitted in 1931 Studiën over topologische Algebra. In this work he coined the now familiar term topological algebra but the thesis is memorable in other ways too. It -
... is a fine example of mathematical style: it consists of a concise string of definitions and theorems organised in such a way that in this context each theorem is obvious and none needs a proof.
He was promoted to extraordinary professor at Delft in 1938 and then an ordinary professor in 1940. The Dutch had tried to remain neutral when World War II broke out in 1939 but in the spring of 1940 German troops, in a strategic move on their way to attack France, entered Holland and the Dutch were defeated in a week. Van Dantzig was dismissed from his chair when the Germans occupied Holland and he was forced to move with his family from the Hague to Amsterdam.
After the war ended, he was appointed professor at the University of Amsterdam in 1946. In Amsterdam he was the cofounder of the research and service institution, the Mathematisch Centrum. He played a major role in both this Centre and in the University of Amsterdam where he continued to hold his chair until his death.
Van Dantzig studied differential geometry, electromagnetism and thermodynamics. His most important work was in topological algebra and in addition to his doctoral thesis which we mentioned above, he wrote a whole series of papers on topological algebra. He studied metrisation of groups rings and fields. One paper classified fields with a locally compact topology.*SAU

1966 Philipp Frank (20 Mar 1884; 22 Jul 1966 at age 82) Austrian-American physicist and mathematician whose theoretical work covered a broad range of mathematics, including variational calculus, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Frank had a deep and lasting interest in the philosophy of science. In a number of writings, he strove to reconcile science and philosophy and “bring about the closest rapprochement between” them. The 1907 paper he wrote analyzing the law of causality caught Einstein's attention, who in 1912 recommended Frank as his successor as professor of theoretical physics at the German University of Prague. He held that position until 1938, when he moved to Harvard University in the U.S., first as visiting lecturer, but remaining there until retirement in 1954. He wrote on misinterpretations of the Theory of Relativity.*TIS

1995  Otakar Boruvka (10 May 1899 in Uherský Ostroh – 22 July 1995 in Brno)   To many people Boruvka is best known for his solution of the Minimal Spanning Tree problem which he published in 1926 in two papers On a certain minimal problem (Czech) and Contribution to the solution of a problem of economical construction of electrical networks (Czech). Let us quote the problem as it appears in the second of these 1926 papers:-
There are n points in the plane whose mutual distances are different. The problem is to join them with a net in such a way that:
1. any two points are joined to each other either directly or by means of some other points;
2. the total length of the net will be minimal.
In modern graph theoretical terms this can be stated as: Given an undirected graph with weights assigned to its edges, find a spanning tree of minimal weight.
In fact the problem had been suggested to Boruvka before he became a university student. He had a friend, Jindrich Saxel, who worked for the firm West-Moravian Powerplants and he suggested the problem which he stated in terms of cities and the distances between them. At the time that Saxel suggested the problem to Boruvka, World War I was still happening and Czech universities were closed. Boruvka was offered a job with West-Moravian Powerplants at this time but declined. The authors write:-
The Minimal Spanning Tree problem is a cornerstone of Combinatorial Optimisation and in a sense its cradle. The problem is important both in its practical and theoretical applications. Moreover, recent development places Boruvka's pioneering work in a new and very contemporary context. One can even say that out of many available Minimal Spanning Tree algorithms, Boruvka's algorithm is presently the basis of the fastest known algorithms.  *SAU

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

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