Saturday, 11 August 2018

On This Day in Math - August 11

 Boy observing Mural along the flood wall in Paducah, Ky

So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.
~Albert Einstein

The 223rd day of the year; 223 is a prime number, and the sum of three consecutive primes (71 + 73 + 79), 223 and also the sum of seven consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43)

Every number can be formed with no more than 36 fifth powers, except one, 223 is the only number that requires 37 fifth powers. This is related to Waring'a problem. In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers to the power of k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. Waring's problem was proposed in 1770 by Edward Waring, after whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909.

Fans of Star Wars may know that this is sometimes called the Star Wars Droid Prime because it uses only the numbers in the names of R2-D2 and C3PO

An interesting note, if you take a prime number less than 223 and reverse it, some are prime, some have two factors, but 223 is the smallest prime whose reversal has three factors (322 = 2 * 7 * 23)

EVENTS

1124 "In the month of August on the 11th day, before the evening service, the Sun began to diminish and perished completely. Great fright and darkness everywhere. And the stars appeared and the Moon (sic). And the Sun began to augment and became full again and everyone in the town was very glad." Refers to a total solar eclipse in Novgorod, Russia, of 11 August 1124. From: Novorodskaya I Letopic. Quoted in Historical Eclipses and Earth's Rotation, by F Richard Stephenson, Cambridge University Press, 1997, page 391. *NSEC

1591 Kepler received his master’s degree from Tübingen and thereupon entered the process of practical preparation for either teaching or being a Protestant pastor. Halfway through his third year, however, an event occurred that completely altered the direction of his life. Georgius Stadius, teacher of mathematics at the Lutheran school in Graz, died; and the local authorities asked Tübingen for a replacement. Kepler was chosen; and although he protested abandoning his intention to became a clergyman, he set out on the career destined to immortalize his name. *www.encyclopedia.com *Thony Christie

In 1835, George B Airy began his 46-year reign as England's seventh Astronomer Royal. He was appointed in June of that year but seems to have assumed duty on August 11. At Greenwich he designed and installed the famous transit circle now named after him, used for timing the passage of stars across the meridian. It is the position of the Airy transit circle that defines the Greenwich meridian and since 1884 that meridian has been the basis of the world’s timekeeping and navigation. Hence Airy can be said to have brought the world’s clocks into step. *assorted sources

1859 Bernhard Riemann was made a corresponding member of the Berlin Academy based on his 1857 paper on Abelian Functions. It was the practice that newly selected members would submit an example of their recent research. Riemann submitted, "On the Number of Prime Numbers Less Than a Given Quantity." The paper contained his now famous Riemann Hypothesis that the non-trivial zeros of the Zeta function all have a real part of 1/2. It is the only paper he ever published on number theory.*John Derbyshire, Prime Obsession

1909 First SOS, The first well documented use of the SOS distress call is by the Arapahoe on August 11, 1909, when it suffered a broken shaft in the Atlantic Ocean, near Cape Hatteras, North Carolina. However, an article titled "Notable Achievements of Wireless" in the September, 1910 Modern Electrics suggests that an earlier SOS distress call was transmitted by the Cunard liner Slavonia, on June 10, 1909.
[The wireless operator aboard S.S. Arapahoe, T. D. Haubner, radioed for help. A few months later, Haubner on the S.S. Arapahoe received an SOS from the SS Iroquois, the second use of SOS in America.(*TIS)]
The first radio distress call to be adopted appears to have been "CQD", by the Marconi International Marine Communication Company​, for Marconi-operated shipboard stations. It was announced on January 7, 1904 by the company's "Circular 57" that "...on and after the 1st February, 1904, the call to be given by ships in distress or in any way requiring assistance shall be 'C.Q.D.'." ("CQ" was a general call to all stations; amateur or "ham" radio operators still use it today when soliciting a contact with any station that hears the call.)

An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

In 1999, the last total eclipse of the millennium occurred. Because it traveled across many populated areas, it was perhaps the most-watched eclipse of all time, seen by possibly 350 million people. Totality occurred first over the mid-Atlantic Ocean. The first land crossed by the moon's shadow was the Isles of Scilly, then the far south-west of England, in Cornwall. Although the sun was obscured by clouds there, a dramatic darkness fell, and the temperature dropped, during the totality lasting 1-min 30-sec. From there the path of totality tracked across Europe, India and Iran. In Egypt, Muslims were ordered by clerics to shut themselves away, but Jordan and Syria declared a national holiday.*TIS

BIRTHS

1730 Charles Bossut(11 August 1730 – 14 January 1814) was a French mathematician who was famed for his textbooks which were widely used throughout France.*SAU

1829 Norman Macleod Ferrers; (11 August 1829 – 31 January 1903) John Venn wrote of him,
.. the Master, Dr Edwin Guest, invited Ferrers, who was by far the best mathematician amongst the fellows, to supply the place. His career was thus determined for the rest of his life. For many years head mathematical lecturer, he was one of the two tutors of the college from 1865. As lecturer he was extremely successful. Besides great natural powers in mathematics, he possessed an unusual capacity for vivid exposition. He was probably the best lecturer, in his subject, in the university of his day.
It was as a mathematician that Ferrers acquired fame outside the university. He made many contributions of importance to mathematical literature. His first book was "Solutions of the Cambridge Senate House Problems, 1848 - 51". In 1861 he published a treatise on "Trilinear Co-ordinates," of which subsequent editions appeared in 1866 and 1876. One of his early memoirs was on Sylvester's development of Poinsot's representation of the motion of a rigid body about a fixed point. The paper was read before the Royal Society in 1869, and published in their Transactions. In 1871 he edited at the request of the college the "Mathematical Writings of George Green" ... Ferrers's treatise on "Spherical Harmonics," published in 1877, presented many original features. His contributions to the "Quarterly Journal of Mathematics," of which he was an editor from 1855 to 1891, were numerous ... They range over such subjects as quadriplanar co-ordinates, Lagrange's equations and hydrodynamics. In 1881 he applied himself to study Kelvin's investigation of the law of distribution of electricity in equilibrium on an uninfluenced spherical bowl. In this he made the important addition of finding the potential at any point of space in zonal harmonics (1881).

Ferrers proved the proposition by Adams that "The number of modes of partitioning (n) into (m) parts is equal to the number of modes of partitioning (n) into parts, one of which is always m, and the others (m) or less than (m). " with a graphic transformation that is named for him. *SAU

1836 Cato Maximilian Guldberg (11 August 1836 – 14 January 1902) Norwegian chemist who, with his brother-in-law Peter Waage, formulated the law of mass action (1864), which details the effects of concentration, mass, and temperature on chemical reaction rates. The law states that the rate of a chemical change depends on the concentrations of the reactants. Thus for a reaction: A + B >> C the rate of reaction is proportional to [A][B], where [A] and [B] are concentrations. In 1870 Guldberg investigated the way in which the freezing point and vapor pressure of a pure liquid are lowered by a dissolved component. In 1890 he formulated Guldberg's law which relates boiling point and critical temperature.*TIS

1842 Enrico D'Ovidio (11 Aug 1842 in Campobasso, Italy - 21 March 1933 in Turin, Italy) D'Ovidio was to work for 46 years in the University of Turin. He was chairman of the Faculty of Science in 1879-80 and rector of the University between 1880 and 1885. Another spell as chairman of the Faculty of Science between 1893 and 1907 ended when he was appointed Commissioner of the Polytechnic of Turin.
Euclidean and noneuclidean geometry were the areas of special interest to D'Ovidio. He built on the geometric ideas which had been introduced by Lobachevsky, Bolyai, Riemann and Cayley. D'Ovidio's most important work is probably his paper of 1877 The fundamental metric functions in spaces of arbitrarily many dimensions with constant curvature.
D'Ovidio also worked on binary forms, conics and quadrics. He had two famous assistants, Peano (1880-83) and Corrado Segre (1883-84). D'Ovidio and Corrado Segre built an important school of geometry at Turin. *SAU

1895 Egon Sharpe Pearson, (Hampstead, 11 August 1895 – Midhurst, 12 June 1980) was the only son of Karl Pearson, and like his father, a leading British statistician.
He went to Winchester School and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal Biometrika.
Pearson is best known for development of the Neyman-Pearson lemma of statistical hypothesis testing.
He was President of the Royal Statistical Society in 1955–56, and was awarded its Guy Medal in Gold in 1955. He was awarded a CBE in 1946.
He was elected a Fellow of the Royal Society in Mar 1966. His candidacy citation read: "Known throughout the world as co-author of the Neyman-Pearson theory of testing statistical hypotheses, and responsible for many important contributions to problems of statistical inference and methodology, especially in the development and use of the likelihood ratio criterion. Has played a leading role in furthering the applications of statistical methods - for example, in industry, and also during and since the war, in the assessment and testing of weapons." *Wik

1912 Norman Levinson (August 11, 1912, Lynn, Massachusetts – October 10, 1975, Boston) set out to become an electrical engineer. Here he describes the events that led to his change of major:
I became acquainted with Wiener in September 1933, while still a student of electrical engineering, when I enrolled in his graduate course. It was at that time really a seminar course. At that level he was a most stimulating teacher. He would actually carry on his research at the blackboard. As soon as I displayed a slight comprehension of what he was doing, he handed me the manuscript of Paley-Wiener for revision. I found a gap in a proof and proved a lemma to set it right. Wiener thereupon sat down at his typewriter, typed my lemma, affixed my name and sent it off to a journal. A prominent professor does not often act as secretary for a young student. He convinced me to change my course from electrical engineering to mathematics.
Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.*SAU

1921 Tom Kilburn (11 August 1921 – 17 January 2001) British electrical engineer who wrote the computer program used to test the first stored-program computer, the Small-Scale Experimental Machine, SSEM, also known as "The Baby." First tested on 21 Jun 1948, the program took 52 minutes to run. The tiny experimental computer had no keyboard or printer, but it successfully tested a memory system developed at Manchester University in England. This system, based on a cathode-ray tube, was the first that could store programs, whereas previous electronic computers had to be rewired to execute each new problem.*TIS

1950 Steve Wozniak, (August 11, 1950; ) Apple inventor, is born
Wozniak and Jobs entered into business after Wozniak designed a single-board personal computer known as the Apple I. In 1976, with specifications in hand and an order for 100 machines at \$500 each from the Byte Shop, he and Jobs founded the business.
While still studying at the University of California-Berkeley in 1972, Wozniak had shown his electronics skill as well as his sense of humor in building his blue box, a tone generator used to make free phone calls, which he sold in dormitories
Wozniak now teaches computer science to school children in his home town of Los Gatos, California. *CHM

1956 Pierre-Louis Lions (August 11, 1956, ) French mathematician who was awarded the Fields Medal in 1994 for his work since the 1980's on partial differential equations. The sources of such equations are many - for example, physical, probabilistic or geometric and other diverse subareas - each studying different phenomena for different nonlinear partial differential equations by utterly different methods. Pierre-Louis Lions has been called unique in his ability to transcend these boundaries and to solve pressing problems throughout the field.*TIS

DEATHS

1464 Nicholas von Cusa died (1401 – August 11, 1464). We know his work in mathematics primarily because a home for the aged in Kues, which he generously endowed, has survived the ravages of time and war. Luckily his own manuscripts were housed there.*VFR
Nicholas is also considered by many to be a genius ahead of his time in the field of science. Nicolaus Copernicus, Galileo Galilei and Giordano Bruno were all aware of the writings of Cusanus as was Johannes Kepler (who called Cusanus 'divinely inspired' in the first paragraph of his first published work). Predating Kepler, Cusanus said that no perfect circle can exist in the universe (opposing the Aristotelean model, and also Copernicus' later assumption of circular orbits), thus opening the possibility for Kepler's model featuring elliptical orbits of the planets around the Sun. He also influenced Giordano Bruno by denying the finiteness of the universe and the Earth's exceptional position in it (being not the center of the universe, and in that regard equal in rank with the other stars). He was not, however, describing a scientifically verifiable theory of the universe: his beliefs (which proved uncannily accurate) were based almost entirely on his own personal numerological calculations and metaphysics.
Cusanus made important contributions to the field of mathematics by developing the concepts of the infinitesimal and of relative motion. He was the first to use concave lenses to correct myopia. His writings were essential for Leibniz's discovery of calculus as well as Cantor's later work on infinity. *Wik

1578 Pedro Nunes or Nunez (1502 – August 11, 1578) was a Portuguese scholar who worked in geometry, spherical trigonometry, algebra as well as geography, physics, and cosmology. *SAU He was the first to propose the idea of a loxodrome and was also the inventor of several measuring devices, including the nonius, named after his Latin surname. *Wik

1854 Macedonio Melloni, (11 April 1798 – 11 August 1854) Italian physicist who was the first to extensively research infrared radiation. Sir William Frederick Herschel discovered infrared radiation in 1800, but research stalled until the invention of a thermopile in 1830. That instrument was a series of strips of two different metals that produced electric current when one end was heated. Melloni improved the thermopile and used it to detect infrared radiation. In 1846, from an observation point high on Mount Vesuvius, he measured the slight heating effect of moonlight. He showed also that rock salt, being transparent to infrared, made suitable lenses and prisms to demonstrate the reflection, refraction, polarization and interference of infrared in the same manner as visible light.*TIS

1892 Enrico Betti (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations, giving early expositions of Galois theory. He also discovered Betti's theorem, a result in the theory of elasticity. *Wik

1955 Robert Williams Wood (May 2, 1868 – August 11, 1955) was an American experimental physicist. He photographed the reflection of sound waves in air, and investigated the physiological effects of high-frequency sound waves. The zone plate he devised could replace the objective lens of a telescope. He invented an improved diffraction grating, did research in spectroscopy, and extended the technique of Raman spectroscopy (a method to study matter using the light scattered by it.) He made photographs showing both infrared and ultraviolet radiation and was the first to photograph ultraviolet fluorescence. Wood was the first to observe the phenomenon of field emission in which charged particles are emitted from conductors in an electric field. *TIS
According to a post at Greg Ross' Futility Closet:
"How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:
The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.
This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”

1977 Sir Frederic Williams, (26 June 1911 Stockport – 11 August 1977 Manchester) British electrical and electronics engineer who, with Tom Kilburn, invented the Williams tube, a cathode-ray tube using the persistence of the image on the phosphor screen for data storage. This made possible the random access memory that launched the digital computer age. As the Chair in Electrotechnics at Manchester University, he incorporated this invention into the Mark I computer, the world's first stored-program digital electronic computer to be commercially produced during the early 1950's. *TIS

1995 Alonzo Church (June 14, 1903 – August 11, 1995) made important contributions to mathematical logic and theoretical computer science.*SAU He is best known for the lambda calculus, Church–Turing thesis, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem. *Wik

2003 Armand Borel (21 May 1923 –11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. *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