Monday 18 May 2020

On This Day in Math - May 18

I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own.  A twelve is very different from a thirteen, for example.  Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants.  Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation....
~Paul Auster, The Music of Chance

The 139th day of the year; 139 and 149 are the first consecutive primes differing by 10.
139 = 9*8+7*6+5*4+3*2-1 *Prime Curios

139 is the sum of five consecutive prime numbers( 19+ 23+ 29 +31+ 37)

139 is also a Happy number, if you square the digits and add, then continue to repeat with each result, you will eventually come to the number one.

139 ---- 91----- 82 ------ 68---- 100 ----- 1 (The earliest I have ever found this term was in an article in The Arithmetic Teacher, Feb 1974. "Happiness is some Intriguing numbers" by Billie Earl Sparks of George Peabody College in Nashville, Tn. Does anyone know of an earlier usage?"

EVENTS

1772 Euler shows that 1 + 1/33 + 1/53 + 1/73 + ... = p/4 log 2 + 2 ∫ 0p/2 f log (sin (f)) df in paper to St. Petersburg Academy (dates in Russia at this time were still on Julian Calendar) *math.dartmouth.edu/~euler/docs/originals/E432.pdf
This value, which Euler approximated to 16 decimal places, 1.2020569031595942, is named Apery'a constant after Roger Apéry, who proved in 1978 that it is irrational. No other odd Zeta(n) has been proven either rational or irrational. It is still not known if it is transcendental.

1825 Faraday isolates benzine. In 1825, Faraday started work on a sample of oil that had been sent to him for analysis by the Portable Oil Company of London. He subjected this oil to fractional distillation, a process that proved to be extremely difficult, and it took him some time to resolve the oil into its pure components. By repeated fractional distillation followed by selective fractional freezing, each stage monitored by analysis, he produced a fairly pure sample of what he called bicarburet of hydrogen. Faraday’s notebook records these procedures, which he carried out on 18 and 19 May 1825. Auguste Laurent suggested the name benzene. *Jennifer Wilson, Celebrating Michael Faraday’s Discovery of Benzene, Ambix,Volume 59, Issue 3

1852 Massachusetts becomes the ﬁrst state to pass a compulsory attendance law for school children. *VFR

1896, the Supreme Court ruled separate-but-equal facilities constitutional on intrastate railroads. For some fifty years, the Plessy v. Ferguson decision upheld the principle of racial segregation. Across the country, laws mandated separate accommodations on buses and trains, and in hotels, theaters, and schools.
In a speech delivered in the Ohio House of Representatives in 1886 and later published as The Black Laws, legislator Benjamin W. Arnett described life in segregated Ohio:

"This foe of my race stands at the school house door and separates the children, by reason of 'color,' and denies to those who have a visible admixture of African blood in them the blessings of a graded school and equal privileges... We call upon all friends of 'Equal Rights' to assist in this struggle to secure the blessings of untrammeled liberty for ourselves and posterity. "
After hearing arguments by NAACP lawyer Thurgood Marshall, the Supreme Court overruled the Plessy decision on May 17, 1954. In Brown v. the Board of Education, a unanimous Court adopted Justice Harlan's position that segregation violated the Thirteenth and Fourteenth Amendments to the Constitution. *Library of  Congress

1901 Charles Sanders Peirce writes George A. Plimpton,  head of Ginn and Company and famous collector of rare mathematical books, describing what the contents of a newly acquired book must be were it indeed the great Liber Abaci (1202) of Fibonacci. In 1949 Carolyn Eisele’s discovery of this letter—still tucked into the back cover of the volume—began her career as a Peirce scholar. [HM 9, 335] *VFR (I have been advised by Adam Shapiro that Plimpton was not head of Ginn & Co until the death of Edwin Ginn in 1914. )

In 1910, Halley's Comet was visible from Earth, moving across the face of the sun. *TIS
1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this.
May 18: Earth to pass through come tail for 6 hours; C.B. Harmon invites college deans to join him in viewing comet from balloon. *Joseph M. Laufer, Halley's Comet Society - USA

1933 John Kieran’s Sports of the Times column in the New York Times is entitled “The Coordinate Clash, or Block that Abscissa.” The column was a humorous analogy between football and the upcoming mathematical contest between Harvard and Army. *VFR

1952 Prof. Willard F. Libby determined the age of Stonehenge on Salisbury Plain, England, at about 1848 BC (+/- 275 years) through analysis of the carbon-14 radioisotope in charcoal remains excavated there there. Update of C-14 ceases when plants or animals die, and the proportion in the organic remains steadily declines through radioactive decay. Since the half-life of C-14 is about 5,600 years, measurement of the remaining proportion in dead organic matter, indicates the age of that sample. Astronomer Sir Joseph Norman Lockyer had previously calculated that on Midsummer Day, 1680 BC, the sun rose directly over a special marking notch that can still be seen on the Heel Stone. Libby's measurements support that estimate. *TIS

1993 A headline in the National Enquior tabloid mocked the National Science Foundation for funding a study by Georgia Southern Professor Jonathon Copeland to study fireflies in Borneo. "Not a bright Idea." It quoted Wisconsin Republican representative (or mis-representative) was quoted as saying he didn't think it was a "bright" idea. Ironically, the same week that the article appeared, an article in Time reported that doctors were using luciferase, the light emitting enzyme of the butterfly, in testing drugs against resistant strains of tuberculosis.*Steven Strogatz, Sync

BIRTHS
1048 Omar Khayyam (18 May, 1048–1131)  (his birthdate is sometimes given as 15 May) Persian poet, mathematician, and astronomer. Khayyam, who was born at Nishapur (now in Iran), produced a work on algebra that was used as a textbook in Persia until this century. In geometry, he studied generalities of Euclid and contributed to the theory of parallel lines. Around 1074, he set up an observatory and led work on compiling astronomical tables, and also contributed to the reform of the Persian calendar. His contributions to other fields of science included developing methods for the accurate determination of specific gravity. He is known to English-speaking readers for his "quatrains" as The Rubáiyát of Omar Khayyám, published in 1859 by Edward Fitzgerald, though it is now regarded as an anthology of which little or nothing may be by Omar. *TIS

"Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved by propositions five and six of Book two of Elements."
Omar Khayyam

1711 Ruggero Giuseppe Boscovich Astronomer and mathematician who gave the first geometric procedure for determining the equator of a rotating planet from three observations of a surface feature and for computing the orbit of a planet from three observations of its position. Boscovich was one of the first in continental Europe to accept Newton's gravitational theories and he wrote 70 papers on optics, astronomy, gravitation, meteorology and trigonometry. Boscovich also showed much ability in dealing with practical problems. He suggested and directed the draining of the Pontine marshes near Rome, and recommended the use of iron bands to control the spread of cracks in the dome of St. Peter's basilica.*TIS  A slightly enlarged description of his life is here

1850 Oliver Heaviside (18 May 1850, 3 Feb 1925) English physicist who predicted the existence of the ionosphere. In 1870, he became a telegrapher, but increasing deafness forced him to retire in 1874. He then devoted himself to investigations of electricity. In 1902, Heaviside and Kennelly predicted that there should be an ionised layer in the upper atmosphere that would reflect radio waves. They pointed out that it would be useful for long distance communication, allowing radio signals to travel to distant parts of the earth by bouncing off the underside of this layer. The existence of the layer, now known as the Heaviside layer or the ionosphere, was demonstrated in the 1920s, when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received. *TIS He adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations (later found to be equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of mathematics and science for years to come. Among many others, he coined the terms for admittance , conductance , impedance , permeability , and inductance. *Wik

1859 Harry Fielding Reid (18 May 1859; 18 Jun 1944 at age 85) who introduced the term elastic rebound in a report (1910) on the 1906 San Francisco earthquake. His early career was as a glaciologist, but then the study of earthquakes became his most significant work. Reid was the first to establish that it is the fault that causes an earthquake, rather than a fault results from an earthquake. His elastic rebound theory, said that an earthquake occurs upon the sudden release of a large amount of stored energy after a long gradual accumulation of stress along a fault line. Later, modern science explained that Earth's surface consists of huge tectonic plates slowly moving relative to each other, and stress (elastic strain energy) gradually builds along their edges moving against each other. *TIS

1872 Bertrand Russell. 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life, he imagined himself in turn a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things, in any profound sense. He was born in Wales, into one of the most prominent aristocratic families in Britain.
Russell led the British "revolt against idealism" in the early 1900s. He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his protégé Ludwig Wittgenstein, and is widely held to be one of the 20th century's premier logicians. He co-authored, with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." His work has had a considerable influence on logic, mathematics, set theory, linguistics, and philosophy, especially philosophy of language, epistemology, and metaphysics. *Wik  (on page 378 they are able to outline a proof for 1+1=2, but first they need to define the operation of addition.... then along comes  Kurt Godel)
I include here a quote from his autobiography that is often shortened so that, what I believe was the critical last part of it, is not told:
At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatever. This was the first time it had dawned upon me that I might have some intelligence. From that moment until Whitehead and I finished Principia Mathematica, when I was thirty-eight, mathematics was my chief interest, and my chief source of happiness. Like all happiness, however, it was not unalloyed. I had been told that Euclid proved things, and was much disappointed that he started with axioms. At first I refused to accept them unless my brother could offer me some reason for doing so, but he said: 'If you don't accept them we cannot go on', and as I wished to go on, I reluctantly admitted them pro tem. The doubt as to the premisses of mathematics which I felt at that moment remained with me, and determined the course of my subsequent work.

1901 Julius Adams Stratton (May 18, 1901 – June 22, 1994) was a U.S. electrical engineer and university administrator. He attended the University of Washington for one year, then transferred to the Massachusetts Institute of Technology (MIT), from which he graduated with a bachelor's degree in 1923 and a master's degree in electrical engineering (EE) in 1926. He then followed graduate studies in Europe and the Technische Hochschule of Zurich (ETH Zurich), Switzerland, awarded him the degree of Doctor of Science in 1927. *Wik He worked with the blind-landing research program during WWII to help develop Glide-slope-approach radar.

1941 Malcolm Sim Longair (18 May 1941 - )Scottish astronomer, noted for his scholarship and teaching, who in 1980 was appointed by Royal Warrant Astronomer Royal for Scotland, a post he held until 31 Dec 1990. The title of Astronomer Royal for Scotland was created in 1834. As Jacksonian Professor of Natural Philosophy and head of Cavendish Laboratory at the University of Cambridge, UK, his research interests include the emission from dust in the distant universe, observational cosmology, galaxy formation, and gravitational lensing. He is the current Public Understanding of Physics Fellow of the Institute of Physics. *TIS

DEATHS

1996 Stefan Schwarz (18 May 1914 in Nové Mesto nad Váhom, Austria-Hungarian Empire (now Slovakia) - 6 Dec 1996 in Bratislava, Slovak Republic) In addition to his work on semigroups, number theory and finite fields, Schwarz contributed to the theory of non-negative and Boolean matrices.
Schwarz organised the first International Conference on Semigroups in 1968. At this conference setting up the journal Semigroup Forum was discussed and Schwarz became an editor from Volume 1 which appeared in 1970, continuing as editor until 1982. This was not his first editorial role since he had been an editor of the Czechoslovak Mathematical Journal from 1945 and continued to edit this journal until he was nearly 80 years old. He also founded the Mathematico-Physical Journal of the Slovak Academy of Sciences in 1950 and continued as an editor of the mathematics part of the journal when it split from the physics part to become Mathematica Slovaca until 1990. *SAU

2007 Pierre-Gilles de Gennes French physicist who was awarded the 1991 Nobel Prize for Physics for "discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers." He described mathematically how, for example, magnetic dipoles, long molecules or molecule chains can under certain conditions form ordered states, and what happens when they pass from an ordered to a disordered state. Such changes of order occur when, for example, a heated magnet changes from a state in which all the small atomic magnets are lined up in parallel to a disordered state in which the magnets are randomly oriented. Recently, he has been concerned with the physical chemistry of adhesion. *TIS

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