## Tuesday 11 October 2022

### On This Day in Math - October 11

Jeannie at the tomb of Tristan (from Tristan and Isolde) near Fowey, Cornwall

Perhaps some day in the dim future it will be possible to advance the computations faster than the weather advances and at a cost less than the saving to mankind due to the information gained. But that is a dream.
— Lewis Fry Richardson

The 284th day of the year; 284 is an amicable (or friendly) number paired with 220. The divisors of 220 add up to 284 and the divisors of 284 add up to 220. Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by which some of these numbers could be derived was invented circa 850 by Thābit ibn Qurra (826-901).(Can you find the next pair?)

jim wilder ‏@wilderlab pointed out a variation of friendly numbers in degree three...
"Along the lines of friendly numbers... 136 = 2³ + 4³ + 4³ and 244 = 1³ + 3³ + 6³"

Because 284 is divisible by four, it must be the difference of two squares.  (related to 284/4 = 71) Algebra students may wish to find the two squares, and then prove the general relation.

EVENTS

1606 Kepler, having heard of Thomas Harriot’s work in natural philosophy from his friend John Erickson writes to ask Harriot’s view on colors, refraction, and causes of the rainbow. *Henry Stevens, Thomas Hariot, the mathematician, the philosopher, and the scholar
Thony Christie sent a tweet reminding me that Harriot's response did not include his knowledge of the law of sines for refraction. The law of refraction is named after Snel, but he was not the first person to discover it. The first discoverer seems to have been Thomas Harriot, who knew it by 1602, based on his observations in 1597 and 1598, but died before he could publish it. Snel's re-discovery of the law came in 1621; but he did not publish it before his death in 1626. Descartes was the first person to publish it, in his famous “Discourse on Method” *rohan.sdsu.edu

1809 Gauss’s wife Johanne died, following the birth of her third child Louis. *VFR

1868 Thomas Alva Edison ﬁled papers for his ﬁrst invention, an electronic vote recorder to rapidly tabulate ﬂoor votes in Congress. Members of Congress rejected it. *VFR

 The macaroni box (1885) *Wik
1887 Patent #371,496 issued for the “comptometer,” the ﬁrst adding machine “absolutely accurate at all times.” It was invented by Dorr Eugene Felt of Chicago; a model was constructed in 1884. It wasn’t ﬁrst. *VFR This patent for the adding machine was granted to Dorr Eugene Felt of Chicago, Illinois. His Comptometer was the first practical key-driven calculator with sufficient speed, reliability and economic benefit. He called his original prototype the "Macaroni box", a rough model that Felt created over the year-end holidays in 1884-85. The casing was a grocery macaroni box, assembled with a jackknife using meat skewers as keys, staples as key guides and elastic bands for springs. Door improved his design, producing his earliest commercial wooden-box Comptometer from 1887 thru 1903, leading to the first steel case Model A (1904 that would be standard for the remainder for all "shoebox" models. Electric motor drive was introduced in the 1920's. *TIS

1939 Albert Einstein “wrote” President F. D. Roosevelt that “Some recent work by E. Fermi and L. Szilard ... leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. ... This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may be constructed.”
The letter, drafted by Fermi, Szilard, and Wigner and seems not to have actually been signed by Einstein until August 10, and was then given to Alexander Sachs, a confident of Roosevelt, who did not deliver it to him until October 30. Roosevelt quickly started the Manhattan Project. Einstein later regretted signing this letter. *(VFR & Brody & Brody); (the letter can be read at Letters of Note) They recognized the process could generate a lot of energy leading to power and possibly weapons. There was also concern the Nazi government of Germany was already searching for an atomic weapon. This letter would accomplish little more than the creation of a "Uranium Committee" with a budget of \$6,000 to buy uranium and graphite for experiments.
Sir Fred Soddy's book, The Interpretation of Radium, inspired H G Wells to write The World Set Free in 1914, and he dedicated the novel to Soddy's book. Twenty years later, Wells' book set Leo Szilard to thinking about the possibility of Chain reactions, and how they might be used to create a bomb, leading to his getting a British patent on the idea in 1936. A few years later Szilard encouraged his friend, Albert Einstein , to write a letter to President Roosevelt about the potential for an atomic bomb. The prize-winning science-fiction writer, Frederik Pohl , talks about Szilard's epiphany in Chasing Science (pg 25),
".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."

1988 A 109 digit number, 11104 +1, was factored by Mark Manasse and Arjen Lenstra using a quadratic sieve and a network of hundreds of computers in the US, Europe, and Australia. *FFF pg 570
For those who care to attempt to find the factors for themselves, here are the digits:
as provided by Wolfram Alpha

1994 The space probe Magellan was carried in the cargo bay by the STS-30 Space Shuttle Atlantis mission launched from Kennedy Space Center in Florida. The space probe was named after the 16th-century Portuguese explorer Ferdinand Magellan. This was the first planetary spacecraft to be released from a shuttle in Earth orbit. It arrived at its planned polar orbit around Venus on 10 Aug 1990, which it circled once every 3-hr 15-min. As the planet rotated slowly beneath it, Magellan collected radar images of the surface in strips about 17-28 km (10-17 mi) wide and radioed back the information. Its mission included taking other measurements. On 11 Oct 1994, it was directed towards the surface, collecting data until it burned up in the atmosphere.*TIS

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BIRTHS

1675 Samuel Clarke (11 October 1675 Norwich – 17 May 1729), defender of Newton’s physical theories against Leibniz. *VFR Clarke was considered the greatest metaphysician in England when Locke died in 1704. In 1706 Newton asked Clarke to translate his Opticks into Latin.*SAU

1758 (Heinrich) Wilhelm (Matthäus) Olbers(11 Oct 1758; 2 Mar 1840) was a German astronomer and physician, born in Arbergen, Germany. While practicing medicine at Bremen, he calculated the orbit of the comet of 1779, discovered the minor planets (asteroids) Pallas (1802) and Vesta (1807), and discovered five comets (all but one already observed at Paris). He also invented a method for calculating the velocity of falling stars. He is also known for Olber's paradox which asks "why is the night sky dark if there are so many bright stars all around to light it?" *TIS

1822 John Daniel Runkle (October 11, 1822 – July 8, 1902) was a U.S. educator and mathematician. B.S. in mathematics, 1851, Harvard College, second president of the Massachusetts Institute of Technology, was associated with the Nautical Almanac computation project from 1849 to 1884. In 1858 he founded the journal Mathematical Monthly and edited it for three years, when publication ceased. In 1860 he was a member of the committee that prepared the “Objects and Plan of an Institute of Technology” which led to the establishment of MIT. In 1862 he became MIT’s first secretary, and in 1865 he joined the new faculty as professor of mathematics, where he remained until 1902. He served as president pro-tem, 1868-1870, and was MIT’s second president, 1870-1878. He was married to Catherine Robbins Bird Runkle. *MIT History

1881 Lewis Fry Richardson (11 Oct 1881; 30 Sep 1953) British physicist and psychologist who first applied mathematics to accurate weather prediction. Richardson applied the mathematical method of finite differences to predicting the weather (1922). In his life, he held various posts: at the National Physical Laboratory, the Meteorological Office, and several university posts in physics or technology. Also, he was a chemist with National Peat Industries and in charge of the physical and chemical laboratory of the Sunbeam Lamp Co. Early application of mathematical techniques for systematically forecasting the weather were limited by extensive computation time: three months to predict weather for the next 24 hours. With electronic computers available after WW II made his methods became practical. He wrote several books applying mathematics to the causes of war. He contributed to calculus and the theory of diffusion for eddy-diffusion in the atmosphere. The Richardson number, a quantity involving gradients (change over distance) of temperature and wind velocity, is named after him.*TIS

1885 Alfréd Haar (11 October 1885, Budapest – 16 March 1933, Szeged) was a Hungarian mathematician who is best remembered for his work on analysis on groups, introducing a measure on groups, now called the Haar measure. *SAU
In 1904 he began to study at the University of Göttingen. His doctorate was supervised by David Hilbert. The Haar measure, Haar wavelet, and Haar transform are named in his honor. Between 1912 and 1919 he taught at Franz Joseph University in Kolozsvár. Together with Frigyes Riesz, he made the University of Szeged a centre of mathematics. He also founded the Acta Scientiarum Mathematicarum magazine together with Riesz. *Wik

1910 Cahit Arf (11 Oct 1910, 26 Dec 1997) Much of Arf's most important work was in algebraic number theory and he invented Arf invariants which have many applications in topology. His early work was on quadratic forms in fields, particularly fields of characteristic 2. His name is not only attached to Arf invariants but he is also remembered for the Hasse-Arf Theorem which plays an important role in class field theory and in Artin's theory of L-functions. In ring theory, Arf rings are named after him. *SAU

1916 Robert Eugene Marshak (October 11, 1916 – December 23, 1992) was an American physicist dedicated to learning, research, and education.
Marshak was born in the Bronx, New York City. His parents were immigrants to New York from Minsk. He was educated at Columbia University.
Marshak received his PhD from Cornell University in 1939. Along with his thesis advisor, Hans Bethe, he discovered many of the fusion aspects involved in star formation. This helped him on his work for the Manhattan Project, in Los Alamos, during World War II.
In 1947, at the Shelter Island Conference, Marshak presented his two-meson hypothesis about the pi-meson, which were discovered shortly thereafter.[1]
In 1957, he and George Sudarshan proposed a V-A ("vector" minus "axial vector") Lagrangian for weak interactions, which was later independently discovered by Richard Feynman and Murray Gell-Mann. His biography below, is explicit about it "Perhaps Marshak's most significant scientific contribution was the proposal of the V-A Theory of Weak Interactions (the fourth force in nature) in collaboration with his student George Sudarshan. Unfortunately, the pair published the theory only in a conference proceedings for a meeting in Italy. Six months later, a different derivation of the same concept was published by Feynman and Gell-Mann in a mainstream scientific journal. Marshak had talked with Feynman about the general problem in California some time before. Though the V-A Concept was considered to be one of the most important contributions to theoretical physics, a Nobel Prize was never awarded for it." Sudarshan himself later commented in a TV interview in 2006 that Murray Gell-Mann got the idea from him, in an informal coffee time!
He was Chairman of the Department of Physics at the University of Rochester for fourteen years (1956 to 1970)
He was the President of the City College of New York from 1970-1979.
Marshak died by accidental drowning in Cancún, Mexico in 1992. *Wik

DEATHS

1697 Stephano Angeli ( 23 September 1623 , Venice -  11 October 1697 , Padua)was an Italian mathematician who worked on infinitesimals and used them to study spirals, parabolas and hyperbolas.
In Bologna he came under the influence of Cavalieri.  Cavalieri was teaching at the University of Bologna, one of the oldest and most famous universities in Europe, dating from the 11th century. After leaving Bologna, Angeli continued his contacts with Cavalieri by correspondence, and was entrusted to publish Cavalieri's final work, Exercitationes geometricae sex, since by 1647 Cavalieri's health had deteriorated to such an extent that he was unable to carry out the work himself. Angeli also corresponded with a number of other mathematicians including Torricelli and Viviani.*SAU

1698 William Molyneux  (17 April 1656; Dublin – 11 October 1698; Dublin) was an Irish scientist and philosopher who worked on optics. Perhaps his best known scientific work was Dioptrica Nova, A treatise of dioptricks in two parts, wherein the various effects and appearances of spherick glasses, both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of humane life, are explained, published in London 1692.
In 1687 he invented a new type of sundial called a Sciothericum telescopicum that used special double gnomon and a telescope to measure the time of noon to within 15 seconds. "measured time by day and night." *SAU

1708 Ehrenfried Walter von Tschirnhaus  (10 April 1651 – 11 October 1708) was a German mathematician who worked on the solution of equations and the study of curves. He is best known for the transformation which removes the term of degree n-1 from an equation of degree n. *SAU The Tschirnhaus transformation, by which he removed certain intermediate terms from a given algebraic equation, is well-known. It was published in the scientific journal Acta Eruditorum in 1683. In 1696, Johann Bernoulli posed the problem of the brachystochrone to the readers of Acta Eruditorum. Tschirnhaus was one of only five mathematicians to submit a solution. Bernoulli published these contributions (including Tschirnhaus') along with his own in the journal in May of the following year.
Von Tschirnhaus produced various types of lenses and mirrors, some of them are displayed in museums. He erected a large glass works in Saxony, where he constructed burning glasses of unusual perfection and carried on his experiments. *Wik

1731 John Craig (1663 – October 11, 1731) Scottish mathematician who published three important textbooks.While he was still a student in Edinburgh, Craig published Methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi which contains Leibniz's dy/dx notation. This notation is also used in the work he published in 1693, Tractatus mathematicus de figurarum curvilinearum quadraturis et locis geometricis which was the first text published in England to contain the integration symbol ∫ . Dale writes "The standard of his work was such that he was noted as a mathematician of the first order ... and the "Acta Eruditorum" of Leipzig ranked him among the originators of the calculus (after Leibniz, but before Newton)". *SAU

1791 Johann Castillon (15 January 1704 in Castiglion Fiorentino, Toskana - 11. October 1791 in Berlin) was an Italian mathematician and astronomer who wrote on the cardioid and may have created the name.*SAU Castillon published the correspondence between Gottfried Wilhelm Leibniz and Johann Bernoulli , edited works of Leonhard Euler and published a review of Newton's Arithmetica Universalis. He also translated Locke's basic concepts of physics into French. *Wik

1852 Ferdinand Gotthold Max Eisenstein (16 Apr 1823, 11 Oct 1852) died of pulmonary tuberculosis at age 29.*VFR German mathematician whose work covered a range of topics including the theory of elliptic functions, and quadratic and cubic forms, which led to cyclotomy, the reciprocity theorem for cubic residues, and also theorems for quadratic and biquadratic residues from partition of prime numbers. *TIS In 1843 he met William Rowan Hamilton in Dublin, who gave him a copy of his book on Niels Henrik Abel's proof of the impossibility of solving fifth degree polynomials, a work that would stimulate Eisenstein's interest in mathematical research. He specialized in number theory and analysis, and proved several results that eluded even Gauss. *Wik

1889 James Prescott Joule (24 Dec 1818, 11 Oct 1889) English physicist who established that the various forms of energy - mechanical, electrical, and heat - are basically the same and can be changed, one into another. Thus he formed the basis of the law of conservation of energy, the first law of thermodynamics. He discovered (1840) the relationship between electric current, resistance, and the amount of heat produced. In 1849 he devised the kinetic theory of gases, and a year later announced the mechanical equivalent of heat. Later, with William Thomson (Lord Kelvin), he discovered the Joule-Thomson effect. The SI unit of energy or work , the joule (symbol J), is named after him. It is defined as the work done when a force of 1 newton moves a distance of 1 metre in the direction of the force.*TIS

1940 Vito Volterra (3 May 1860, 11 Oct 1940)Italian mathematician who made important contributions to calculus, and mathematical theories in astronomy, elasticity and biometrics. His mathematical talent appeared as a young boy. In 1905, he began to develop the theory of dislocations in crystals that led to improved understanding of the behaviour of ductile materials. During WWI he established the Italian Office of War Inventions and designed weapons for use by airships, for which he proposed the use of helium instead of flammable hydrogen. He is remembered for achievements in function theory and differential equations. In biology, in 1925, he formulated a pair of differential equations relating populations of prey and predators (also independently proposed by Alfred J. Lotka in 1925)*TIS (His date of death is sometimes given as 10 October, so that date is also listed)

1943 Geoffrey Thomas Bennett (30 June 1868, 11 Oct 1943) His most famous paper is the two page paper A new four-piece skew mechanism which he published in the journal Engineering in 1903. In it Bennett considers a skew hinged four-bar mechanism in three dimensional space. The angle between the hinges in a bar is called the twist. This mechanism is movable only if the opposite sides are equal. Then it follows as a consequence that the sines of the twists are proportional to the lengths of the bars. This remarkable mechanism Bennett called a skew isogram. It uses the fewest rods possible to build a useful mechanism. In a subsequent 22 page paper The skew isogram mechanism which he published in 1914, Bennett presented many interesting properties of the skew isogram, some without proofs. These proofs were not written down until Bernard Groeneveld's thesis Geometrical considerations on space kinematics in connection with Bennett's mechanism presented to the Technische Hogeschool te Delft in 1954. In 1922 Bennett published The three-bar sextic curve. In this paper he obtained the characteristics of the curve (now called the couple curve) as the locus of the Laguerre images of the conjugate points on the Hessian of an elliptic cubic. He therefore treated a curve defined in the area of kinematics by the methods of algebraic geometry. *SAU A 1913 Paper on The skew Isogram by Bennett

1979 Franciszek Leja (January 27, 1885 in Grodzisko Górne near Przeworsk – October 11, 1979 in Kraków, Poland) Polish mathematician who greatly influenced Polish Mathematics in the period between the two World Wars.
He was born to a poor peasant family in the southeastern Poland. After graduating from the University of Lwów he was a teacher of mathematics and physics in high schools from 1910 until 1923, among others in Kraków. From 1924 until 1926 he was a professor at the Warsaw University of Technology and from 1936 until 1960 in the Jagiellonian University.
During the Second World War he lectured on the underground universities in Łańcut and Lezajsk. But after the German invasion of Poland in 1939 life there became extremely difficult. There was a strategy by the Germans to wipe out the intellectual life of Poland. To achieve this Germans sent many academics to concentration camps and murdered others. In one of such actions he was sent to the Sachsenhausen concentration camp which he fortunately survived.
Since 1948 he worked for the Institute of Mathematics of the Polish Academy of Sciences. He was a co-founder of the Polish Mathematics Society in 1919 and from 1963 until 1965 the chairman. Since 1931 he was a member of the Warsaw Science Society (TNW).
His main scientific interests concentrated on analytic functions, in particular the method of extremal points and transfinite diameters. *Wik

1989 Mark Grigorievich Krein (3 April 1907 – 17 October 1989) was a Soviet Jewish mathematician, one of the major figures of the Soviet school of functional analysis. He is known for works in operator theory (in close connection with concrete problems coming from mathematical physics), the problem of moments, classical analysis and representation theory.
He was born in Kiev, leaving home at age 17 to go to Odessa. He had a difficult academic career, not completing his first degree and constantly being troubled by anti-Semitic discrimination. His supervisor was Nikolai Chebotaryov.
He was awarded the Wolf Prize in Mathematics in 1982 (jointly with Hassler Whitney), but was not allowed to attend the ceremony.
He died in Odessa.
On 14 January 2008, the memorial plaque of Mark Krein was unveiled on the main administration building of I.I. Mechnikov Odessa National University. *Wik

1996 Lars Valerian Ahlfors (18 Apr 1907, 11 Oct 1996) Finnish mathematician who was awarded one of the first two Fields Medals in 1936 for his work with Riemann surfaces. He also won the Wolf Prize in 1981.*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