## Tuesday, 23 January 2018

### On This Day in Math - January 23

 Me Considering Pascal Considering the Roulette

Nature creates curved lines while humans create straight lines.
~Hideki Yukawa

The 23rd day of the year; 23! is 23 digits long (22, 23, and 24 each solve n! is n digits in length (decimal)). 23 is also the answer to the classic Birthday Problem. (How many randomly selected people in a group makes the probability greater than 50% that (at least)two share a common birthdate.)

There are only two values of $x>0$ so that $x^3 + (x+1)^3 +(x+2)^3$is a perfect square. The largest is 23. $23^3+24^3 + 25^3 = 41616 = 204^2$ *@BenVitale

decimal # 11111111111111111111111 is prime (23 ones) . *

EVENTS

1656 Blaise Pascal wrote the ﬁrst of his eighteen Provincial Letters.

1640 John Pell wrote Mersenne that Thomas Harriot (1560–1621) had found the law of refraction, now known as Snell’s law.*VFR The first known accurate description of the law was by the scientist Ibn Sahl at Baghdad court, when in 984 he used the law to derive lens shapes that focus light with no geometric aberrations in the manuscript On Burning Mirrors and Lenses.
Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction:
$\frac{sin (\theta_1)}{sin(\theta_2)}=\frac{v_1}{v_2}= \frac{n_2}{n_1}$ *Wik

1675 Christiaan Huygens drew a sketch in his notebook of a watch mechanism with a coiled spring regulator and then, “Eureka – I have found it”. He believed he had found a method of regulating a clock that would keep accurate time and not be affected by motion for use in attacking the problem of longitude. (Hooke had presented a watch regulated by a spring in the early 1660’s to the Royal Society for exactly the same goal in response to Huygen’s first pendulum clock. ) *Lisa Jardine, Ingenious Pursuits, pg 148

1764 Harvard Hall, the last of Harvard’s original buildings, burned down in a nor'easter, taking with it almost the entire College library & John Harvard's book collection.  The job of replacing the valuable scientific instruments housed in the building fell to John Winthrop, the second Hollis professor of mathematics and natural philosophy at Harvard. He was also friend and advisor of George Washington. *VFR

1812, the second day of powerful earthquakes struck, with an epicenter in the far southeast corner of Missouri. It was a part of a three-month series in the central Mississippi River valley, known as the New Madrid earthquakes. They began on 16 Dec 1811, with the first two major earthquakes, six hours apart, each with an epicenter in northeastern Arkansas. All were felt hundreds of miles away. All were powerful, about magnitude 7-7.5. There were many aftershocks, and an a final major earthquake on 7 Feb 1812. Contemporary accounts tell of houses damaged, chimneys toppled, remarkable geological phenomena and landscapes changed. They remain among the most powerful earthquakes in the United States. The New Madrid fault remains a concern (especially in my neighborhood here in Possum Trot, Ky, only 100 or so miles away). *TIS

1848 Gold discovered in California. Jonas Clark soon was on hand with a wagon load of shovels and so made a wagon load of money. He used it to found Clark University in Worcester, MA, which,in the early 1890’s, had the strongest mathematics department in the country. *VFR

1883 The first session of the Edinburgh Mathematical Society, *Proceedings of the Edinburgh Mathematical Society, Volumes 1-4

1896, Wilhelm Roentgen first made a public lecture-demonstration of his X-ray device, in Würzburg, Germany. *TIS

1896 Two months after Rontgen discovered X-rays (the x was for unknonwn), Henri Poincare was sent photographs of these X-rays and was so amazed that he passed them on to two doctors and asked if they could duplicate Rontgen's work. On January 23 they would present a paper on their results at the French Academy with Henri Becquerel in the audience. Within months he would discover rays coming from Uranium. *Brody & Brody, The Science Class You Wished You Had

1911, Marie Curie's nomination to the French Academy of Sciences, having already won one Nobel Prize, is nevertheless voted down by the Academy's all-male membership. She went on to win a second Nobel Prize. *TIS

1913 Russian mathematician Andrei Andreyevich Markov addressed the Imperial Academy of Sciences in St. Petersburg, reading a paper titled “An example of statistical investigation of the text Eugene Onegin concerning the connection of samples in chains.” The idea he introduced that day is the mathematical and computational device we now know as a Markov chain.
Markov’s 1913 paper was not his first publication on “samples in chains”; he had written on the same theme as early as 1906, but it was the 1913 paper that was widely noticed, both in Russia and abroad, and that inspired further work in the decades to come. The earlier discussions were abstract and technical, giving no hint of what the new probabilistic method might be good for; in 1913 Markov demonstrated his technique with a novel and intriguing application—analyzing the lexical structure of Alexander Pushkin’s poem Eugene Onegin. Direct extensions of that technique now help to identify genes in DNA and generate gobbledygook text for spammers. *Brian Hayes

1930 Clyde Tombaugh photographed the planet Pluto, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. *TIS
*Northwestern University

1986 Science reported that a statistical analysis of word frequencies on a newly discovered poem attributed to Shakespeare concluded “There is no convincing evidence for rejecting the hypothesis that Shakespeare wrote it.” Otherwise said, the poem “ﬁts Shakespeare as well as Shakespeare ﬁts Shakespeare.” [Mathematics Magazine 59 (1986), p 183]. *VFR

1959 Robert Noyce Conceives the Idea for a Practical Integrated Circuit:
Robert Noyce, as a co-founder and research director of Fairchild Semiconductor, was responsible for the initial development of silicon mesa and planar transistors, which led to a commercially applicable integrated circuit. In 1968 Noyce went on to found Intel Corp. with Gordon Moore​ and Andy Grove.*CHM

2003 And Then it was gone.... The final, very weak signal from Pioneer 10 was received on January 23, 2003 when it was 12 billion kilometers (80 AU) from Earth. Launched on Mar 10,1972, Pioneer 10 crossed the orbit of Saturn in 1976 and the orbit of Uranus in 1979. On June 13, 1983, Pioneer 10 crossed the orbit of Neptune, the outermost planet at the time, and so became the first man-made object to leave the proximity of the major planets of the solar system.
The last successful reception of telemetry was received from Pioneer 10 on April 27, 2002; subsequent signals were barely strong enough to detect, and provided no usable data. *Wik
2013 The Institute for Applied Computational Science of the Harvard School of Engineering and Applied Sciences celebrated the centenary of Markov’s 1913 paper which promoted the wide study and use of Markov Chains. (see 1913 above) **Brian Hayes

2013 On January 23rd Dr. Curtis Cooper of Central Missouri University discovered the 48th known Mersenne prime, 257,885,161-1, a 17,425,170 digit number. The GIMP site records this as the 25th of January, so I shall use both dates until I figure out why two different dates reported.

BIRTHS

1693 Georg Bernhard Bilfinger (23 Jan 1693; 18 Feb 1750) German philosopher, mathematician, statesman, and author of treatises in astronomy, physics, botany, and theology. He is best known for his Leibniz-Wolffian philosophy, a term he coined to refer to his own position midway between those of the philosophers Gottfried Wilhelm Leibniz and Christian Wolff.*TIS

1719 John Landen (23 Jan 1719; died 15 Jan 1790) British mathematician who made important contributions on elliptic integrals. As a trained surveyor and land agent (1762-88), Landen's interest in mathematics was for leisure. He sent his results on making the differential calculus into a purely algebraic theory to the Royal Society, and also wrote on dynamics, and summation of series. Landen devised an important transformation, known by his name, giving a relation between elliptic functions which expresses a hyperbolic arc in terms of two elliptic ones. He also solved the problem of the spinning top and explained Newton's error in calculating the precession. Landen was elected a Fellow of the Royal Society in 1766. He corrected Stewart's result on the Sun-Earth distance (1771).*TIS

1785 Matthew Stewart (15 Jan 1717 in Rothesay, Isle of Bute, Scotland - 23 Jan 1785 in Catrine, Ayrshire, Scotland)was a Scottish geometer who wrote on geometry and planetary motion. Stewart's fame is based on General theorems of considerable use in the higher parts of mathematics (1746), described by Playfair as, "... among the most beautiful, as well as most general, propositions known in the whole compass of geometry." *SAU

1806 Ernst Ferdinand Adolf Minding (23 Jan 1806 in Kalisz,Russian Empire (now Poland) - 3 May 1885 in Dorpat, Russia (now Tartu, Estonia))His work, which continued Gauss's study of 1828 on the differential geometry of surfaces, greatly influenced Peterson. In 1830 Minding published on the problem of the shortest closed curve on a given surface enclosing a given area. He introduced the geodesic curvature although he did not use the term which was due to Bonnet who discovered it independently in 1848. In fact Gauss had proved these results, before either Minding of Bonnet, in 1825 but he had not published them.
Minding also studied the bending of surfaces proving what is today called Minding's theorem in 1839. The following year he published in Crelle's Journal a paper giving results about trigonometric formulae on surfaces of constant curvature. Lobachevsky had published, also in Crelle's Journal, related results three years earlier and these results by Lobachevsky and Minding formed the basis of Beltrami's interpretation of hyperbolic geometry in 1868.
Minding also worked on differential equations, algebraic functions, continued fractions and analytic mechanics. In differential equations he used integrating factor methods. This work won Minding the Demidov prize of the St Petersburg Academy in 1861. It was further developed by A N Korkin. Darboux and Émile Picard pushed these results still further in 1878. *SAU

1840 Ernst Abbe (23 Jan 1840, 14 Jan 1905) German physicist who made theoretical and technical innovations in optical theory. He improved microscope design, such as the use of a condenser lens to provide strong, even illumination (1870). His optical formula, now called the Abbe sine condition, applies to a lens to form a sharp, distortion-free image He invented the Abbe refractometer for determining the refractive index of substances. In 1866, he joined Carl Zeiss' optical works, later became his partner in the company, and in 1888 became the owner of the company upon Zeiss' death. Concurrently, he was appointed professor at the Univ. of Jena in 1870 and director of its astronomical and meteorological observatories in 1878.*TIS

1853 Kazimierz Żorawski (June 22, 1866 – January 23, 1953) was a Polish mathematician. His work earned him an honored place in mathematics alongside such Polish mathematicians as Wojciech Brudzewski, Jan Brożek (Broscius), Nicolas Copernicus, Samuel Dickstein, and Stefan Banach,.
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these disciplines was to prove important in other fields of mathematics and science, such as differential equations, geometry and physics (especially astrophysics and cosmology).*Wik

1857 Andrija Mohorovicic (23 Jan 1857; 18 Dec 1936) Croatian meteorologist and geophysicist who discovered the boundary between the Earth's crust and mantle, a boundary now named the Mohorovicic discontinuity. In 1901 he was appointed head of the complete meteorological service of Croatia and Slavonia, he gradually extended the activities of the observatory to other fields of geophysics: seismology, geomagnetism and gravitation. After the Pokuplje (Kupa Valley) earthquake of 8 Oct 1909, he analyzed the spreading of seismic waves with shallow depths through the Earth. From these, he was the first to establish, on the basis of seismic waves, a surface of velocity discontinuity separating the crust of the Earth from the mantle, now known as the Mohorovicic discontinuity.
*TIS

1862 David Hilbert (23 Jan 1862; 14 Feb 1943) German mathematician who reduced geometry to a series of axioms and contributed substantially to the establishment of the formalistic foundations of mathematics. In his book, Foundations of Geometry, he presented the first complete set of axioms since Euclid. His work in 1909 on integral equations led to 20th-century research in functional analysis (in which functions are studied as groups.) Today Hilbert's name is often best remembered through the concept of Hilbert space in quantum physics, a space of infinite dimensions.*TIS
He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.*Wik
In Constance Reid's "Hilbert", she describes his mother thus: "She was an unusual woman-in the German way of expression, 'an original' - interested in philosophy and astronomy and fascinated by prime numbers."

1872 Paul Langevin (23 Jan 1872; 19 Dec 1946) French physicist who was the first to explain (1905) the effects of paramagnetism and diamagnetism (the weak attraction or repulsion of substances in a magnetic field) using statistical mechanics. He further theorized how the effects could be explained by how electron charges behaved within the atom. He popularized Einstein's theories for the French public. During WW I, he began developing a source for high intensity ultrasonic waves, which made sonar detection of submarines possible. He created the ultrasound from piezoelectric crystals vibrated by high-frequency radio circuits. In WW II, he spoke out against the Nazis, for which he was arrested and imprisoned, though he managed to escaped and fled to Switzerland.*TIS

1876 Alfredo Niceforo (23 Jan 1876;2 Mar 1960) Italian sociologist, criminologist, and statistician who posited the theory that every person has a "deep ego" of antisocial, subconscious impulses that represent a throwback to precivilized existence. Accompanying this ego, and attempting to keep its latent delinquency in check, according to his concept, is a "superior ego" formed by man's social interaction. This theory, which he published in 1902, bears some resemblance to the discoveries of psychoanalysis that were being made about the same time. *TIS

1878 Edwin Plimpton Adams (23 Jan 1878 in Prague - 31 Dec 1956 in Princeton, USA) studied at Harvard, Göttingen and Cambridge and became Physics Professor at Princeton. He is best known for his translations of some of Einstein's lectures. *SAU

1907 Hideki Yukawa (23 Jan 1907; 8 Sep 1981) Japanese physician and physicist who shared the 1949 Nobel Prize for Physics for “his prediction of the existence of mesons on the basis of theoretical work on nuclear forces.” In his 1935 paper, On the Interaction of Elementary Particles*, he proposed a new field theory of nuclear forces that predicted the existence of the previously unknown meson. Mesons are particles heavier than electrons but lighter than protons. One type of meson was subsequently discovered in cosmic rays in 1937 by American physicists, encouraging him to further develop meson theory. From 1947, he worked mainly on the general theory of elementary particles in connection with the concept of the “non-local” field. He was the first Japanese Nobel Prize winner. *TIS (Yukawa donated a bronze crane that works as a wind chime when pushed against a traditional peace bell from which it is suspended at the Children's Peace Museum in Hiroshima. On the bell in his handwriting is the wish, "A Thousand Paper Cranes. Peace on Earth and in the Heavens."(Is this crane still there? I understood it had been moved."

1924 Sir Michael James Lighthill (23 Jan 1924, 17 Jul 1998) was a British mathematician who contributed to supersonic aerofoil theory and, aeroacoustics which became relevant in the design of the Concorde supersonic jet, and reduction of jet engine noise. Lighthill's eighth power law which states that the acoustic power radiated by a jet is proportional to the eighth power of the jet speed. His work in nonlinear acoutics found application in the lithotripsy machine used to break up kidney stones, the study of flood waves in rivers and road traffic flow. Lighthill also introduced the field of mathematical biofluiddynamics. Lighthill followed Paul Dirac as Lucasian professor of Mathematics (1969) and was succeeded by Stephen Hawking (1989) *TIS

1947 Peter Jephson Cameron (23 January 1947;Toowoomba, Queensland, Australia -) is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London.
Cameron received a B.Sc. from the University of Queensland and a D.Phil. in 1971 from University of Oxford, with Peter M. Neumann as his supervisor. Subsequently he was a Junior Research Fellow and later a Tutorial Fellow at Merton College, Oxford, and also lecturer at Bedford College, London. He was awarded the London Mathematical Society's Whitehead Prize in 1979 and is joint winner of the 2003 Euler Medal.
Cameron specialises in algebra and combinatorics; he has written books about combinatorics, algebra, permutation groups, and logic, and has produced over 250 academic papers.[3] He has an Erdős number of 1, with whom he posed the Cameron–Erdős conjecture. *Wik

DEATHS

1805 Claude Chappe (25 Dec 1763, 23 Jan 1805)French engineer who invented the semaphore visual telegraph. He began experimenting in 1790, trying various types of telegraph. An early trial used telescopes, synchronised pendulum clocks and a large white board, painted black on the back, with which he succeeded in sending a message a few sentences long across a 16km (10mi) distance. To simplify construction, yet still easily visible to read from far away, he changed to using his semaphore telegraph in 1793. Smaller indicators were pivoted at each end of large horizontal member. The two indicators could each be rotated to stand in any of eight equally spaced positions. By setting them at different orientations, a set of corresponding codes was used to send a message.*TIS

1810 Johann Wilhelm Ritter (16 Dec 1776, 23 Jan 1810) German physicist who discovered the ultraviolet region of the spectrum (1801) and thus helped broaden man's view beyond the narrow region of visible light to encompass the entire electromagnetic spectrum from the shortest gamma rays to the longest radio waves. After studying Herschel's discovery of infrared radiation, he observed the effects of solar radiation on silver salts and deduced the existence of radiation outside the visible spectrum. He also made contributions to spectroscopy and the study of electricity. *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