Friday 14 February 2020

On This Day in Math - February 14

Happy Valentine's day to my Jeannie

 I can testify that she is a great mathematician, but that she is a woman, I cannot swear.
{When asked to comment whether Emmy Noether was a great woman mathematician,}
 ~Edmund Landau

The 45th day of the year; 45 is the third Kaprekar number.  (452 = 2025 and 20 + 25 = 45)
The next two Kaprekar numbers both have two digits, can you find them?
BONUS: I found these on a post at the Futility Closet by Greg Ross:
452 = 2025
20 + 25 = 45

453 = 91125
9 + 11 + 25 = 45

454 = 4100625
4 + 10 + 06 + 25 = 45

45 is a palindrome in base 2 {101101} and base 8{55}

And a paradoxical anagram about 45; Over fifty = forty-five


1535 Only eight days before his mathematical contest with Fiore, Tartaglia discovers a general method for solving cubics of the form ax3 + bx = c. On the day of the contest this turned out to give him a huge advantage. Thony Christie at the Renaissance Mathematicus described it this way, "Tartaglia sat down and almost instantly gave the correct answers to Fiore’s entire list, who was completely unable to solve a single one of Tartaglia’s questions. This whitewash made Tartaglia a star amongst the reckoning masters." In Mario Livio's "The Equation That Couldn't be Solved" he says that Tartaglia finished all 30 of Fiore's questions in less than two hours. All 30 of Fiore's questions were of the form ax3 + bx = c, the type Tartaglia had discovered a general solution for  only eight days before the contest.

 1747 Founding of the Ecole des Ponts et Chauss´ees (The School of Bridges and Roads) in Paris. Many famous French mathematicians, including Cauchy, Fresnel, and Henri Becquere were students there. Often referred to as "les Ponts", is the world's oldest civil engineering school. It remains to this day one of the most prestigious and selective French Grandes Écoles. *Wik

In 1747, a paper on the discovery of Earth's wobbling motion on its axis by British astronomer, James Bradley was read at the Royal Society. For this variation, he coined the name nutation (from Latin "nutare" to nod). Bradley first noticed the fluctuation during his studies of parallax at Molyneux's observatory. Attributing it to the moon's gravitational influence, he withheld any announcement until he had observed a full cycle of the motion of the moon's nodes, taking about 18.6 years. In 1748, he was honored with the Copley Medal of the Royal Society *TIS

1761 Euler uses his circles (Euler diagrams) in four letters, CII to CV of Volume I, written between February 14 and February 24, 1761. *Ed Sandifer, Letters to a German Princess

1814 Laplace presented his Essai phlosophique sur les probabilit´es (A Philosophical Essay on Probabilities) to the Acad´emie des Sciences in Paris. *VFR

1832 Gauss writes in a letter to Gerling: “Let me add further that I have this day received from Hungary a little work on the Non-Euclidean geometry, in which I find all my own ideas and results developed with greater elegance, although in a form so concise as to offer great difficulty to anyone not familiar with the subject. ... I regard this young geometer [Janos] Bolyai as a genius of the first order.” *G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 309

1946 John Mauchly and J. Presper Eckert Unveil The ENIAC:
John Mauchly and J. Presper Eckert unveil the much-anticipated ENIAC at the University of Pennsylvania. The ENIAC calculated 5,000 operations per second -- 1,000 times faster than its contemporaries. Impressive in size as well as strength, the machine occupied over 1,500 square feet of space, weighed 30 tons, and used 18,000 vacuum tubes. *CHM

1981 The first computerized wedding took place. The couple recorded their vows on an Apple computer. *VFR The bride and groom approached the electronic altar. It positively glowed. The minister's words walked across their computer screen: " long as you both shall live?" The bride and groom both typed: "I will." The minister said: "You may kiss the bride," and the groom inputted: "((((KISS))))." Then these words popped up on the screen: "Sniff, sniff." There's one at every wedding—even at the world's first nationally computerized wedding, the happy ending to a computerized courtship and the ultimate in modern matrimony. *People Magazine

1990 The Pale Blue Dot photograph of Earth is sent back from the Voyager 1 probe after completing its primary mission, from around 3.5 billion miles away. *Wik  A Valentine back to the Earth  from the edge of the solar system.  Subsequently, the title of the photograph was used by Carl Sagan as the main title of his 1994 book, Pale Blue Dot: A Vision of the Human Future in Space

2017 A paper in arxiv on this date gave two sets of 12 integers that each had the same set of 4-sums (all possible outcomes from summing four of the integers) This disproved a flawed 1968 proof by J. Ewell that no such sets were possible. The area of interest was first introduced by L. Mosel who asked for which numbers n are all sets of n elements completely determined by the set of all k-sums. That is, If I tell you all the sums possible from adding four of the numbers, can you tell me the 12 numbers. The counter-example in 2017 was published by J. E. Isomurodov and K. P. Kokhas . The two sets are A=(0, 0, 1, -1, 2, -2, 4, 4, 7, -7, 7, -7) and B=(1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 8, -8)


1468 Johann Werner,(14 Feb 1468 in Nuremberg, Germany - May 1522 in Nuremberg, Germany) discoverer of prosthaphaeresis early in the sixteenth century, born "The first person to publish an account of prosthaphaeresis was Nicolaus Reimers Baer who attributed his knowledge of it to Jost Bürgi who he said had learnt it from Paul Wittich. It was at this point that Tycho claimed that he had discovered the technique together with Wittich, as part of his dispute with Baer on the origins of the so-called Tychonic astronomical system. Tycho accused Baer of having stolen the system. However Tycho’s claim is highly dubious, although Bürgi and Baer both obviously fully understood the prosthaphaerasis method and could utilise it perfectly, Tycho just as obviously didn’t understand it properly and made serious errors when using it. Not the achievements of somebody who supposedly invented the method. Given these facts it is now accepted that Wittich either re-invented the method or had access to a manuscript containing Johannes Werner’s original discovery and taught the method to both Bürgi who understood it and Tycho who didn’t really." *Thony Christie

1827 George Bassett Clark (14 Feb 1827, 20 Dec 1891) Elder son in the American family of telescope makers and astronomers, Alvan Clark & Sons of Cambridge, Mass., who figured importantly in the great expansion of astronomical facilities which occurred during the second half of the 19th century. Before the family business began, George made a telescope in 1844 out of the melted-down brass of his school's broken dinner bell. His father, Alvan Clark, was at the time an established portrait painter, but his son's interest also spurred his father to begin making refractor telescopes. (Refractor telescopes use paired lenses to focus light.) The father taught himself to be a master optician, and eventually in business with his sons made the finest refractor telescopes of their time including five of the world's largest.*TIS

1839 Hermann Hankel (14 Feb 1839 in Halle, Germany - 29 Aug 1873 in Schramberg (near Tübingen), Germany). Hankel studied at Leipzig, Gottingen, and Berlin and was later Professor at Erlangen and Tubingen. He worked in Function Theory and the History of Mathematics. *VFR

1877 Edmund Georg Hermann Landau (14 Feb 1877 in Berlin, Germany - 19 Feb 1938 in Berlin, Germany) Although famous as a number theorist, he is best known for his textbooks which are written in an austere definition-theorem-proof style. His Grundlagen der Analysis is an excellent treatment of the development of our number systems from the Peano postualates. Reading this book is a good way to learn mathematical German. But if you are lazy, it has been translated into English. *VFR Landau gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.*SAU Legend has it that at the age of three, when is mother forgot her umbrella in a carriage, he replied, "It was number 354," and the umbrella was quickly re-acquired.
Landau is remembered as a somewhat "difficult" man to get along with. In fact his position at Gottingen supposedly was a very close decision between Landau and Oscar Peron. Klein selected Landau because he thought, "it is better if we don't have a man who is not easy."
Landau's father, on the other hand seems to have been an exceptionally kind man, as described by the following clip from Marcus du Sautoy's Music of the Primes:

1869 C.T.R. Wilson (14 Feb 1869, 15 Nov 1959)Scottish physicist who, with Arthur H. Compton, received the Nobel Prize for Physics in 1927 for his invention of the Wilson cloud chamber, which became widely used in the study of radioactivity, X rays, cosmic rays, and other nuclear phenomena. His discovery was a method of rendering visible the tracks of such electrically charged particles. It is based upon the formation of clouds, which develop when sufficiently moist air is suddenly expanded, thus dropping the temperature below the dew-point. Thereafter, vapour condenses into small drops, formed round dust particles, or even, an electrically charged atomic particle. The formation of droplets is so dense that photographs show continuous tracks of particles traveling through the chamber as white lines. *TIS

1896 Edward Arthur Milne (14 Feb 1896; 21 Sep 1950 at age 54) English astrophysicist and cosmologist best known for his development of kinematic relativity. Poor eyesight prevented him from active service in WWI, he did important war service in research in ballistics and sound ranging, and problems related to the atmosphere of the earth.. From 1920-29, he studied problems of radiative equilibrium and the theory of stellar atmospheres. He extended work done earlier by Schuster and by Schwarzschild, which he combined in a mathematical interesting integral equation now known as Milne's integral equation. Later, he turned to the theory of stellar structure and cosmology. After 1932, he concentrated on a new form of relativity called kinematic relativity, an alternative to Einstein's general theory.*TIS (In Eurekas and Euphorias Walter Gratzer tells an interesting story about Milne's rejected offer to provide his services to the war effort in WWII. Milne had given important service (above) in WWI and wrote to offer his services for this war as well, but received a rather dismissive letter to which he took offense. He used his extensive connections to have his anger made known to the higher-ups at the War Office. Eventually he received a request from a Brigadier General to come to his office. Milne arrived and amidst his tirade advised the General that the War Office should know that this war would be a scientific one, and the way he was treated was not the way to make the best use of eminent scientists. The General waited out Milne's outburst, and then asked a single question, "Did you win the Adams Prize in your year?" When Milne said he had not, but asked what that had to do with anything, the General replied, "I did!"
I'm not sure what, if any, Milne's contributions to the war effort in WWII were.)

1898 Fritz Zwicky (14 Feb 1898, 8 Feb 1974 at age 76) Swiss-American astronomer and physicist who proposed dark matter exists in the universe, and made valuable contributions to the theory and understanding of supernovas (stars that for a short time are far brighter than normal).*TIS

1917 Herbert A. Hauptman (14 Feb 1917, )American mathematician and crystallographer who, along with Jerome Karle, received the Nobel Prize for Chemistry in 1985. They developed mathematical methods for deducing the molecular structure of chemical compounds from the patterns formed when X rays are diffracted by their crystals. *TIS

1954 Vladimir Gershonovich Drinfel'd (February 4, 1954, ) is a Soviet-born mathematician at the University of Chicago.
The work of Drinfeld related algebraic geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced the notion of a quantum group (independently discovered by Michio Jimbo at the same time) and made important contributions into mathematical physics, including the ADHM construction of instantons, algebraic formalism of the Quantum inverse scattering method, and the Drinfeld–Sokolov reduction in the theory of solitons. He was awarded the Fields Medal in 1990.*Wik


1744 John Hadley (16 Apr 1682, 14 Feb 1744 at age 61) British mathematician and inventor who perfected methods for grinding and polishing telescope lenses. Hadley improved the reflecting telescope (first introduced by Newton in 1668) and produced the first of its kind having sufficient accuracy and power to be useful in astronomy. It had a 6 inch mirror. He is also known for the reflecting octant (1730) used at sea to measure the altitude of the Sun or a celestial body above the horizon to within one second of arc. It was the ancestor of the modern nautical sextant. He was a prominent member of the Royal Society, of which he was vice-president from 21 Feb 1728. John Hadley was the older brother of George Hadley. *TIS

1814 Eugene Charles Catalan (30 May 1814 in Bruges, French Empire (now Belgium)
- 14 Feb 1894 in Liège, Belgium) was a Belgian mathematician who defined the numbers called after him, while considering the solution of the problem of dissecting a polygon into triangles by means of non-intersecting diagonals. *SAU The Catalan numbers have a multitude of uses in combinatorics.

1943 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. (This may be somewhat exaggerated... Moritz Pasch and Giusseppe Peano had reworked Euclid and were important in Hilber's re-working of Geometry .) 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

1950 Karl Guthe Jansky (22 Oct 1905; 14 Feb 1950) was an American electrical engineer who discovered cosmic radio emissions in 1932. At Bell Laboratories in NJ, Jansky was tracking down the crackling static noises that plagued overseas telephone reception. He found certain radio waves came from a specific region on the sky every 23 hours and 56 minutes, from the direction of Sagittarius toward the center of the Milky Way. In the publication of his results, he suggested that the radio emission was somehow connected to the Milky Way and that it originated not from stars but from ionized interstellar gas. At the age of 26, Jansky had made a historic discovery - that celestial bodies could emit radio waves as well as light waves. *TIS

2001 Helmut Wielandt (19 December 1910 Niedereggenen, Lörrach, Germany – 14 February 2001) worked on finite groups and on finite and infinite permutation groups.*SAU

2007 James Eells (25 Oct 1926 in Cleveland, Ohio, USA - 14 Feb 2007 in Cambridge, England) made substantial and deep contributions to mathematics. His most important work was probably his 1964 paper Harmonic Mappings of Riemannian Manifolds. Eells went on to publish two definitive surveys on the topic with Luc Lemaire who studied for a doctorate under Eells' supervision. These were A report on harmonic maps (1978) and Another report on harmonic maps (1988) both published in the Bulletin of the London Mathematical Society. In 1992 a selection of Eells' papers on Harmonic maps was published as a book with this title in 1992. In this book Eells points out that:-
... harmonic maps pervade differential geometry and mathematical physics: they include geodesics, minimal surfaces, harmonic functions, Abelian integrals, Riemannian fibrations with minimal fibres, holomorphic maps between Kähler manifolds, chiral models, and strings. *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

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