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| Charles Minard's Napoleon's March, |
Modern science, as training the mind to an exact and impartial analysis of facts, is an education specially fitted to promote citizenship.
~Karl Pearson
The 86th day of the year; 86 is conjectured to be the largest number n such that 2n (in decimal) doesn't contain a 0. *Tanya Khovanova, Number Gossip
The 86th prime is 443, and 4433 = 86,938,307. There is no other two digit n, such that the cube of the nth prime starts with n.
(An unknown, by their choice, contributor supplied that he found only one one digit number, 2; [2nd prime is 3 and 3^3=27] and only one three digit number, [The 522nd prime is 3,739, its cube is 52,271,672,419 which starts with 522], and only one 4-digit number [The 3,512th prime is 32,749, its cube is 35,123,204,285,749 which starts with 3,51] ; but both six and seven digit primes have more than one example.)
86 is the sum of four consecutive integers, 86= 20 + 21 + 22 + 23
and of four consecutive squares, 86= 32 + 42 + 52 + 62
The multiplicative persistence of a number is the number of times the iteration of finding the product of the digits takes to reach a one digit number. For 86, with persistence of three, we produce 8*6= 48, 4*8 = 32, and 3*2 = 6.... and 48+32+6 = 86. (how frequently does that occur?)
There are 86 abundant numbers(the sum of the proper divisors is greater than the number) in a non-leap year, but 86 is not one of them. All the abundant year days are even numbers. The smallest odd abundant number is 945.
EVENTS
86 is the sum of four consecutive integers, 86= 20 + 21 + 22 + 23
and of four consecutive squares, 86= 32 + 42 + 52 + 62
The multiplicative persistence of a number is the number of times the iteration of finding the product of the digits takes to reach a one digit number. For 86, with persistence of three, we produce 8*6= 48, 4*8 = 32, and 3*2 = 6.... and 48+32+6 = 86. (how frequently does that occur?)
There are 86 abundant numbers(the sum of the proper divisors is greater than the number) in a non-leap year, but 86 is not one of them. All the abundant year days are even numbers. The smallest odd abundant number is 945.
The Marquis de Condorcet's most important work was on probability and the philosophy of mathematics. *MacTutor
In 1785, Condorcet published his Essay on the Application of Analysis to the Probability of Majority Decisions, one of his most important works. This work described several now famous results, including Condorcet's jury theorem, which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases as the number of members of the group increases, and Condorcet's paradox, which shows that majority preferences can become intransitive with three or more options – it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.
The paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the alternative method of aggregating preferences put forth by Jean-Charles de Borda (based on summed rankings of alternatives). Condorcet was one of the first to systematically apply mathematics in the social sciences.*Wik
In 1827, Charles Darwin, aged 18, submitted his first report of an original scientific discovery to the Plinian Society in Edinburgh, Scotland. Darwin had discovered several things about the biology of tiny marine organisms found along the Scottish coast. *TIS
From Darwin's description, the Plinian "consisted of students and met in an underground room in the university for the sake of reading papers on natural science and discussing them." Activities also included excursions to the countryside around Edinburgh. Meetings appear to have been weekly.
Papers presented by the students were often of high quality, inspired by their lecturers. Commonly, papers took the form of a critique of the work of established experts, together with the student's own thoughts. They covered a wide range of subjects including the circulation of ocean currents, identification of plants found in the nearby countryside, the anatomy of sea animals they had collected and principles of classification.
Darwin's discovery, new to science, was he observed cilia moving the microscopic larvae of a species of the bryozoan Flustra, and discovered that black spores often found in oyster shells were the eggs of a skate leech. He was disappointed when Grant(Dr Robert Edmond Grant) announced these finds to the Wernerian on 24 March 1827, and Darwin presented both discoveries at the Plinian Society on 27 March.
Bicentennial portrait by Anthony Smith of Darwin as a student, in the courtyard at Christ's College, Cambridge, where he had rooms
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1878 Christine Ladd to JJ Sylvester:
1921 On the morning of Easter Sunday, Otto Loewi awoke with the memory he had had an important dream during the night and written down some notes, but when he tried to retrieve them, the writing was hopelessly illegible. After trying to recall the dream all day, he retired early in the evening and eventually the dream came again. The dream was about a way to determine if transmissions between nerve cells was chemical or not. He immediately got out of bed and went to his laboratory. With a single experiment on a frog's heart he confirmed his own thesis of seventeen years before, that the transfer was indeed a chemical process. *Michael Brooks, Free Radicals (pg 24-25)
He discovered the role of acetylcholine as an endogenous neurotransmitter. For this discovery, he was awarded the Nobel Prize in Physiology or Medicine in 1936, which he shared with Sir Henry Dale, who was a lifelong friend that helped to inspire the neurotransmitter experiment.
1936 The Associated Press released a story that a new 155 digit perfect number had been found by Dr. S. I. Krieger of Chicago. The number was \(2^{256}(2^{257} - 1)\) by proving the \(2^{257} -1\) was prime. This was shocking since D. H. Lehmer and M. Kraitcik had announced that the number was composite in 1922. The perfection of the number was doubted by most mathematicians, but the actual factoring to prove it was composite didn't happen until 1952 when the SWAC confirmed it was composite by finding a proper divisor. *Beiler, Recreations in the Theory of Numbers.
Lehmer in particular said he could not confirm the factors as he had determined the composite nature by " means of a machine which he constructed with the aid of a grant from the Carnegie Institution of Washington, and advice of Dr. R. C. Burt of Pasadena." "A photo-electric number sieve,"
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| D. H. Lehmer |
1958 The first national high-school mathematics competition in the U.S. was held. Since 1983 it has been known as the American High School Mathematics Examination (AHSME). [The College Mathematics Journal, 16 (1985), p. 331] *VFR
The Metropolitan New York Society branch had been holding a contest since 1950. The !958 test involved over 80,000 students in over 2,600 high schools.
1976 20-Year Old Bill Gates Gives Opening Address to Hobbyists:
Bill Gates gives the opening address at the First Annual World Altair Computer Convention in Albuquerque, N.M. MITS, the company that developed the Altair, had set up shop in the southwestern city to develop its kit computer, which was a hit among hobbyists after it graced the cover of "Popular Mechanics" magazine. Gates, then a 20-year-old erstwhile Harvard student, had helped develop the form of BASIC sold with the Altair. *CHM
BIRTHS
1824 Johann Wilhelm Hittorf (27 Mar 1824, 28 Nov 1914) German physicist who was a pioneer in electrochemical research. His early investigations were on the allotropes (different physical forms) of phosphorus and selenium. He was the first to compute the electricity- carrying capacity of charged atoms and molecules (ions), an important factor in understanding electrochemical reactions. He investigated the migration of ions during electrolysis (1853-59), developed expressions for and measured transport numbers. In 1869, he published his laws governing the migration of ions. For his studies of electrical phenomena in rarefied gases, the Hittorf tube has been named for him. Hittorf determined a number of properties of cathode rays, including (before Crookes) the deflection of the rays by a magnet. *TIS
1845 Wilhelm Conrad Röntgen (27 Mar 1845 - 10 Feb 1923 at age 77) was a German physicist who discovered the highly penetrating form of radiation that became known as X-rays on 8 Nov 1895. He received the first Nobel Prize for Physics (1901), “in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him.” This high-energy radiation, though first called Röntgen rays, became known as X-rays. His discovery initiated revolutionary improvements in making medical diagnoses and enabled many new advances in modern physics. *TIS "In 1901 he became the first physicist to receive a Nobel prize." *VFR
First medical X-ray by Wilhelm Röntgen of his wife Anna Bertha Ludwig's hand
1855 Sir Alfred Ewing (27 Mar 1855, 7 Jan 1935) was a Scottish physicist who discovered and named hysteresis (1881), the resistance of magnetic materials to change in magnetic force. Ewing was born and educated in Dundee and studied engineering on a scholarship at Edinburgh University. He helped Sir William Thomson, later Lord Kelvin in a cable laying project. In 1878 he became professor of Mechanical Engineering and Physics at Tokyo University, where he devised instruments for measuring earthquakes. In 1903 he moved to the Admiralty as head of education and training, where during WW I, he and his staff took on the task of deciphering coded messages. *TIS
1857 Karl Pearson (27 Mar 1857; 27 Apr 1936 at age 79) English mathematician who was one of the founders of modern statistics. His lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS
1897 Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser.
Atomic structure calculations
In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical analysis to the new quantum theory. He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required. V. Fock published the "equations with exchange" now known as Hartree–Fock equations. These are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions. Today, the Hartree-Fock equations are of great importance to the field of computational chemistry, and are applied and solved numerically within most of the density functional theory programs used for electronic structure calculations of molecules and condensed phase systems.*Wik
1905 László Kalmár (27 March 1905 in Edde (N of Kaposvar), Hungary - 2 Aug 1976 in Mátraháza, Hungary) worked on mathematical logic and theoretical computer science. He was acknowledged as the leader of Hungarian mathematical logic. *SAU
2016 Horst Sachs (27 March 1927 – 25 April 2016) was a German mathematician, an expert in graph theory, a recipient of the Euler Medal (2000).
He earned the degree of Doctor of Science (Dr. rer. nat.) from the Martin-Luther-Universität Halle-Wittenberg in 1958. Following his retirement in 1992, he was professor emeritus at the Institute of Mathematics of the Technische Universität Ilmenau.
His encyclopedic book in spectral graph theory, Spectra of Graphs. Theory and Applications (with Dragos Cvetković and Michael Doob) has several editions and was translated in several languages.
Two theorems in graph theory bear his name. One of them relates the coefficients of the characteristic polynomial of a graph to certain structural features of the graph. Another one is a simple relation between the characteristic polynomials of a graph and its line graph. Sachs subgraphs are also named after Sachs.
DEATHS
1850 Wilhelm Beer (4 Jan 1797, 27 Mar 1850 at age 53) German banker and amateur astronomer who owned a fine Fraunhofer refractor which he used in his own a private observatory. He worked jointly with Johann Heinrich von Mädler, to produce the first large-scale moon map to be based on precise micrometric measurements. Their four-year effort was published as Mappa Selenographica (1836). This fine lithographed map provided the most complete details of the Moon's surface in the first half of the 19th century. It was the first lunar map divided in quadrants, and recorded the Moon's face in great detail detail. It was drawn to a scale of scale of just over 38 inches to the moon's diameter. Mädler originated a convention for naming minor craters with Roman letters appended to the name of the nearest large crater (ex. Egede A,B, and C).
1888 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik
1923 Sir James Dewar (20 Sep 1842; 27 Mar 1923) British chemist and physicist. Blurring the line between physics and chemistry, he advanced the research frontier in several fields at the turn of the century, and gave dazzling lectures. His study of low-temperature phenomena entailed making an insulating double-walled flask of his own design by creating a vacuum between the two silvered layers of steel or glass (1892). This Dewar flask that has been named for him led to the domestic Thermos bottle. In June 1897, The Scientific American reported that "Dewar has just succeeded in liquefying fluorine gas at a temperature of -185 degrees C." He obtained liquid hydrogen in 1898. Dewar also invented cordite, the first smokeless powder.*TIS
1925 Carl Gottfried Neumann,(7 May 1832 in Königsberg, Germany (now Kaliningrad, Russia) - 27 March 1925 in Leipzig, Germany) He worked on a wide range of topics in applied mathematics such as mathematical physics, potential theory and electrodynamics. He also made important pure mathematical contributions. He studied the order of connectivity of Riemann surfaces.
During the 1860s Neumann wrote papers on the Dirichlet principle and the 'logarithmic potential', a term he coined. In 1890 Émile Picard used Neumann's results to develop his method of successive approximation which he used to give existence proofs for the solutions of partial differential equations.*SAU
1929 Samuil Shatunovsky (25 March 1859 – 27 March 1929) was a Russian mathematician. focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry. Independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis. However, most of his activity was devoted to teaching at Odessa University and writing associated books and study materials.*Wik
1972
Maurits Cornelius Escher (17 June 1898 in Leeuwarden, Netherlands - 27 March 1972 in Laren, Netherlands) an artist whose works have included a considerable mathematical content. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *Wik
2010 Sheila Christina Tinney (née Power; 15 January 1918 – 27 March 2010) was an Irish mathematical physicist. Her 1941 PhD from the University of Edinburgh, completed under the supervision of Max Born in just two years, is believed to make her the first Irish-born and -raised woman to receive a doctorate in the mathematical sciences.
Returning to Dublin, she became an assistant lecturer at University College Dublin, and was also one of the first three scholars appointed to the brand new Dublin Institute for Advanced Studies (DIAS), in October 1941. While at the DIAS she worked with Paul Dirac, Arthur Eddington and Erwin Schrödinger. She developed a great interest in quantum physics, and wrote papers with Schrödinger, Hideki Yukawa, and Walter Heitler. She remained at DIAS (on a part-time basis) until the summer of 1948.
Even at University College Dublin, Tinney faced the entrenched prejudice against women. One professor emeritus recalls the sympathy she received when, early in her career, she was passed over for promotion in favour of a younger, and demonstrably less academically qualified, male colleague. During her time at UCD she gained a reputation for helping younger female colleagues who were trying to develop their careers.A new portrait of the pioneering mathematical physicist Dr. Sheila Tinney was unveiled at the Dublin Institute for Advanced Studies (DIAS) on 15 January 2019 to mark the 101st anniversary of her birth. The portrait – by artist Judith Henihan – was acquired by DIAS thanks to support from the International Women's Forum (Ireland) and benefactors from the ‘Friends of DIAS’ initiative. *Wik
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| With Dirac and Eddington |
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2025 Shmuel Agmon (February 1922 – 21 March 2025) was an Israeli mathematician who was known for his work in analysis and partial differential equations.
Shmuel Agmon was born in Tel Aviv to writer Nathan Agmon and Chaya Gutman. During his childhood, the family moved to Nazareth for a few years before settling in Jerusalem. A member of the HaMahanot HaOlim youth movement, Agmon studied at the Gymnasia Rehavia and joined a hakhshara program at kibbutz Na'an after graduating from high school.
He began his studies in mathematics at the Hebrew University of Jerusalem in 1940 but enlisted in the British Army before graduating, serving in an anti-aircraft unit and then the Jewish Brigade. He served for four years in Cyprus, Italy and Belgium during World War II.
After his discharge, he completed his undergraduate and master's degrees at the Hebrew University and went to France for further studies. He obtained a PhD from Paris-Sorbonne University in 1949, under the supervision of Szolem Mandelbrojt. He returned to Jerusalem after working as a visiting scholar at Rice University from 1950 to 1952, and was appointed full professor at the Hebrew University in 1959.
Agmon died on 21 March 2025, at the age of 103.
Agmon's contributions to partial differential equations include Agmon's method for proving exponential decay of eigenfunctions for elliptic operators.
Agmon was awarded the 1991 Israel Prize in mathematics. He received the 2007 EMET Prize "for paving new paths in the study of partial-elliptical differential equations and their problematic language and for advancing the knowledge in the field, as well as his essential contribution to the development of the Spectral Theory and the Distribution Theory of Schrödinger Operators." He has also received the Weizmann Prize and the Rothschild Prize. In 2012, he became a fellow of the American Mathematical Society. *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
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