Wednesday, 26 April 2017

On This Day in Math - April 26

Mathematics is like childhood diseases. The younger you get it, the better.
~Arnold Sommerfeld

The 116th day of the year; 116! + 1 is prime! *Prime Curios (Students might investigate how often n!+1 is prime)
116^2 + 1 is prime

The number 1 appears 116 times in the first 1000 digits of pi. Thanks to *Math Year-Round ‏@MathYearRound

Impress your History teacher, the 100 Years war between France and England..... lasted 116 years.

and Jiroemon Kimura died in 2013 in Japan. He was 116 years old.  Two years later his record was broken by an even older Japanese citizen who died.


1514 Nicolaus Copernicus (1473-1543) made his first observation of Saturn. Copernicus later proposed that the sun is stationary and that the Earth and the planets move in circular orbits around it. * Saturn_Project

1760 Euler was asked to tutor the niece of Frederick the Great, the Princess of Anhalt-Dessau. Euler wrote over 200 letters to her in the early 1760s. On this date he sent the third of these letters. The letter covered the physics of sound and he gave a speed of one thousand feet per second. He closes by telling the Princess that we are incapable of hearing a string vibrating at less than 30 vibrations per second, or one that is more than 7552 vibrations per second.

1766 D’Alembert after writing to Frederick II in praise of Lagrange writes to Lagrange about an offer to move to Berlin:
My dear and illustrious friend, the king of Prussia has charged me to write you that, if you would like to come to Berlin to occupy a place in the Academy, he would give you a pension of 1,500 crowns, which are 6,000 French pounds … Mr Euler, unhappy for reasons of which I do not know the details, but in which I see that everyone thinks him wrong, requests permission to leave and wants to go to St. Petersburg. The king, who was not too anxious to grant it, would definitely give it to him if you accept the proposition that he has made
Frederick II of Prussia had more than once invited both d’Alembert and Lagrange to move to Berlin. The encyclopaedist had declined the offer and suggested the name of his Turinese friend. But Lagrange, even though he was on good terms with Euler, did not relish a "cohabitation" with him in the Berlin Academy. *Mauro ALLEGRANZA, Stack Exchange

1826 The first class of 10 students graduated from Renssalaer Polytechnic Institute on 26 Apr 1826. The Renssalaer School was founded in 1824 in Troy, N.Y., by Stephen van Renssalaer becoming the first engineering college in the U.S. It opened on 3 Jan 1825, with the purpose of instructing persons, who may choose to apply themselves, in the application of science to the common purposes of life." The first director and senior professor was Amos Eaton who served from Nov 1824 - 10 May 1842. The name of Renssalaer Institute was adopted on 26 Apr 1832, and Renssalaer Polytechnic Institute on 8 Apr 1861. *TIS

1861 Richard Owen gives the longest ever discourse at a Royal Institution lecture, ‘On the Scope and Appliances of a National Museum of Natural History’.
Discourse speakers were supposed to aim to speak for exactly one hour but Owen kept talking for two. (It may be coincidence but this is the last discourse he gave.) *Royal Institution web page

In 1882, a perpetual motion machine was patented by John Sutliff in the U.S. (No. 257,103). *TIS (Wouldn't you love to be the guy that approved that one.)

1892 Hermite to Stieltjes: “You state this result and then try to mortify me by saying that it is easy to prove. Since I can’t succeed in doing it I appeal to your good nature to help me out of this difficulty.” [Two Year Journal, 11, 49] *VFR (Boy, haven't we all been there?)

1920 Shapley and Curtis debate the nature of the nebulae. In astronomy, the Great Debate, also called the Shapley–Curtis Debate, was an influential debate between the astronomers Harlow Shapley and Heber Curtis which concerned the nature of spiral nebulae and the size of the universe. more here.

1921 the first U.S. broadcast of the weather was made from St. Louis, Missouri, over station WEW for the federal government. *TIS
Radio Station WEW, the original radio station of Saint Louis University, played an important role in the history of early radio. In 1921 it became only the second radio station in the U.S. and the first station west of the Mississippi River. In 1939 it became the first station to broadcast Sacred Heart Radio, a Catholic religious program which eventually grew to include over a thousand stations around the world. Finally, in 1947 WEW became the first FM radio station in St. Louis.

1962 The UK became the world's third spacefaring country, after the US and the USSR, with the launch of the satellite Ariel 1. It was built by Nasa in collaboration with British scientists to study the properties of the upper atmosphere and cosmic rays, and formed the first of six missions. "The big legacy is that, despite the fact we are a relatively small country, we are a major international player in space research," said Martin Barstow, an astrophysicist and head of the college of science and engineering at the University of Leicester. *The Guardian


1968 Time magazine (p. 41) reports a “Trial by Mathematics” in which a couple was convicted on the basis of mathematical probability. Later the reasoning was found to be incorrect. The discussion there is of interest. See also Journal of Recreational Mathematics, 1(1968), p. 183. *VFR See details here.

1985 A 22-cent commemorative stamp for Public Education in America issued in Boston.

1986 Nuclear reactor number 4 at Chernobyl, USSR, exploded and released a large amount of radioactive material into the atmosphere. [A. Hellemans and B. Bunch. The Timetables of Science, p. 597].


1711 David Hume, (7 May[O.S. 26 April]1711,– 25 August 1776) was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment. Hume is often grouped with John Locke, George Berkeley, and a handful of others as a British Empiricist *Wik

Robert Tucker (26 April 1832 in Walworth, Surrey, England - 29 Jan 1905 in Worthing, England) A major mathematical contribution made by Tucker was his work as editor of William Kingdon Clifford's papers. Fifty-seven of Clifford's papers were collected and edited by Tucker and published in 1882 as Mathematical Papers. Tucker also wrote many biographies including those of Gauss, Sylvester, Chasles, Spottiswoode, and Hirst, all of which appeared in Nature. But, like a number of schoolmaster's at this time, he also made a contribution to research in geometry. He wrote over 40 research papers which were published in leading journals. These papers, although sometimes not of the highest quality, do contain a number of interesting ideas. Hill specially singles out for special mention his work on the Triplicate-Ratio Circle, the group of circles sometimes known as Tucker Circles, and the Harmonic Quadrilateral. *SAU

1874 Edward Vermilye Huntington (April 26 1874, Clinton, New York, USA – November 25, 1952, Cambridge, Massachusetts, USA) . This enthusiastic and innovative teacher was professor of mechanics at Harvard from 1919 to 1941. He made many contributions to the logical foundations of mathematics. His book, The Continuum (1917), was the standard introduction to set theory for many years. In 1928 he recommended the “method of equal proportion” for the apportionment of representatives to Congress; in 1941 this method was adopted by Congress. *VFR (now often called the Huntington-Hill method)

1879 Sir Owen Willans Richardson (26 Apr 1879; 15 Feb 1959 at age 79) English physicist who was awarded the Nobel Prize for Physics in 1928 for “his work on the thermionic phenomenon [electron emission by hot metals] and especially for the discovery of the law named after him.”This effect is why a heated filament in a vacuum tube releases a current of electrons to travel an anode, which was essential for the development of such applications as radio amplifiers or a TV cathode ray tube. Richardson's law mathematically relates how the electron emission increases as the absolute temperature of the metal surface is raised. He also conducted research on photoelectric effects, the gyromagnetic effect, the emission of electrons by chemical reactions, soft X-rays, and the spectrum of hydrogen.*TIS

1889 Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.*Wik This noted philosopher introduced the word “tautology” in his Tractatus Logico Philosophicus of 1921. *VFR

1900 Charles Richter(April 26, 1900, Hamilton, Ohio - September 30, 1985, Pasadena, California ) This American seismologist developed the earthquake magnitude scale which bears his name. *VFR The scale is logarithmic (base ten). When an earthquake occurs, the maximum amplitude of the shake is measured on a seismometer and assigned a Richter number. A quake with a value of 5 on the Richter scale is 10 times more powerful than a quake with a value of 4. The choice of a log scale seems to have come from his associate, Beno Gutenberg,

1922 Asger Hartvig Aaboe (April 26, 1922 – January 19, 2007) was a historian of the exact sciences and mathematician who is known for his contributions to the history of ancient Babylonian astronomy. He studied mathematics and astronomy at the University of Copenhagen, and in 1957 obtained a PhD in the History of Science from Brown University, where he studied under Otto Neugebauer, writing a dissertation "On Babylonian Planetary Theories". In 1961 he joined the Department of the History of Science and Medicine at Yale University, serving as chair from 1968 to 1971, and continuing an active career there until retiring in 1992. In his studies of Babylonian astronomy, he went beyond analyses in terms of modern mathematics to seek to understand how the Babylonians conceived their computational schemes.*Wik

1933 Arno Allan Penzias (26 Apr 1933, ) is a German-American astrophysicist who shared one-half of the 1978 Nobel Prize for Physics with Robert Woodrow Wilson for their discovery of a faint electromagnetic radiation throughout the universe. Their detection of this radiation lent strong support to the big-bang model of cosmic evolution. (The other half of the prize was awarded to Pyotr Kapitsa for unrelated research.)*TIS

1938 Manuel Blum (26 April 1938; Caracas, Venezuela -) is a computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking".
Blum attended MIT, where he received his bachelor's degree and his master's degree in EECS in 1959 and 1961 respectively, and his Ph.D. in Mathematics in 1964 under professor Marvin Minsky.
He worked as a professor of computer science at the University of California, Berkeley until 1999. In 2002 he was elected to the United States National Academy of Sciences.
He is currently the Bruce Nelson Professor of Computer Science at Carnegie Mellon University, where his wife, Lenore Blum, and son, Avrim Blum, are also professors of Computer Science. *Wik


1600 Cunradus Dasypodius ((c. 1530–1532 – April 26, 1600) whose fame is based on the “construction of an ingeneous and accurate astronomical clock in the cathedral of Strasbourg, installed between 1571 and 1574.” *VFR The Strasbourg astronomical clock is located in the Cathédrale Notre-Dame of Strasbourg, Alsace, France. The current, third clock dates from 1843. Its main features, besides the automata, are a perpetual calendar (including a computus), an orrery (planetary dial), a display of the real position of the Sun and the Moon, and solar and lunar eclipses. The main attraction is the procession of the life-size figures of Christ and the Apostles which occurs every day at 12:30pm,(not sure if I read this right, but that seems to be when the clock reads noon (corrections anyone?))*Wik
[A minor point on language, the "orrery" was proabably not so-named in that period, according to a post at the Univ of Penn Library, "The name Orrery comes from the following train of facts. When George Graham, the celebrated London mechanic and watchmaker, employed one Rowley to construct his planetarium, said Rowley retained a model, and was afterward patronized by Charles Boyle, Earl of Orrery, in making a large machine which, though only representing one or two of the heavenly bodies, was sold to George the First for a thousand guineas. Sir Richard Steele in the work entitled "A New and General Biographical Dictionary", published in 1761, attributed this invention to the Earl of Orrery. Hence compilers of the British Encyclopaedia, which was republished in Philadelphia, followed his lead and such machines have since been known as Orreries. ]

1815 Carsten Niebuhr(March 17, 1733 Lüdingworth – April 26, 1815 Meldorf, Dithmarschen), German mathematician, cartographer, and explorer in the service of Denmark. Niebuhr's first book, Beschreibung von Arabien, was published in Copenhagen in 1772, the Danish government providing subsidies for the engraving and printing of its numerous illustrations. This was followed in 1774 and 1778 by the two volumes of Niebuhr's Reisebeschreibung von Arabien und anderen umliegenden Ländern. These works (particularly the one published in 1778), and most specifically the accurate copies of the cuneiform inscriptions found at Persepolis, were to prove to be extremely important to the decipherment of cuneiform writing. Before Niebuhr's publication, cuneiform inscriptions were often thought to be merely decorations and embellishments, and no accurate decipherments or translations had been made up to that point. Niebuhr demonstrated that the three trilingual inscriptions found at Persepolis were in fact three distinct forms of cuneiform writing (which he termed Class I, Class II, and Class III) to be read from left to right. His accurate copies of the trilingual inscriptions gave Orientalists the key finally crack the cuneiform code, leading to the discovery of Old Persian, Akkadian, and Sumerian. *Wik

1876 Osip Ivanovich Somov (1 June 1815 in Otrada, Moscow gubernia (now oblast), Russia - 26 April 1876 in St Petersburg, Russia) Somov was the first in Russia to develop a geometrical approach to theoretical mechanics. He studied the rotation of a solid body about a point, studying examples arising from the work of Euler, Poinsot, Lagrange and Poisson. Other topics Somov studied included elliptic functions and their application to mechanics. *SAU

1902 Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a German mathematician who contributed important research in the field of linear differential equations. He was born in Mosina (located in Grand Duchy of Poznań) and died in Berlin, Germany.
He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation; Fuchsian differential equations are those with regular singularities. Fuchs is also known for Fuchs's theorem. *Wik

1920 Srinivasa Aaiyangar Ramanujan died at age 32. This self educated mathematician, who was discovered by G. H. Hardy of Cambridge, is remembered for his notebooks crammed with complicated identities. *VFR
Although self-taught, he was one of India's greatest mathematical geniuses. He worked on elliptic functions, continued fractions, and infinite series. His remarkable familiarity with numbers, was shown by the following incident. While Ramanujan was in hospital in England, his Cambridge professor, G. H. Hardy, visited and remarked that he had taken taxi number 1729, a singularly unexceptional number. Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=13+123=93+103 *TIS
I later learned from a blog at John D. Cooks The Endeavour blog that there is a little more to the story. Here is how John writes it:
This story has become famous, but the rest of the conversation isn’t as well known. Hardy followed up by asking Ramanujan what the corresponding number would be for 4th powers. Ramanujan replied that he did not know, but that such a number must be very large.

Hardy tells this story in his 1937 paper “The Indian Mathematician Ramanujan.” He gives a footnote saying that Euler discovered 635318657 = 158^4 + 59^4 = 134^4 + 133^4 and that this was the smallest number known to be the sum of two fourth powers in two ways. It seems odd now to think of such questions being unresolved. Today we’d ask Hardy “What do you mean 653518657 is the smallest known example? Why didn’t you write a little program to find out whether it really is the smallest?”
His readers seem to find that Euler was correct. No suprise there.

1946 Louis Bachelier, the French mathematician, is now recognized internationally as the father of financial mathematics,..Bachelier was ahead of his time and his work was not appreciated in his lifetime. In the light of the enormous importance of international derivative exchanges (where the pricing is determined by financial mathematics) the remarkable pioneering work of Bachelier can now be appreciated in its proper context and Bachelier can now be given his proper place. *SAU

1951 Arnold (Johannes Wilhelm) Sommerfeld (5 Dec 1868, 26 Apr 1951 at age 82) was a German physicist whose atomic model permitted the explanation of fine-structure spectral lines. His first work was on the theory of the gyroscope (with Klein), and then on wave spreading in wireless telegraphy. More significant was his major contribution to the development of quantum theory, generally, and in its application to spectral lines and the Bohr atomic model. He evolved also a theory of the electron in the metallic state valuable to the study of thermo-electricity.*TIS

1976 Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was a historian of sciences, and especially mathematics. David Foster Wallace called him the "Gibbon of math history". He wrote the books History of Analytic Geometry, The History of the Calculus and Its Conceptual Development, A History of Mathematics, and The Rainbow: From Myth to Mathematics. He served as book-review editor of Scripta Mathematica. *Wik
His History of analytic Geometry is excellent.

1980 Stanisław Gołąb (July 26, 1902 – April 30, 1980) was a Polish mathematician from Kraków, working in particular on the field of affine geometry.
In 1932, he proved that the perimeter of the unit disc can take any value in between 6 and 8, and that these extremal values are obtained if and only if the unit disc is an affine regular hexagon. *Wik

2006 Yuval Ne'eman (14 May 1925, 26 Apr 2006 at age 80) Israeli theoretical physicist, who worked independently of Gell-Mann but almost simultaneously (1961) devised a method of grouping baryons in such a way that they fell into logical families. Now known as the Eightfold Way (after Buddha's Eightfold Path to Enlightenment and bliss), the scheme grouped mesons and baryons (e.g., protons and neutrons) into multiplets of 1, 8, 10, or 27 members on the basis of various properties. He had served as the head of his Israel's atomic energy commission, and founded the country's space program.*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

Tuesday, 25 April 2017

On This Day in Math - April 25

Pure mathematics is the world's best game.
It is more absorbing than chess,
more of a gamble than poker,
and lasts longer than Monopoly.
It's free.
It can be played anywhere -
Archimedes did it in a bathtub.
~Richard J. Trudeau, Dots and Lines

The 115th day of the year; 115 is the 26th "Lucky" number. Lucky numbers are produced by a sieve method created by Stan Ulam around 1955. The term was introduced in 1955 in a paper by Gardiner, Lazarus, Metropolis and Ulam. They suggest also calling its defining sieve, "the sieve of Josephus Flavius" because of its similarity with the counting-out game in the Josephus problem. They are interesting explorations for both elementary and advanced students. Whether there are an infinite number of primes in the lucky numbers is still an open question.

115 (or 5! - 5) is the smallest composite number of the form p! - p, where p is prime.

\( \pi (115) = 30 \) occurs at the 115th decimal digit of pi. It is the smallest integer n, in which the number of primes less than n occurs at the nth decimal place of pi. Once more for the HS students, there are 30 prime numbers less than 115, and the 115th &116th decimal digits of pi are 3, 0, so the two digit value beginning at the 115th decimal place counts the number of primes less than 115. There is no smaller number for which this is true. You may want to find the next one.

1611 Galileo (1564 1642) visited Rome at the height of his fame in 1611 and was made the sixth member of the Accademia dei Lincei (Lynx Society) at a banquet on (14 Apr/25Apr). The word 'telescopium' was first applied to his instrument at this dinner. He showed sunspots to several people. The term “telescope” was introduced by Prince Federico Cesi at a banquet given in Galileo’s honor. It derives from the Greek “tele” meaning “far away” and “skop´eo” meaning “to look intently.” For a change, a term which derives from the Greek was actually coined by a Greek, namely Ioannes Demisiani. [Willy Ley, Watchers of the Skies, p. 112]*VFR Thony Christie at the Renaissance Mathematicus blog has an enjoyable review of the telescope and how it got its name.

1661 Two days after attending the Coronation of Charles II, John Evelyn attends another spectacular, "to the Society where were many diverse experiments in Mr. Boyle's Pneumatic Engine." *Lisa Jardine, Ingenious Pursuits, pg 54

1832 In a debate over the apportionment of the House, Senator Dickerson of New Jersey invoked the language of Berkeley’s Analyst when he railed against using Jefferson’s apportionment method wherein fractions are ignored: “These quasi-representitives, these infinitesimal, evanescent Rep­resentatives, these ideal Representatives, these ghosts of Representatives, after being counted in order to give the favored States their full proportion of a House of 250, are dismissed the service.” *VFR (for my students.) Bishop Berkeley wrote a paper called "The Analyst" in which he tried to refute Newton's use of fluxions (derivatives). The idea that we treat "h" as not zero to cancel in the difference quotient, then dismiss it in the final limit disturbed him (and lots of others).. He wrote, "And what are these fluxions? The velocities of evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?"

1810 Exactly a week after he was elected a member of the Berlin Academy of Sciences, Wilhelm von Humboldt sends Gauss an offer of 1500 Thalers a year to serve as ordentliches Mitglied of the Academy with the assurance that, " are only requested to lend your name as a full professor to the new university, and, as much as your leisure and health allow, to teach a course from time to time." *Dunnington, Gray & Dohse; Carl Friedrich Gauss: Titan of Science

1828 Christopher Hansteen, Director of the Observatory in Christiana, set out from Berlin to confirm his belief that the earth had more than one magnetic axis. 

1834 William Whewell In a single letter to Faraday on 25 April, 1834;  invented the terms cathode, anode and ion. The letter is on display at the Wren Library at Trinity College, Cambridge, UK. He is known for creating scientific words. He founded mathematical crystallography and developed Mohr's classification of minerals. He created the words scientist and physicist by analogy with the word artist. They eventually replaced the older term natural philosopher. (actually the use of scientist was a very slow process often not well received. see more of the interesting story here) Other useful words were coined to help his friends: biometry for Lubbock; Eocine, Miocene and Pliocene for Lyell; and for Faraday, anode, cathode, diamagnetic, paramagnetic, and ion (whence the sundry other particle names ending -ion).

In 1953, Francis Crick and James Watson reached their conclusion about the double helix structure of the DNA molecule. They made their first announcement on Feb 28, and their paper, A Structure for Deoxyribose Nucleic Acid, was published in the 25 Apr 1953 issue of journal Nature. *TIS
Greg Ross at Futility Closet posted a note Crick created to respond to the deluge of requests the discovery created:
Deluged with mail after his discovery of the double helix, Francis Crick began sending a printed card in response to invitations:
crick demurral

1961 Noyce patent issued for the semiconductor. *VFR ---nicknamed "the Mayor of Silicon Valley", co-founded Fairchild Semiconductor in 1957 and Intel in 1968. He is also credited (along with Jack Kilby) with the invention of the integrated circuit or microchip. While Kilby's invention was six months earlier, neither man rejected the title of co-inventor. Noyce was also a mentor and father-figure to an entire generation of entrepreneurs, including Steve Jobs at Apple, Inc

1990 The Hubble Space Telescope is released from the payload bay of Discovery *David Dickinson ‏ @Astroguyz

2038 The next time that Easter will occur on April 25, the latest possible date. The last time Easter was on April 25 was in 1943.


1769 Sir Marc Isambard Brunel French-born English engineer and inventor who solved the historic problem of underwater tunneling. A prolific inventor, Brunel designed machines for sawing and bending timber, boot making, stocking knitting, and printing. As a civil engineer, his designs included the Île de Bourbon suspension bridge and the first floating landing piers at Liverpool. In 1818, however, Brunel patented the tunneling shield, a device that made possible tunneling safely through waterbearing strata. On 2 Mar 1825 operations began for building a tunnel under the Thames River between Rotherhithe and Wapping. The Thames Tunnel was eventually opened on 25 Mar 1843. It has a twin horseshoe cross-section with height of 23-ft (7m), width of 37-ft (11m), and total length 1,506-ft (406m) *Wik

1849 Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.*Wik He recommended the teaching of calculus in the German secondary schools. *VFR
[In mathematics, the Klein bottle is a non-orientable surface, informally, a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.) The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is sometimes claimed that it was originally named the Kleinsche Fläche "Klein surface" and that this was incorrectly interpreted as Kleinsche Flasche "Klein bottle," which ultimately led to the adoption of this term in the German language as well.*Wik

1874 Guglielmo Marconi Italian inventor, born in Bologna. He was a physicist, who invented the wireless telegraph in 1935 known today as radio. Nobel laureate (1909). In 1894, Marconi began experimenting on the "Hertzian Waves" (the radio waves Hertz first produced in his laboratory a few years earlier). Lacking support from the Italian Ministry of Posts and Telegraphs, Marconi turned to the British Post Office. Encouraging demonstrations in London and on Salisbury Plain followed. Marconi obtained the world's first patent for a system of wireless telegraphy, in 1897, and opened the world's first radio factory at Chelmsford, England in 1898. In 1900 he took out his famous patent No. 7777 for "tuned or syntonic telegraphy." *TIS

1898 Pavel Sergeevich Aleksandrov  Soviet mathematician who made important contributions to the field of topology, the study of related physical or abstract elements that remain unchanged under certain distortions. *TIS

1879 Edwin Bidwell Wilson born. As a student of Willard Gibbs at Yale he codified the physicist’s lectures on vector analysis into a textbook (1901) that profoundly influenced the use and nota­tion of the subject. In 1912 he published a comprehensive text on advanced calculus that was the first really modern book of its kind in the U.S. *VFR

1900 Wolfgang Pauli, Austrian-born American winner of the Nobel Prize for Physics in 1945 for his discovery in 1925 of the Pauli exclusion principle, which states that in an atom no two electrons can occupy the same quantum state simultaneously. This principle clearly relates the quantum theory to the observed properties of atoms. Pauli was known for having an acid tongue. He was once challenged by another arrogant physicist, Lev Davidovich Landau who had explained his ideas to Pauli, whom he knew was skeptical of his ideas. Landau asked, "Well now do you think my ideas are nonsense?". Pauli's reply was, "No, not at all.; Your ideas are so confused I can't tell if they are nonsense, or not."

1903 Andrey Nikolayevich Kolmogorov  Russian mathematician whose basic postulates for probability theory that have continued to be an integral part of analysis. This work had diverse applications such as his study of the motion of planets (1954), or the turbulent air flow from a jet engine (1941). In topology, he investigated cohomology groups. He made a major contribution to answering the probability part of Hilbert's Sixth Problem, and completely resolved (1957) Hilbert's Thirteenth Problem. Kolmogorov was active in a project to provide special education for gifted children, not only by writing textbooks and in teaching them, but in expanding their interests to be not necessarily in mathematics, but with literature, music, and healthy activity such as on hikes and expeditions. *TIS
The theory of probability as mathematical discipline can and should be developed from axioms in exactly the same way as Geometry and Algebra."
*Foundations of the Theory of Probability
A nice article about him as at the Nautilus (issue 004)

1918 Gerard Henri de Vaucouleurs (25 Apr 1918; 7 Oct 1995 at age 77) French-born U.S. astronomer whose pioneering studies of distant galaxies contributed to knowledge of the age and large-scale structure of the universe. He produced three Reference Catalogues of bright galaxies (1964, 1976, 1991). Each was a homogenization of data from widely different sources, so that the catalogues would not be merely finding lists or data collection lists, but astrophysically useful databases. Using data in the Reference Catalogues, he was able to develop new distance indicators and refine others. His unique philosophy on distance matters was "spreading the risks," that is, applying as many different and independent techniques as possible to check for scale and zero-point errors. *TIS


1472 Leon Battista Alberti (Feb. 14, 1404 Genoa April 25, 1472 also given as April 20) Artist and geometrist. As an artist, he "wrote the book," the first general treatise Della Pictura (1434) on the the laws of perspective, establishing the scienceof projective geometry. Alberti also worked on maps (again involving his skill at geometrical mappings) and he collaborated with Toscanelli who supplied Columbus with the maps for his first voyage. He also wrote the first book on cryptography which contains the first example of a frequency table.*TIS
"When I investigate and when I discover that the forces of the heavens and the planets are within ourselves, then truly I seem to be living among the gods. "

1744 Anders Celsius (27 November 1701 – 25 April 1744) Swedish astronomer, physicist and mathematician who is famous for the temperature scale he developed. Celsius was born in Uppsala where he succeeded his father as professor of astronomy in 1730. It was there also that he built Sweden's first observatory in 1741. He and his assistant Olof Hiortner discovered that aurora borealis influence compass needles. Celsius' fixed scale (often called centigrade scale) for measuring temperature defines zero degrees as the temperature at which water freezes, and 100 degrees as the temperature at which water boils. This scale, an inverted form of Celsius' original design, was adopted as the standard and is still used in almost all scientific work. *TIS
There is a Plaque to Anders Celsius in the church at Gamla Uppsala

1840 Siméon-Denis Poisson ( 21 June 1781 – 25 April 1840) French mathematician known for his work on definite integrals, advances in Fourier series, electromagnetic theory, and probability. The Poisson distribution (1837) describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. His works included applications to electricity and magnetism, and astronomy. He is also known for the Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity.

1999 Sir William Hunter McCrea (13 Dec 1904, 25 Apr 1999 at age 94)
was an Irish theoretical astrophysicist whose early work was in quantum physics, relativity and pure mathmatics, but he gradually turned to applying theoretical physics in astronomy. He ranged from considering the stellar atmospheres, planet formation, cosmology and indeed, the formation of stars and the universe. He was an early advocate that stars have a high hydrogen content. He studied gas dynamics, as in the formation of hydrogen in molecular form in dusty interstellar clouds, and developed a theory of the transition from increasing density to conditions sufficient for gravitational collapse and possible star formation. Although he at first was open-minded to the steady state theory of the universe proposed by Hermann Bondi, Thomas Gold and Fred Hoyle, McCrea's work and others accumulated evidence for the Big Bang theory.*TIS
"Our experience shows that not everything that is observable and measurable is predictable, no matter how complete our past observations may have been. "

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

Monday, 24 April 2017

On This Day in Math - April 24

Simplicibus itaque verbis gaudet Mathematica Veritas, cum etiam per se simplex sit Veritatis oratio.
(So Mathematical Truth prefers simple words
since the language of Truth is itself simple.)
~ Tycho Brahe

The 114th day of the year; this day begins a string of thirteen consecutive day numbers that are composite. There is no string of more composite year day numbers. The next such string of composite day numbers will include Halloween.

The sum of the first 114 digits of e after the decimal point, is prime. This is the third consecutive day number with this property.

The largest gap between two consecutive six digit primes is 114.


1066 Halley's Comet heralded an invasion when it appeared over England. A monk spotted it and predicted the destruction of the country. The monk, Eilmer of Malmesbury (also known as Oliver due to a scribe's miscopying, or Elmer) was an 11th-century English Benedictine monk best known for his early attempt at a gliding flight using wings. He seems to have predicted the destruction of England when he saw the comet and wrote, "You've come, have you? – You've come, you source of tears to many mothers. It is long since I saw you; but as I see you now you are much more terrible, for I see you brandishing the downfall of my country." William of Malmesbury, who provides almost all the known information about Eilmer, writes that, in Eilmer's youth, he had read and believed the Greek fable of Daedalus. Thus, Eilmer fixed wings to his hands and feet and launched himself from the top of a tower at Malmesbury Abbey.*Wik (well, he got the invasion part right)

1610 Galileo comes to demonstrate his telescope but is poorly received.
from a Letter from Martin Horky to Kepler, April, 1610
Galileo Galilei, the mathematician of Padua, came to us in Bologna and he brought with him that spyglass through which he sees four fictitious planets. On the twenty-fourth and twenty-fifth of April I never slept, day and night, but tested that instrument of Galileo's in innumerable ways, in these lower as well as the higher [realms]. On Earth it works miracles; in the heavens it deceives, for other fixed stars appear double. Thus, the following evening I observed with Galileo's spyglass the little star that is seen above the middle one of the three in the tail of the Great Bear, and I saw four very small stars nearby, just as Galileo observed about Jupiter. I have as witnesses most excellent men and most noble doctors, Antonio Roffeni, the most learned mathematician of the University of Bologna, and many others, who with me in a house observed the heavens on the same night of 25 April, with Galileo himself present. But all acknowledged that the instrument deceived. And Galileo became silent, and on the twenty-sixth, a Monday, dejected, he took his leave from Mr. Magini very early in the morning. And he gave no thanks for the favors and the many thoughts, because, full of himself, he hawked a fable. Mr. Magini provided Galileo with distinguished company, both splendid and delightful. Thus the wretched Galileo left Bologna with his spyglass on the twenty-sixth.
Beneath the letter in German he has written, "Unknown to anyone, I have made an impression of the spyglass in wax, and when God aids me in returning home, I want to make a much better spyglass than Galileo's." *Timothy J. McGrew, Western Michigan Univ.

Len Fisher ‏@LenFisherScienc sent a clip that pointed out that Galileo's fellow Pisano, was one of those who refused to look through the glass at all:
*from "Weighing the Soul"

1676 In a letter to the Royal Society, Leeuwenhock describes what happens after he put pepper water in his study for three weeks and then observed it through his scope, "I looked upon it the 24th of April, 1676 and discerned to my great wonder, an incredible number of very small animals of divers kinds." *Lisa Jardine, Incredible Pursuits, pg 92

1800 The Library of Congress established . $5000 was appropriated for the purchase of such books as may be necessary for the use of Congress at the said city of Washington and for filling up a suitable apartment for containing them and for placing them therein." The first catalog, dated April 1802, listed 964 volumes and 9 maps. *VFR

1897 The Chicago Section of the American Mathematical Society held its organizational meeting in Chicago under the chairmanship of E. H. Moore. It was the first section of the AMS. [Cajori, Historical Introduction to the Mathematical Literature, p. 34] *VFR

In 1925, Darwin's theory of evolution was reputed to be taught in Dayton, Tennessee, by teacher John Scopes, who used the high school textbook, Civic Biology by George Hunter. For this, Scopes, 24, was prosecuted under the Butler Act, a state law enacted in the previous month, on 21 Mar 1925. It prohibited the teaching of evolution in public schools. The trial , which began 10 Jul 1925) was used as a platform to challenge the legality of the statute. Scopes was supported by the American Civil Liberties Union. At its end, on 21 Jul 1925, Scopes was convicted and fined $100. On appeal, the state supreme court upheld the constitutionality of the 1925 law but acquitted Scopes on the technicality that he had been fined excessively. The law was not repealed until 17 May 1967. *TIS

In 1928, the fathometer was patented by Herbert Grove Dorsey (No. 1,667,540). His invention was an electro-mechanical sounding instrument that measured underwater depths by using a series of electrical sounds signals and their echoes. He coined the name fathometer. The same instrument could measure both very shoal water and very deep water. His fathometers not only improved hydrographic surveying but also were valuable to the maritime shipping industry by saving time over line soundings. His instruments helped delineate much of the continental shelf and slope of the United States and its territories as well as much of the deep sea, in particular the northeast Pacific Ocean, the mid-Atlantic shelf and slope, and Gulf of Mexico.*TIS

A model of 1862 Apollo viewed from the pole (top) and from the equator (bottom). The irregular shape of asteroids like 1862 Apollo means that photons adsorbed and re-emitted from the surface can produce a net torque that gradually makes the asteroids spin faster – what is known to astronomers as the "YORP" effect. Image credit: Mikko Kaasalainen and Josef Durech
1932 Minor Planet Apollo Discovered on April 24 by K. Reinmuth at Heidelberg. This object is named for the god of the Sun. Patrick Poitevin ‏@PatrickPoitevin
The prototype asteroid of the Apollo group. In 1932 it approached Earth to within 10.5 million km (0.07 AU), but was then lost until 1973. Apollo can come as close to Earth as 4.2 million km (0.028 AU) and also make near passes of Venus and Mars, whose orbits it crosses at perihelion and aphelion,respectively.*

1949 Columbia issued a stamp honoring the mathematician Julio Garavito Armero (1865{1920). [Scott #573] *VFR [He is also on the 20,000 peso bank note] As an astronomer of the observatory, he did many useful scientific investigations such as calculating the latitude of Bogotá, studies about the comets which passed by the Earth between 1901 and 1910 (such as Comet Halley), and the 1916 solar eclipse (seen in the majority of Colombia). But perhaps the most important were his studies about celestial mechanics, which finally turned into studies about lunar fluctuations and their influence on weather, floods, polar ice, and the Earth's orbital acceleration (this was corroborated later). He worked also in other areas such as optics (this work was left unfinished at his death), and economics, by which he helped the country recover from the rough civil war. With this objective, he gave lectures and conferences in economics and the human factors which affected it, such as war or overpopulation. *Wik

1980 The winning number in the Pennsylvania lottery was 666. On this day a group of men bet some $20,000 on all combinations involving just 4 and 6. The state lost two million. In 1982 two men were convicted of a lottery fix. Ironically, on the day they went to prison, Delaware's daily number came up 555.

1981 first IBM personal computer was introduced.IBM's own Personal Computer (IBM 5150) was introduced in August 1981, only a year after corporate executives gave the go-ahead to Bill Lowe, the lab director in the company's Boca Raton, Fla., facilities. He set up a task force that developed the proposal for the first IBM PC. Early studies had concluded that there were not enough applications to justify acceptance on a broad basis and the task force was fighting the idea that things couldn't be done quickly in IBM. One analyst was quoted as saying that "IBM bringing out a personal computer would be like teaching an elephant to tap dance." During a meeting with top executives in New York, Lowe claimed his group could develop a small, new computer within a year. The response: "You're on. Come back in two weeks with a proposal." *IBM

1981 Apple Computer introduces its Apple IIc, a portable machine designed to have the same operating capacity as the standard IIe model. The machine came with 128 kilobytes of RAM and a 5 1/4 inch floppy disk drive. *CHM

In 1990, space shuttle Discover was launched from Cape Canaveral, carrying the Hubble Space Telescope to be placed into orbit. *TIS

1562 Xu Guang-qi ( April 24, 1562 - November 8, 1633 ,aged 71) was a Chinese mathematician who made Western mathematics available by translating works into Chinese. *SAU

1620 John Graunt(24 April 1620 – 18 April 1674)His book Natural and Political Observations Made upon the Bills of Mortality (1662) used analysis of the mortality rolls in early modern London as Charles II and other officials attempted to create a system to warn of the onset and spread of bubonic plague in the city. Though the system was never truly created, Graunt's work in studying the rolls resulted in the first statistically-based estimation of the population of London. It was his only book but it was the foundations of both statistics and demography. *VFR [A nice essay on his "Bills of Mortality" and life is at the Rice University Stats Page by Thompson. Some personal history is at The Renaissance Mathematicus

1750 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU

1863 Giovanni Vailati (24 April 1863 – 14 May 1909) was an Italian proto-analytic philosopher, historian of science, and mathematician. Vailata's main historical interests concerned mechanics, logic, and geometry, and he was an important contributor to a number of areas, including the study of post-Aristotelian Greek mechanics, of Galileo's predecessors, of the notion and rôle of definition in the work of Plato and Euclid, of mathematical influences on logic and epistemology, and of the non-Euclidean geometry of Gerolamo Saccheri. He was particularly interested in the ways in which what might be seen as the same problems are addressed and dealt with at different times.
His historical work was interrelated with his philosophical work, involving the same fundamental views and methodology. Vailati saw the two as differing in approach rather than subject matter, and believed that there should be co-operation between philosophers and scientists in the pursuit of historical studies. He also held that a complete history demanded that one take into account the relevant social background. *Wik

1899 Oscar Zariski (24 April 1899 in Kobrin, Russian Empire (now Belarus) - 4 July 1986 in Brookline, Massachusetts, USA) Zariski's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties. *SAU

1919 David H. Blackwell (April 24, 1919 – July 8, 2010) American Statistician, President of the Institute of Mathematical Statistics. Many more honours were to come his way. He was elected Vice President of the American Statistical Association, Vice President of the International Statistical Institute, and Vice President of the American Mathematical Society. In 1965 he was elected to the National Academy of Sciences. He received the John von Neumann Theory Prize from the Operations Research Society of America in 1979 for his work in dynamic programming and the R A Fisher Award from the Committee of Presidents of Statistical Societies in 1986.*SAU
and a nice links for more information, with thanks to Dave Bee:
For the extensive “An Oral History With David Blackwell”, conducted by Nadine Wilmot in 2002 and 2003.

1924 Isadore Manuel Singer (April 24, 1924, ) is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology. He is noted for his work with Michael Atiyah proving the Atiyah–Singer index theorem in 1962, which paved the way for new interactions between pure mathematics and theoretical physics.
He was born in Detroit, Michigan, and received his undergraduate degree from the University of Michigan in 1944. After obtaining his M.S. and Ph.D. from the University of Chicago in 1948 and 1950 respectively, he taught at UCLA and MIT, where he has spent the majority of his career.
Singer won the Abel Prize in 2004(shared with Michael Atiyah for the Atiyah-Singer Index Theorem) *Wik

1947 Ovide Arino (24 April 1947 - 29 September 2003) mathematician working on delay differential equations. His field of application was population dynamics. He was a quite prolific writer, publishing over 150 articles in his lifetime. He also was very active in terms of student supervision, having supervised about 60 theses in total in about 20 years. Also, he organized or coorganized many scientific events. But, most of all, he was an extremely kind human being, interested in finding the good in everyone he met. *

1572 Petrus Ramus (1515, 24 Apr 1572 [Wik gives his death on 26 August]).
(Pierre de La Ramée) French mathematician and logician who challenged Aristotelian philosophy. As early as in his Master of Arts thesis (1536) he held that quaecumque ab Aristotle dicta essent, commentitia esse ("everything which Aristotle said is invented or contrived"). His book Aristotelicae animadversiones (1543) led to a decree from Francis I (Mar 1544) prohibiting such teachings. Though the decree was rescinded three years later by Henry II, Ramus continued to draw hostility from other scholars. He was an early adherent of the Copernican system. Ramus was murdered during the St. Bartholomew's Day massacre, but his theories remained influential after his death. *TIS

1656 Thomas Fincke (6 January 1561 – 24 April 1656) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years. His lasting achievement is found in his book Geometria rotundi (1583), in which he introduced the modern names of the trigonometric functions tangent and secant.
His son in law was the Danish physician and natural historian, Ole Worm, who married Fincke's daughter Dorothea.*Wik

1952 Hendrik Anthony Kramers (17 Dec 1894 - 24 Apr 1952 at age 57)Dutch physicist who, with Ralph de Laer Kronig, derived important equations relating the absorption to the dispersion of light. He also predicted (1924) the existence of the Raman effect, an inelastic scattering of light. Kramer's work covers almost the entire field of theoretical physics. He published papers dealing with mathematical formalism of quantum mechanics, and others on paramagnetism, magneto-optical rotation, ferro-magnetism, kinetic theory of gases, relativistic formalisms in particle theory, and on theory of radiation. His work shows outstanding mathematical skill and careful analysis of physical principles. *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

Sunday, 23 April 2017

On This Day in Math - April 23

"Whatever is worth saying,
can be stated in fifty words or less"
~ Stanislaw Ulam *bt (before twitter)
Thanks to @cytiaB for this one

TThe 113th day of the year; 113 is prime, its reversal (311) is prime, and the number you get by any reordering of its digits is still prime. Students might try to find other of these "absolute" or "permutable" primes.

Also the sum of the first 113 digits of e is prime. That was also true of yesterday's number, and tomorrow's. (I was just wondering to myself, what is the longest known string of consecutive n for which the first n digits of e are prime? And a similar question for pi? "Anyone...anyone??? Bueller???)

355 is almost exactly \(113 \pi = 354.9999699.. \) No year day is closer,

There are 13 consecutive divisible integers (non-primes) between 113 and 127. How far until the next streak as long, or longer?


1635 The 1st public school in the United States, Boston Latin School, was founded. It is still enrolling students. *George Costanza

1827 Sir William Hamilton presented his Theory of Systems of Rays at the Royal Irish Academy in Dublin. Although he was still an undergraduate, only 21 years old, his work is one of the important works in optics, for it provided a single function that brings together mechanics, optics and mathematics. It led to establishing the wave theory of light, which gives that light is a form of energy that travels in waves. *TIS

1906 First American automobile meets the first American speed bump. In March of 1906, residents of Chatham Borough, New Jersey had begun construction of a speed control device, crosswalks that were five Inches high, constructed of flagstones and cobblestones. Their creation was a plan to slow down the "very fast pace" (10-15 miles per hour) of the new motor carriages that have begone to take over the roads of the center of town. On "April 22, 1906 with great fanfare and many spectators. Bystanders set up seating and vendors sold hot dogs and pop corn to serve the growing group of onlookers. The next day local newspapers reported on the wreckage and carnage from the newly discovered speed reducers." Here is the article from the New York Times on April 23:
There were several persons in the machine, and when the heavy rubber tires struck the elevation there was a palpitation of the machinery and the car shot up several feet in the air. Goggles, hats, a monkey wrench, sidecombs, hairpins and other articles flew in all directions. The crowd gave a cheer and decided the borough’s plan was effective. The ‘bumps' installed by the borough officials of the village of Chatham to check the speed of automobiles through the village had their first test yesterday, and proved a decided success.
 The more conventional speed bumps we are familiar with were not invented until June of 1953.  They were created by Nobel Prize winning physicist, Arthur Holly Compton, while  he was Chancellor of Washington University in St. Louis, Missouri. *Quora.Com, Wik

 1948 Contract signed by A. Nielsen for UNIVAC I. The UNIVAC I (UNIVersal Automatic Computer I) was the first commercial computer produced in the United States. It was designed principally by J. Presper Eckert and John Mauchly, the inventors of the ENIAC. Design work was begun by their company, Eckert-Mauchly Computer Corporation, and was completed after the company had been acquired by Remington Rand. (In the years before successor models of the UNIVAC I appeared, the machine was simply known as "the UNIVAC".) The image is not the computer, but the operators console... (no mouse for that monster)
The first UNIVAC was delivered to the United States Census Bureau on March 31, 1951, and was dedicated on June 14 that year. The fifth machine (built for the U.S. Atomic Energy Commission) was used by CBS to predict the result of the 1952 presidential election. With a sample of just 1% of the voting population it correctly predicted that Dwight Eisenhower would win. The UNIVAC I computers were built by Remington Rand's UNIVAC division (successor of the Eckert-Mauchly Computer Corporation, bought by Rand in 1950 which later became part of Sperry, now Unisys). *Wik

In 1962, the first American satellite to reach the moon surface, the Ranger IV, was launched at 3:50pm from Cape Canaveral, Florida. As intended, it impacted on the moon three days later at 7:50pm on 26 Apr, travelling at 5,963 mph. The launch vehicle was an Atlas-Agena B rocket, 102 feet high, 16 feet in diameter at the base. The distance the satellite would travel was about 229,541 miles. *TIS

1964 SEAC Computer Retired:
The National Bureau of Standards retires its SEAC (Standards Eastern Automatic Computer), which it built in Washington 15 years earlier as a laboratory for testing components and systems for setting computer standards. The SEAC was the first computer to use all-diode logic, a technology more reliable than vacuum tubes, and the first stored-program computer completed in the United States. Magnetic tape in the external storage units stores programming information, coded subroutines, numerical data, and output.*CHM

1973 The US issued a commemorative stamp honoring the 500th year of the publication of Copernicus' De Revolutionibus.

In 1994, physicists at the Department of Energy's Fermi National Accelerator Laboratory discovered the subatomic particle called the top quark.*TIS

2012 An active sunspot period leads to incredible aurora in US Midwest. The aurora borealis put on a dazzling show in more than a dozen states Monday night, according to
A particularly spectacular display was seen in Fergus Falls in western Minnesota, and Douglas Kiesling was on hand to film a stunning time-lapse video of the event,


1628 Johann Hudde was a Dutch mathematician who worked on maxima and minima and the theory of equations. He gave an ingenious method to find multiple roots of an equation. He worked on improving the algebraic methods of René Descartes, seeking to extend them to the solution of equations of a higher degree by applying an algorithm. He also developed an algorithm based on Fermat's method to deal with the maxima, minima and tangents to curves of algebraic functions. Later, he served as burgomaster of Amsterdam for 30 years. During this time time he made a mathematical study of annuities. Hudde continued with an interest in physics and astronomy, producing lenses and microscopes. He collaborated with Baruch Spinoza, of Amsterdam, on telescopes. Hudde determine that in a telescope, a plano-convex lenses were better than concavo-convex. *TIS He is buried in #58 in the high choir of the Oude kerk (old church) in Amsterdam. (Help, send pictures please?) Unfortunatly, Donovan Carroll informed me that his stone is covered over by the choir loft. More about Hudde and the "lost calculus" here.  And the Renaissance Mathematics has a nice article about Hudde's circle of associates that is both political and mathematical, and involves a violent murder....

1743 Samuel Williams (23 Apr 1743; 2 Jan 1817 at age 73) American natural philosopher and clergyman who organized the first expedition of its kind in the U.S. (departing on 9 Oct 1780) to observe a total solar eclipse in Penobscot Bay, Maine, although it was held by the British enemy. The eclipse was very slightly less than being total, and he is believed to be the first to observe the “ Baily's Beads” phenomenon seen along the sun's last sliver. Previously, with John Winthrop (under whom he studied) he travelled to St. John's, Newfoundland (1761) to observer the Transit of Venus. When Wintrop died, Williams succeeded him (1779) as the Hollis Professor of Mathematics and Natural Philosophy at Harvard University. He researched and taught astronomy, meteorology, and magnetism. He resigned in June 1788. He also engaged in state boundary surveys: NY and Mass. (1785-88), and Vermont and Canada (1795).*TIS

1853 Alphonse Bertillon (23 Apr 1853, 13 Feb 1914 at age 60) French criminologist who was chief of criminal identification for the Paris police from 1880. He developed an identification system known as anthropometry, or the Bertillon system, that came into wide use in France and other countries. The system records physical characteristics (eye colour, scars, deformities, etc.) and specified measurements (height, fingertip reach, head length and width, ear, foot, arm and finger length, etc) These are recorded on cards and classified according to the length of the head. After two decades this system was replaced by fingerprinting in the early 1900s because Bertillon measurements were difficult to take with uniform exactness, and could change later due to growth or surgery. *TIS

1858 Max Plank, (April 23, 1858 – October 4, 1947)  German physicist, born. He studied at Munich and Berlin, where he studied under Helmholz, Clausius and Kirchoff and subsequently joined the faculty.he became professor of theoretical physics (1889-1926). His work on the law of thermodynamics and the distribution of radiation from a black body led him to abandon classical Newtonian principles and introduce the quantum theory (1900), for which he was awarded the Nobel Prize for Physics in 1918. This assumes that energy is not infinitely subdivisible, but ultimately exists as discrete amounts he called quanta (Latin, "how much"). Further, the energy carried by a quantum depends in direct proportion to the frequency of its source radiation.*TIS

1910 Sheila Scott Macintyre (née Sheila Scott, April 23, 1910 - March 21, 1960) was a Scottish mathematician well known for her work on the Whittaker constant. Macintyre is also well known for creating a multilingual scientific dictionary: written in English, German, and Russian; at the time of her death, she was working on Japanese.*Wik

1911 Felix Adalbert Behrend (23 April 1911 in Charlottenburg, Berlin, Germany -27 May 1962 in Richmond, Victoria, Australia) Behrend studied number theory for his doctorate at the University of Berlin with Erhard Schmidt as his advisor. He was awarded his doctorate in 1933 for his dissertation Über numeri abundantes. Even before the award of his doctorate he had published three papers on number theory, the first two being Über einen Satz von Herrn Jarnik (1932) and Über numeri abundantes (1932). Of course 1933, the year that Behrend was awarded his doctorate, was also the year that Hitler came to power in Germany.
Like many Germans who fled from the Nazi threat, he found himself in England which was at war with his native Germany. He continued his work on number theory and published "On obtaining an estimate of the frequency of the primes by means of the elementary properties of the integers" in the Journal of the London Mathematical Society in 1940. The fact that he was passionately anti-Nazi did nothing to help save him from being interned as an enemy alien in 1940 and he was put on the ship the Dunera bound for Australia. He served periods of internment at Hay, Orange and Tatura in Australia. His experiences in Camp 7 at Hay during 1940-41 are related in . One should not think that internment meant an end to mathematics, for he gave lecture courses at the Camp and prepared some of his younger fellow internees for mathematics examinations at the University of Melbourne.
After his release in 1942, Behrend was appointed as a tutor at the University of Melbourne. He continued his research in number theory and published On the frequency of the primes in the Journal of the Royal Society of New South Wales in 1942. This paper was a continuation of the one he had published in London two years earlier. In the following year he published a paper on a totally different topic. This was A polyhedral model of the projective plane which also appeared in the Journal of the Royal Society of New South Wales. Behrend is commemorated by the 'Behrend memorial lecture in mathematics', established at the University of Melbourne in 1963 with funds provided by his widow. *SAU

1970 My Oldest son is born, "Happy Birthday Beau".

1914 Georgii Nikolaevich Polozii (23 April 1914 in Transbaikal, Russia - 26 Nov 1968 in Kiev, Ukraine) Polozii studied at Saratov University which had been founded in 1919. He graduated in 1937 and then was appointed to the teaching staff of the university. In 1949 Polozii was appointed to the University of Kiev and he remained at Kiev until his death in 1968.
Polozii's major pure mathematical contributions were to the theory of functions of a complex variable, approximation theory, and numerical analysis. He also made major contributions to mathematical physics and applied mathematics in particular working on the theory of elasticity.

Between 1962 and 1966 Polozii developed the theory for a new class of (p,q) analytic functions.
In approximation theory Polozii worked mainly with the aim of developing effective methods to solve boundary value problems which arise in mathematical physics. He work here produced the method of summary representation.*SAU


1616 Miguel de Cervantes Saavedra died and William Shakespeare both died on this date, the former in Madrid, Spain, the latter in Stratford-on-Avon, England. Which one died first? This is not a trick question; they died several days apart. All you need to solve it is some knowledge of the calendar. *VFR (Curiously, Shakespeare was also born on this date in 1564. If you see April 26th, that is date of his baptism.)

1839 The Very Reverend James Wood (14 December 1760 – 23 April 1839) was a mathematician, Dean of Ely and Master of St John's College, Cambridge.
Wood was born in Holcombe where his father ran an evening school and taught his son the elements of arithmetic and algebra. From Bury Grammar School he proceeded to St John's College, Cambridge in 1778, graduating as senior wrangler in 1782. On graduating he became a fellow of the college and in his long tenure there produced several successful academic textbooks for students of mathematics. (The Elements of Algebra (1795); The Principles of Mechanics (1796); The Elements of Optics (1798))
Wood remained for sixty years at St. John's, serving as both President (1802–1815) and Master (1815–1839); on his death in 1839 he was interred in the college chapel and bequeathed his extensive library to the college, comprising almost 4,500 printed books on classics, history, mathematics, theology and travel, dating from the 17th to the 19th centuries.[3]
Wood was also ordained as a priest in 1787 and served as Dean of Ely from 1820 until his death.{He was succeeded by another eminent mathematician, George Peacock)*Wik

1930 Henry Ernest Dudeney, (10 April 1857–23 April 1930)  England's greatest puzzlist. He was unusually skilled at geometrical dissections, cutting a polygon into the smallest number of pieces that can be refitted to make a different type of polygon. He was also the first to apply digital roots, a term he coined, to recreational mathematics. *VFR
In April 1930, Dudeney died of throat cancer in Lewes, where he and his wife had moved in 1914 after a period of separation to rekindle their marriage. Alice Dudeney survived him by fourteen years and died November 21, 1945, after a stroke. Both are buried in the Lewes town cemetery. Their grave is marked by a copy of an 18th century Sussex sandstone obelisk, which Alice had copied after Ernest's death to serve as their mutual tombstone.(would love a photo if anyone is in that area)
For samples of his puzzles, the Amazon Kindle edition is free.

1960 Max von Laue (9 Oct 1879, 23 Apr 1960 at age 80)German physicist who was a recipient of the Nobel Prize for Physics in 1914 for his discovery of the diffraction of X-rays in crystals. This enabled scientists to study the structure of crystals and hence marked the origin of solid-state physics, an important field in the development of modern electronics. *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