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

~Arnold SommerfeldThe 117th day of the year; 117 can be written as the difference of prime squares (11

^{2}- 2

^{2}) or prime cubes (5

^{3}- 2

^{3}). *Prime Curios (Can you find another number which can be expressed as both the difference of squared primes and cubed primes?)

117 is the smallest possible length for the longest side of a Heronian tetrahedron (one whose sides are all integers, and all surface areas and volume are rational). The other edges are 51, 52, 53, 80, & 84. (Are the areas / volume integral?)

EVENTS

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. *astronomy.wikia.com Saturn_Project1760 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 madeFrederick 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].

BIRTHS

**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

DEATHS

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=1

^{3}+12

^{3}=9

^{3}+10

^{3}*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.His readers seem to find that Euler was correct. No suprise there.

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?”

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