## Friday, 24 March 2017

### On This day in Math - March 24

 Harrison H1

But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.
~Marston Morse

The 83rd day of the year; 83 is the smallest prime number which is the sum of a prime number of consecutive prime numbers in a prime number of different ways, i.e., 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23. *Prime Curios (Whew! say that three times in a hurry)

The smallest prime with a digit sum of 83 is 3999998999.
83 is the smallest prime whose square, 6889, is a strobogrammatic number. (you can rotate it 180 degrees and it reads the same)

83 is The number of permutations of the 10 distinct digits taken 9 at a time that are perfect squares. These range from 101242 = 102495376 to 303842 = 923187456.*Prime Curios

EVENTS
1789 Throughout his life, Jefferson was avid to keep up with the mathematical world, and to spread knowledge about it to others. How deeply he explored mathematics depended obviously on what else was happening in his life at the time, but he was always keen to pass on what he had learned to his correspondents. Staying in Paris in 1789 he was eager to pass on information about the latest work by Lagrange In a letter to Harvard President Joseph Willard on March 24, 1789 he writes, "A very remarkeable work is the 'Mechanique Analytique' of La Grange in 4to. He is allowed to be the greatest mathematician now living, and his personal worth is equal to his science. The object of his work is to reduce all the principles of Mechanics to the single one of the Equilibrium, and to give a simple formula applicable to them all. The subject is treated in the Algebraic method, without diagrams to assist the conception. My present occupation not permitting me to read any thing which requires a long and undisturbed attention, I am not able to give you the character of this work from my own examination. It has been received with great approbation in Europe." *John Fauval, Lecture at Univ of Va.
Good book about Jefferson's Scientific interests and contributons:

1899 Ren´e Louis Baire defended his doctoral thesis on the theory of functions of a real variable. He was inﬂuential in introducing transﬁnite set theory into analysis. *VFR

1930 Planet X  was officially named Pluto on March 24, 1930:  On the nights of Jan 23 and 30th of January, 1930, Tombaugh found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. *Wik

1959 TI Demonstrates Integrated Circuit Invented by Jack Kilby:
Texas Instruments demonstrates the first integrated circuit. Its inventor, Jack Kilby (b. Nov 8, 1923), created the device to prove that resistors and capacitors could exist on the same piece of semiconductor material. His circuit consisted of a sliver of germanium with five components linked by wires. It was Fairchild's Robert Noyce, however, who filed for a patent within months of Kilby and who made the IC a commercially-viable technology. Both men are credited as co-inventors of the IC.*CHM

BIRTHS

1693 John Harrison (24 Mar 1693; 24 Mar 1776 at age 83)
English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. He was prompted to begin this work after a huge reward was offered by the British government for new navigational tools to avoid further disasters at sea. John Harrison took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. *TIS [The Dictionary of Scientific Biographies  shows an uncertainty in the date of birth as 24 Mar(?) 1693.] See deaths below for notes on a popular biography.

1809 Joseph Liouville   (24 Mar 1809, 8 Sep 1882) French mathematician who discovered transcendental numbers (those which are not the roots of algebraic equations having rational coefficients), and that there are infinitely many of them. He also did work in real and complex analysis, number theory, and differential geometry. His name is remembered in the Sturm-Liouville theory of differential equations that generalizes Joseph Fourier's ideas, and are important in mathematical physics. He studied celestial mechanics. Liouville founded in 1836, and edited for nearly four decades, the Journal de Mathématique which remains a leading French mathematical publication. He edited and published (1843) the manuscripts left behind upon the untimely death of Evariste Galois 22 years earlier.*TIS Liouville was one of Lord Kelvin's mathematical heroes, and he once stopped a lecture in Glascow to ask his students, "Do you know what a mathematician is?" He then wrote on the blackboard the equation

and, pointing to the board stated, A mathematician is one to whom that  is as obvious as twice two are four is to you.  Liouville was a  mathematician." *Walter Gratzer, Eurekas and Euphorias, pg 21

1835 Josef Stefan (24 Mar 1835, 7 Jan 1893) Austrian physicist who proposed a law of radiation (1879) stating that the amount of energy radiated per second from a black body is proportional to the fourth power of its absolute temperature. (A black body is a theoretical object that absorbs all radiation that falls on it.) This law is known as Stefan's law or the Stefan-Bolzmann law. He also studied electricity, the kinetic theory of gases and hydrodynamics.*TIS

1848 Jules Tannery (March 24, 1848 – December 11, 1910) was a French mathematician who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard.
He discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."
He notably influenced Paul Painlevé, Jules Drach, and Émile Borel to take up science.
His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.*Wik

1892 Harold Calvin Marston Morse (24 March 1892 in Waterville, Maine, USA - 22 June 1977 in Princeton, New Jersey, USA) developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis*SAU

1893 Walter Baade (24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

1941 Joseph H. Taylor Jr. (24 Mar 1941,   )American radio astronomer and physicist who, with Russell A. Hulse, was the corecipient of the 1993 Nobel Prize for Physics for their joint discovery of the first binary pulsar (1974). This unique phenomenon, two stars orbiting each other - one of them giving off regular radio-frequency "beeps" - has been important as a deep space proving ground for Einstein's general theory of relativity. Their research group at Princeton used the 1,000 foot radio telescope at Arecibo, Puerto Rico, the largest and most sensitive in the world for catching radio waves from space. *TIS

1948 Alice Chang (24 March 1948 in Ci-an, China)is a Chinese American mathematician specializing in aspects of mathematical analysis ranging from harmonic analysis and partial differential equations to differential geometry. She is a professor of mathematics and chair of the department at Princeton University.*Wik Her husband Paul Yang works on a.o. differential geometry -currently Princeton U. (HT to C L O ‏@cldm_ish)

DEATHS
1776 John Harrison (24 Mar 1693; 24 Mar 1776 at age 83)
English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. He was prompted to begin this work after a huge reward was offered by the British government for new navigational tools to avoid further disasters at sea. John Harrison took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. *TIS
Dava Sobel's book, below, is a fun read, but it is important to point out that historians of science often find it less than satisfactory.  Here is one clip from Rebekah Higgitt, an excellent young science historian at the Univ of Kent and former Curator of History of Science and Technology at the National Maritime Museum and the Royal Observatory, Greenwich. "Sobel’s book is well-done but greatly simplified journalistic history, in which she unashamedly creates a story by identifying heroes and villains, and by making astronomy and timekeeping rival rather than complementary methods for finding longitude. It has annoyed professional historians of science because it plays to some of the ‘sins’ of our field, typified by the notion of the “lone genius”, and causes angst because our preferred version of history is always richer and more complex," In a personal note she wrote, [The book] "Unfairly & inaccurately creates a villain (Maskleyne) as a foil."

1956 Christine Mary Hamill (July 24, 1923 – March 24, 1956) was an English mathematician who specialized in group theory and finite geometry. After receiving her Ph.D. at the University of Cambridge in 1951, she was appointed to a lectureship in the University of Sheffield and later was appointed lecturer in the University College, Ibadan, Nigeria.*Wik

1956 Sir Edmund Taylor Whittaker (24 Oct 1873; March 24 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS

1962 Auguste Antoine Piccard (28 January 1884 – 24 March 1962) was a Swiss physicist, inventor and explorer. Piccard and his twin brother Jean Felix were born in Basel, Switzerland. Showing an intense interest in science as a child, he attended the Swiss Federal Institute of Technology (ETH) in Zurich, and became a professor of physics in Brussels at the Free University of Brussels in 1922, the same year his son Jacques Piccard was born. He was a member of the Solvay Congress of 1922, 1924, 1927, 1930 and 1933.
In 1930, an interest in ballooning, and a curiosity about the upper atmosphere led him to design a spherical, pressurized aluminum gondola that would allow ascent to great altitude without requiring a pressure suit. Supported by the Belgian Fonds National de la Recherche Scientifique (FNRS) Piccard constructed his gondola.
An important motivation for his research in the upper atmosphere were measurements of cosmic radiation, which were supposed to give experimental evidence for the theories of Albert Einstein, whom Piccard knew from the Solvay conferences and who was a fellow alumnus of ETH.
On May 27, 1931, Auguste Piccard and Paul Kipfer took off from Augsburg, Germany, and reached a record altitude of 15,781 m (51,775 ft). (FAI Record File Number 10634) During this flight, Piccard was able to gather substantial data on the upper atmosphere, as well as measure cosmic rays. On 18 August 1932, launched from Dübendorf, Switzerland, Piccard and Max Cosyns made a second record-breaking ascent to 16,201 m (53,153 ft). (FAI Record File Number 6590) He ultimately made a total of twenty-seven balloon flights, setting a final record of 23,000 m (75,459 ft).
In the mid-1930s, Piccard's interests shifted when he realized that a modification of his high altitude balloon cockpit would allow descent into the deep ocean. By 1937, he had designed the bathyscaphe, a small steel gondola built to withstand great external pressure. Construction began, but was interrupted by the outbreak of World War II. Resuming work in 1945, he completed the bubble-shaped cockpit that maintained normal air pressure for a person inside the capsule even as the water pressure outside increased to over 46 MPa (6,700 psi). Above the heavy steel capsule, a large flotation tank was attached and filled with a low density liquid for buoyancy. Liquids are relatively incompressible and can provide buoyancy that does not change as the pressure increases. And so, the huge tank was filled with gasoline, not as a fuel, but as flotation. To make the now floating craft sink, tons of iron were attached to the float with a release mechanism to allow resurfacing. This craft was named FNRS-2 and made a number of unmanned dives in 1948 before being given to the French Navy in 1950. There, it was redesigned, and in 1954, it took a man safely down 4,176 m (13,701 ft).
Piccard was the inspiration for Professor Cuthbert Calculus in The Adventures of Tintin by Belgian cartoonist Hergé. Piccard held a teaching appointment in Brussels where Hergé spotted his unmistakable figure in the street.
Gene Roddenberry named Captain Jean-Luc Picard in Star Trek after one or both of the twin brothers Auguste and Jean Felix Piccard, and derived Jean-Luc Picard from their names. *Wik

1995 (Noël) Joseph (Terence Montgomery) Needham (9 Dec 1900, 24 Mar 1995 at age 94)was an English biochemist, embryologist, and historian of science who wrote and edited the landmark history Science and Civilization in China, a remarkable multivolume study of nearly every branch of Chinese medicine, science, and technology over some 25 centuries. As head of the British Scientific Mission in China (1942-46) he worked to assure adequate liaison between Chinese scientists and technologists and their colleagues in the West. As an historian of science and technology he wanted to break through the parochial, Europe-centred views of most of his colleagues by disclosing the achievements of traditional China and the contributions made by China leading up to the scientific revolution. *TIS

1976 Francis Dominic Murnaghan (4 Aug 1893 in Omagh, Co. Tyrone, Ireland- 24 March 1976 in Baltimore, Maryland, USA) was an Irish mathematician, former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics (Murnaghan and Birch–Murnaghan equations of state).*SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Thursday, 23 March 2017

### On This Day in Math - March 23

 Interior of Iranian Mosque *Cliff Pickover@pickover

Science does not have a moral dimension. It is like a knife. If you give it to a surgeon or a murderer, each will use it differently.
~Wernher von Braun

The 82nd day of the year; 82 is the sum of the 10th(8+2) prime and the 16th(8x2) prime. It is the smallest number with this property.  Can you find the next?

82 is a happy number. Take the sum of the square of the digits, repeat on the result, and you eventually arrive at 1.

82 is the number of different ways you can arrange 6 regular hexagons by joining their adjacent sides:

82 can be written as :
The sum of Fibonacci numbers, 82 = 1 + 5 + 21 + 55
The sum of consecutive integers, 82= 19 + 20 + 21 + 22

EVENTS
4BC A lunar eclipse may have coincided with the death of one of the most notorious kings of all time. Historian Flavius Josephus notes that an eclipse of the Moon preceded the death of the biblical king Herod. Three eclipses fit the bill as occurring in the right time frame and being visible from the Middle East, but the favorite contender is the March 23, 4 B.C. rising total lunar eclipse that may have marked the demise of Herod.*12 Famous Eclipses in History

In 1840, Englishman J.W. Draper took the first successful photo of the full Moon. He made a daguerreotype, a precursor of the modern photograph.*TIS The photo from this night was destroyed in a fire in a New York University. The one at right is one he took three days later, and displayed at the New York Lyceum on April 13, 1840.
Daguerre himself is believed to be the first person to take a photograph of the moon, using his daguerreotype process, on January 2, 1839. Unfortunately, in March of that same year, his entire laboratory burnt to the ground, destroying all his written records and much of his early experimental work–and that historical image of the moon. *lightsinthedark *APS.org
Appropriately, it was an astronomer who coined the term photography in 1839, when Johann Heinrich von Madler combined “photo” (from the Greek word for “light”) and “graphy” (“to write”).

1857 The Otis Elevator Company completes the first commercial passenger elevator installation at a five-story department store, the E. V . Haughwout Company at Broadway and Broome Street in what is now New York City’s SoHo district. After very slow sales the company's first few years, Otis decided to make a dramatic demonstration at the New York Crystal Palace, a grand exhibition hall built for the 1853 Worlds Fair.
Perched on a hoisting platform high above the crowd at New York’s Crystal Palace, a pragmatic mechanic (Otis himself, it seems) shocked the crowd when he dramatically cut the only rope suspending the platform on which he was standing. The platform dropped a few inches, but then came to a stop. His revolutionary new safety brake had worked, stopping the platform from crashing to the ground. “All safe, gentlemen!” the man proclaimed.
Otis’ demonstration had the desired effect. He sold seven elevators that year, and 15 the next. *Wired, HT Rick Brutti@Rbrutti

1881 J J Sylvester writes to Arthur Cayley to announce, "I believe that I have proved Gordan's Theorem, and can assign a superior limit to the number of fundamental invariants." His proof was founded on the prospect that a certain sequence increased without bound. By October he knew that it did not.

1920 When Professor Johann Palisan of the University of Vienna discovered an asteroid on this date, he chose to name it after Herbert Hoover, who would later become the President of the USA. As head of the American Relief Administration, after WWI, Hoover organized shipments of food for millions of starving people in Central Europe. In Finnish it is common to use the word “hoover” with the meaning, “to help”. (at least it was, can someone tell me if this is still so) It seems strange that today most history books in his home country preserve his name in the term “Hooverville’s” for hobo camps and shanty towns where displaced peoples lived during the American Great Depression. *Wik

In 1950, the U.N. World Meteorological Organization was established. *TIS The World Meteorological Organization (WMO) is a specialized agency of the United Nations. It is the UN system's authoritative voice on the state and behaviour of the Earth's atmosphere, its interaction with the oceans, the climate it produces and the resulting distribution of water resources. *WMO webpage

1981 The March 23 issue carried the first mention of Rubik's Cube in Time Magazine. *Mark Longridge, A Rubik's Cube Chronology
Rubik had begun distribution in Hungary in 1977, and by early 1979 Mathematical Intelligencer carried an introduction in of "The Hungarian Magic Cube" by David Singmaster with the note, "A new mathematical toy has been slowly becoming available in western Europe and is becoming more popular than the Soma Cube, Instant Insanity, and may well surpass the popularity of Mastermind or Sam Loyd's Fifteen puzzle."

In 1989, fusion at room temperature was claimed by Martin Fleischmann and Stan Pons, two Utah electrochemists. They believed they had sustained a controlled nuclear fusion reaction in a bench-top fusion percolator made up of two electrodes with heavy water which generated up to 100 per cent more energy than they put in. There were sporadic sightings of excess heat, which Fleischmann said cannot be accounted for by chemistry alone. However, the idea of cold fusion was discredited because leading scientists were unable to replicate the work and found no hallmarks of nuclear processes, especially none of the subatomic particles called neutrons. Their tantalizing promise of a limitless supply of cheap energy were invalid.*TIS

2012 Sonia Kovalevsky Day.. "Her birthday is January 15, but today gets to be her day. Cathy O'Neil (aka Mathbabe) started Sonia Kovalevsky Day at Barnard College in 2006, and it sounds like it's been going strong ever since." *Sue VanHattum at MathMama Writes blog.

BIRTHS
1709 Hans Ulrich Grubenmann (23 Mar 1709; 24 Jan 1783 at age 73)  Swiss carpenter, who with his brother Johannes, built a bridge (1758) over the Limmat River at the town of Wettingen, near Zürich, that is believed to be the first timber bridge to employ a true arch in its design. The brothers' ingenious combination of the arch and truss principles made it possible to construct bridges longer and better than ever before. They constructed churches as well as other bridges. *TIS

1754 (Jurij)Georg Freiherr von Vega (23 Mar 1754 in Zagorica, Ljubljana, Slovenia - 26 Sept 1802 in Vienna, Austria) wrote about artillery but he is best remembered for his tables of logarithms and trigonometric functions. Vega calculated π to 140 places, a record which stood for over 50 years. This appears in a paper which he published in 1789.
In September 1802 Vega was reported missing. A search was unsuccessful until his body was found in the Danube near Vienna. The official cause of death was an accident but many suspect that he was murdered. *SAU

1795 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850.
Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik

1827 Pierre Simon, Marquis de Laplace (23 Mar 1749, 5 Mar 1827 at age 78) was a French mathematician, physicist, statistician and astronomer known for his mathematical analysis of the stability of the solar system (1773), alleviating Isaac Newton's concerns about perturbations between planets. He took an exact approach to science. He developed an explanation of surface tension of a liquid in terms of inter-molecular attractions, investigated capillary action and the speed of sound. He assisted Antoine Lavoisier (1783) investigating specific heat and heats of combustion, initiating the science of thermochemistry. He believed the solar system formed from a collapsing nebula. He contributed to the mathematics of probability and calculus, in which a differential equation is known by his name, and was involved in establishing the metric system.*TIS His last words were, “What we know is very slight; what we don’t know is immense.” *Eves, Mathematical Circles Revisited, 319◦

1829 Norman Robert Pogson (23 Mar 1829; 23 Jun 1891 at age 62) English astronomer who devised the magnitude scale of the brightness of stars (1850) now in use. He divided the classical scale in which a first magnitude star is one hundred times brighter than a sixth magnitude star using five integer steps. Each step represents a fifth-root of 100 (about 2.512) increase in brightness. The Sun's magnitude on this scale is -26.91, whereby negative numbers denote objects brighter than first magnitude. Sirius is magnitude -1.58, Aldebaran is 1 and the faintest star detected is 30. His interest in astronomy began in his youth; by age 18 he had calculated orbits for two comets. He discovered 8 asteroids, 21 new variable stars and compiled a massive star catalogue. In 1860 he moved to India for the remainder of his life's work.*TIS

1837 Richard Anthony Proctor (23 Mar 1837, 12 Sep 1888) English astronomer who first suggested (1873) that meteor impacts caused lunar craters, rather than volcanic action. He studied the motion of stars, their distribution, and their relation to the nebulae. In 1867 he prepared a map of the surface of Mars on which he named continents, seas, bays and straits (in the same manner that Riccioli used on his map of the moon). However, he did not perceive "canals" on the surface, which later Schiaparelli identified. Proctor participated in expeditions of 1874 and 1882 to observe the transit of Venus. He was very successful popularizing astronomy by his writings in books, periodicals, and lectures he gave as far abroad as Australia and America (where he stayed after 1881).*TIS

1855 Franklin H(enry) Giddings (23 Mar 1855; 11 Jun 1931 at age 76) American sociologist, one of the first in the United States to turn sociology from a branch of philosophy into a research science dependent on statistics. He was noted for his doctrine of the "consciousness of kind," which he derived from Adam Smith's conception of "sympathy," or shared moral reactions. His explanation of social phenomena was based this doctrine - his theory that each person has an innate sense of belonging to particular social groups. He encouraged statistical studies in sociology. *TIS

1862 Eduard Study (23 March 1862 in Coburg, Germany - 6 Jan 1930 in Bonn, Germany)Study became a leader in the geometry of complex numbers. He reformulated, independently of Severi, the fundamental principles of enumerative geometry due to Schubert. He also worked on invariant theory helping to develop a symbolic notation. In 1923 he published important work on real and complex algebras of low dimension publishing these results. Study's contribution is summarized by W Burau as follows, "... Study demonstrated what he considered to be a thorough treatment of a problem. ... With Corrado Segre, Study was one of the leading pioneers in the geometry of complex numbers. ... Adept in the methods of invariant theory ... Study, employing the identities of the theory, sought to demonstrate that geometric theorems are independent of coordinates. ... Study was the first to investigate systematically all algebras possessing up to four generators over R and C. "
Other areas which Study worked on were straight lines in elliptic space, with his student at Bonn J L Coolidge, and he simplified the method of differential operators. In 1903 he published Geometrie der Dynamen which considered euclidean kinematics and the mechanics of rigid bodies. *SAU

1882 Amalie Emmy Noether (23 Mar 1882; 14 Apr 1935 at age 53) German mathematician best known for her contributions to abstract algebra, in particular, her study of chain conditions on ideals of rings. In theoretical physics, she produced Noether's Theorem, which proves a relationship between symmetries in physics and conservation principles. This basic result in the general theory of relativity was praised by Einstein. It was her work in the theory of invariants which led to formulations for several concepts of Einstein's general theory of relativity. For her obituary in The New York Times, Albert Einstein wrote: “Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began. *TIS Someone once described her as the daughter of the mathematician Max Noether. To this Edumund Landau replied “Max Noether was the father of Emmy Noether. Emmy is the origin of coordinates in the Noether family.” *H. Eves, Introduction to the History of Mathematics
Emmy Noether’s house in Erlangen is in a blog at The Renaissance Mathematicus

1897 John Lighton Synge (March 23, 1897–March 30, 1995) was an Irish mathematician and physicist. Synge made outstanding contributions to different fields of work including classical mechanics, general mechanics and geometrical optics, gas dynamics, hydrodynamics, elasticity, electrical networks, mathematical methods, differential geometry, and Einstein's theory of relativity. He studied an extensive range of mathematical physics problems, but his best known work revolved around using geometrical methods in general relativity.
He was one of the first physicists to seriously study the interior of a black hole, and is sometimes credited with anticipating the discovery of the structure of the Schwarzschild vacuum (a black hole).
He also created the game of Vish in which players compete to find circularity (vicious circles) in dictionary definitions. *Wik

1907 Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes. *SAU

1912 Wernher Magnus Maximilian von Braun (23 Mar 1912; 16 Jun 1977 at age 65) was a German-American rocket engineer who was one of the most important developers of rockets and their evolution to applications in space exploration. His interest began as a teenager in Germany, and during WW II he led the development of the deadly V–2 ballistic missile for the Nazis (which role remains controversial). After war, he was taken to use his knowledge to produce rockets for the U.S. Army. In 1960, he transferred to the newly formed NASA and became director of Marshall Space Flight Center and chief architect of the Saturn V launch vehicle used to put men on the moon. His contributions include the Explorer satellites; Jupiter, Pershing, Redstone and Saturn rockets, and Skylab. *TIS "My experiences with science led me to God. They challenge science to prove the existence of God. But must we really light a candle to see the sun? "

1928 Computer Pioneer Jean Sammet Is Born :
Jean Sammet, an early pioneer of computing, is born in New York. Sammet attended Mount Holyoke College and the University of Illinois, where she launched a teaching career. Trained in math, she moved into industry in 1961, developing the language FORMAC at IBM. The language was the first commonly used language for manipulating non-numeric algebraic expressions. She also wrote one of the classic histories of programming languages in her book, "Programming Languages: History and Fundamentals." *CHM

DEATHS
1924 Thomas Corwin Mendenhall (4 Oct 1841, 23 Mar 1924 at age 82) American physicist and meteorologist who was the first to propose the use of a ring pendulum for measuring absolute gravity. From 1889 to 1894 he served both as Director of the U.S. Coast and Geodetic Survey and also Superintendent of the U.S. Standard Weights and Measures where he oversaw the shift in the fundamental standards of the U.S. from the English yard and pound to the international meter and kilogram. Mendenhall devised a quarter second's pendulum for gravity measurements and instituted improvements in the measurement of base lines with wire tapes, in the construction of instruments for precise leveling and in the methods used in triangulation and gravity work, and developed a comprehensive plan for the study of terrestrial magnetism. *TIS

1945 Sir (William) Napier Shaw (4 Mar 1854; 23 Mar 1945 at age 90) was an English meteorologist who applied his training in mathematics. He studied the upper atmosphere, using instruments carried by kites and high-altitude balloons. He measured (1906) the movement of air in two anti-cyclones, finding descent rates of 350 and 450 metres per day. He calculated the reduction in pressure due to a certain depression to correspond to the removal of two million million tons of air. He introduced the millibar unit for measurement of air pressure (1000 millibar = 1 bar = 1 standard atmosphere) and the tephigram to illustrate the temperature of a vertical profile of the atmosphere. He also co-authored an early work on atmospheric polluiton, The Smoke Problem of Great Cities (1925).*TIS

1946 Gilbert Newton Lewis (23 Oct 1875, 23 Mar 1946 at age 70) American chemist who collaborated with Irving Langmuir in developing an atomic theory. He developed a theory of valency, which introduced the covalent bond (c. 1916), whereby a chemical combination is made between two atoms by the sharing of a pair of electrons, one contributed from each atom. This was part of his more general octet theory, published in Valence and the Structure of Atoms and Molecules (1923). Lewis visualized the electrons in an atom as being arranged in concentric cubes. The sharing of these electrons he illustrated in the Lewis dot diagrams familiar to chemistry students. He generalized the concept of acids and bases now known as Lewis acids and Lewis bases. *TIS

Max Mason (26 Oct 1877; 23 Mar 1961) American mathematical physicist, educator, and science administrator. During World War I he invented several devices for submarine detection - several generations of the Navy's "M," or multiple-tube, passive submarine sensors. This apparatus focused sound to ascertain its source. To determine the direction from which the sound came, the operator needed only to seek the maximum output on his earphones by turning a dial. The final device had a range of 3 miles. Mason's special interest and contributions lay in mathematics (differential equations, calculus of variations), physics (electromagnetic theory), invention (acoustical compensators, submarine-detection devices), and the administration of universities and foundations. *TIS

1963 Thoralf Skolem,(23 May 1887 in Sandsvaer, Buskerud, Norway - 23 March 1963 in Oslo, Norway) number theorist and logician. At the International Congress of Mathematicians in Cambridge in 1950 he said “We ought not to regard all that is written in the traditional textbooks as something sacred.” It was this attitude that earlier allowed him to discover that the real numbers could have countable models, a fact known as Skolem’s paradox. *Wik This Norwegian logician was the ﬁrst to introduce non-standard models of the natural numbers. *VFR

1979 Ivo Lah (AKA Ivan Lah; September 5, 1896 Štrukljeva vas near Cerknica, Austria-Hungary, now Slovenia,– March 23, 1979, Ljubljana, SFR Yugoslavia, now Slovenia) was a Slovenian mathematician and actuary, best known for his discovery of the Lah numbers in 1955. His scientific bibliography contains about 120 items covering a wide spectrum of topics from Mathematics to Statistics, Demographics, etc. For instance one can find 10 items in Maths Reviews, and 19 items in Zentralblatt für Mathematik. His most important mathematical result, published in 1955, is the so-called "Lah identity" where he shows how the rising powers can be expressed in terms of falling powers. The reviewer of his paper was a leading combinatorialist of that time, John Riordan. *Wik Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a set of n elements can be partitioned into k nonempty linearly ordered subsets. Lah numbers are related to Stirling numbers.*Wik

1981 Beatrice Muriel Hill Tinsley (27 January 1941 – 23 March 1981) was a British-born New Zealand astronomer and cosmologist whose research made fundamental contributions to the astronomical understanding of how galaxies evolve, grow and die.
Tinsley completed pioneering theoretical studies of how populations of stars age and affect the observable qualities of galaxies. She also collaborated on basic research into models investigating whether the universe is closed or open. Her galaxy models led to the first approximation of what protogalaxies should look like.
In 1974 she received the American Astronomical Society's Annie J. Cannon Award in Astronomy, awarded for "outstanding research and promise for future research by a postdoctoral woman researcher", in recognition of her work on galaxy evolution.
In 1977, Tinsley, with Richard Larson of Yale, organized a conference on 'The Evolution of Galaxies and Stellar Populations'.
Shortly after, in 1978, she became the first female professor of astronomy at Yale University. Her last scientific paper, submitted to the Astrophysical Journal ten days before her death, was published posthumously that November, without revision. *Wik

2007 Paul Joseph Cohen (2 April 1934 in Long Branch, New Jersey, USA- 23 March 2007 in Palo Alto, California, USA) Cohen used a technique called forcing to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Wednesday, 22 March 2017

### On This Day in Math - March 22

 1727 Eclipse Map *greatamericaneclipse.com

We [he and Halmos] share a philosophy about linear algebra:
we think basis-free,
we write basis-free,
but when the chips are down
we close the office door and compute with matrices like fury.

~Irving Kaplansky

The 81st day of the year; 81 is the only integer (except 1) which is the square of the sum of its digits.

The smallest 10 digit pandigital number is 1023456789, 81 or  34 is a factor.  The other two factors are both four digit numbers.

81 is one of only three non-trivial numbers for which the sum of the digits * the reversal of the sum yields the original number (8+1 = 9; 9*9 = 81). The other two are the famous Hardy-Ramanujan taxicab # 1729, which is the smallest number which is the sum of two positive cubes in two ways.(1+7+2+9 = 19; 19*91 = 1729), and 1458 (1+4+5+8 = 18; 18*81=1458) which is also unique for being the maximum determinant possible for a 11x11 matrix with only ones and zeros. The Hardy-Ramanujan number's properties were first noted by Frénicle de Bessy in 1657(without mention of a taxicab).

EVENTS
1129 Chinese accounts state “there was a Black spot within the Sun” on March 22, 1129, which “died away” on April 14th. This may well have been one of the sunspots John of Worcester had observed 104 days earlier (8 December, 1128), on the other side of the world. Worcester's observation prompted the earliest known drawing of sunspots, which appear in his Chronicle recorded in 1128. *Joe Hanson, itsokaytobesmart.com

1675. John Evelyn records in his diary a visit with William Petty and the story of the rejuvenation of Anne Greene after she was hanged until dead. "Supped at Sir William Petty's, with the Bishop of Salisbury, and divers honorable persons. ..grown famous...for his recovering a poor wench that had been hanged for felony; and her body having been begged (as the custom is) for the anatomy lecture, he bled her, put her to bed to a warm woman, and, with spirits and other means, restored her to life." *The Diary of John Evelyn

1727 The first detailed documentation and map of an eclipse in the New World came from Mexico in 1727. (At Top of page)
This map in the pamphlet Spherographia de la Obscuration de la Tierra en el Eclypse de Sol de 22. de Marzo de 1727 has several interesting features. It predates the earliest eclipse map from the United States by 104 years. Curiously, it also seems to predate any known eclipse map from Spain. Of special interest to historians of cartography, this map shows California as an island. *http://www.greatamericaneclipse.com

1818 The last time that Easter fell on this date, the earliest possible. It will not happen again until the year 2285. By definition Easter is the ﬁrst Sunday after the ﬁrst full moon on or after the vernal equinox. Since the Roman Catholic Church defined the vernal equinox to be 21 March and uses a tabulated moon, not the real moon, this is a mathematical issue, not an astronomical event. *VFR

1880 The New York Times comments, somewhat tongue-in-cheek, on the Fifteen Puzzle that was sweeping the country, “No pestilence has ever visited this or any other country which has spread with the awful celerity of what is popularly called the ‘Fifteen Puzzle.’ ...it now threatens our free institutions, inasmuch as from every town and hamlet there is coming up a cry for a ‘strong man’ who will stamp out this terrible puzzle at any cost of Constitution or freedom” *Jerry Slocum, Dic Sonneveld, The 15 Puzzle

1945 On 22 March 1945, the first female Fellows were elected to the Royal Society. This followed a statutory amendment in 1944 that read "Nothing herein contained shall render women ineligible as candidates", and was contained in Chapter 1 of Statute 1. Following approval by the Council, Marjory Stephenson (From Burwell in the Fens of East Anglia, and just west of my old school in Lakenheath) and Kathleen Lonsdale were elected as Fellows.

1960 The first laser was patented (U.S. No. 2,929,922) by Arthur Schawlow and Charles Hard Townes under the title “Masers and Maser Communications System.” What distinguished this invention as the first laser is that it was the first to operate in the visible light spectrum. The patent was assigned to the Bell Telephone Laboratories, where they had done the research. *TIS

1993 Intel Begins Shipping "Pentium" Chip":
Intel announces it is shipping its Pentium microprocessor. Engineers Federico Faggin, Ted Hoff, San Mazor, and Matsatoshi Sima, an engineer from the Japanese firm of Busicom, invented the world's first microprocessor at Intel in 1971 -- the Intel 4004. The new processor continued the exponential increase in speed and power for personal computers, also allowing for a smoother incorporation of speech, sound, handwriting, and photographs into documents.*CHM

1997 Comet Hale-Bopp makes its closest approach to the Earth at 1.315 AU. The comet was discovered independently on July 23, 1995 by two observers, Alan Hale and Thomas Bopp, both in the United States. *David Dickinson‏@Astroguyz, *Wik

BIRTHS

1394 Ulugh Beg (22 Mar 1394- 27 Oct 1449) The only important Mongol scientist, mathematician, and the greatest astronomer of his time. His greatest interest was astronomy, and he built an observatory (begun in 1428) at Samarkand. In his observations he discovered a number of errors in the computations of the 2nd-century Alexandrian astronomer Ptolemy, whose figures were still being used. His star map of 994 stars was the first new one since Hipparchus. After Ulugh Beg was assassinated by his son, the observatory fell to ruins by 1500, rediscovered only in 1908. Written in Arabic, his work went unread by the world's next generation of astronomers. When his tables were translated into Latin in 1665, telescopic observations had surpassed them. *TIS

1644 Otto Mencke (22 March (OS) April 2, 1644 – 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1784 Samuel Hunter Christie (22 March 1784 – 24 January 1865) was a British scientist and mathematician.
He studied mathematics at Trinity College, Cambridge, where he won the Smith's Prize and was second wrangler. It may help to understand the difficulty of this exam by looking at some of the great achievers who did NOT win Senior Wrangler. A short list of Second Wranglers, include Alfred Marshall, James Clerk Maxwell, J. J. Thomson, and Lord Kelvin.
Those who have finished between third and 12th include Karl Pearson and William Henry Bragg (third), George Green and G. H. Hardy (fourth), Adam Sedgwick (fifth), John Venn (sixth), Bertrand Russell and Nevil Maskelyne (seventh), Thomas Malthus (ninth), and John Maynard Keynes (12th).

Christie was particularly interested in magnetism, studying the earth's magnetic field and designing improvements to the magnetic compass. Some of his magnetic research was done in collaboration with Peter Barlow. He became a Fellow of the Royal Society in 1826, delivered their Bakerian Lecture in 1833 and served as their Secretary from 1837 to 1853. In 1833 he published his 'diamond' method, the forerunner of the Wheatstone bridge, in a paper on the magnetic and electrical properties of metals, as a method for comparing the resistances of wires of different thicknesses. However, the method went unrecognized until 1843, when Charles Wheatstone proposed it, in another paper for the Royal Society, for measuring resistance in electrical circuits. Although Wheatstone presented it as Christie's invention, it is his name, rather than Christie's, that is now associated with the device.
Christie taught mathematics at the Royal Military Academy, Woolwich, from 1838 until his retirement in 1854. He died at Twickenham, on 24 January 1865. *Wik

1799 Friedrich Wilhelm August Argelander (22 Mar 1799, 17 Feb 1875 at age 75)
German astronomer who established the study of variable stars as an independent branch of astronomy and is renowned for his great catalog listing the positions and brightness of 324,188 stars of the northern hemisphere above the ninth magnitude. He studied at the University of Königsberg, Prussia, where he was a pupil and later the successor of Friedrich Wilhelm Bessel. In 1837, Argelander published the first major investigation of the Sun's motion through space. In 1844 he began studies of variable stars.*TIS

1868 Robert Andrews Millikan (22 Mar 1868, 19 Dec 1953) American physicist who was awarded the 1923 Nobel Prize for Physics for "his work on the elementary charge of electricity and on the photoelectric effect." Millikan's famous oil-drop experiment (1911) was far superior to previous determinations of the charge of an electron, and further showed that the electron was a fundamental, discrete particle. When its value was substituted in Niels Bohr's theoretical formula for the hydrogen spectrum, that theory was validated by the experimental results. Thus Millikan's work also convincingly provided the first proof of Bohr's quantum theory of the atom. In later work, Millikan coined the term "cosmic rays" in 1925 during his study of the radiation from outer space.*TIS

1868 Nathan Rosen (22 Mar 1909, 18 Dec 1995) U.S.-born Israeli theoretical physicist who in 1935 collaborated with Albert Einstein and Boris Podolsky on a much-debated refutation of the theory of quantum mechanics; he later came to accept the theory. The famous Einstein-Podolsky-Rosen critique of quantum mechanics was published in the 1935 Physical Review. (A New York Times obituary described The Physical Review as "one of the most impenetrable periodicals in the English language.") Rosen founded the Institute of Physics at Technion in Haifa.*TIS

1917 Irving "Kap" Kaplansky (22 March 1917 in Toronto, Ontario, Canada - 25 June 2006 in Sherman Oaks, Los Angeles, California) was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act. In this video she talks about her dad a few years after his death, and sings the song which is amazingly nice, but listen for it, she misses a digit in there I think...

He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

1931 Burton Richter (22 Mar 1931, ) American physicist who was jointly awarded the 1976 Nobel Prize for Physics with Samuel C.C. Ting for the discovery of a new subatomic particle, the J/psi particle. *TIS He led the Stanford Linear Accelerator Center (SLAC) team which co-discovered the J/ψ meson in 1974, alongside the Brookhaven National Laboratory (BNL) team led by Samuel Ting. This discovery was part of the so-called November Revolution of particle physics. He was the SLAC director from 1984 to 1999.*Wik

DEATHS

1772 John Canton (31 Jul 1718, 22 Mar 1772 at age 53) British physicist and teacher, who educated himself about science, and for developing a new method of preparing artificial magnets, won election to the Royal Society (1749). In July 1752, he was the first Englishman to repeat French experiments verifying Franklin's hypothesis that lightning was just a huge electric spark, (as seen from charged Leyden jars). Following this, he studied the polarity of the charge on a cloud. He invented a portable electroscope to detect charge present in a system, and he remains well-known for electrostatic induction experiments. Canton proved that water is slightly compressible (1762). Noting compass needle irregularities during a prominent aurora borealis he made the first observations of magnetic storms (1756-9). *TIS

1840 Étienne Bobillier (April 17, 1798 – March 22, 1840) was a French mathematician.
At the age of 19 he was accepted into the École Polytechnique and studied there for a year. However, due to a shortage of money, in 1818 he became an instructor in mathematics at the École des Arts et Métiers in Châlons-sur-Marne. In 1829, he was sent to Angers to be director of studies. The following year he served in the national guard during the 1830 revolution. In 1832 he returned to Châlons after his post was abolished, and was promoted to professor.
In 1836 he began suffering from health problems, but continued teaching; declining to take a leave to recuperate. As a result he died in Châlons at the relatively early age of 41.
He is noted for his work on geometry, particularly the algebraic treatment of geometric surfaces and the polars of curves. He also worked on statics and the catenary.
The crater Bobillier on the Moon is named after him.*Wik

1926 Joseph Jean Baptiste Neuberg (30 Oct 1840 in Luxembourg City, Luxembourg - 22 March 1926 in Liège, Belgium) Neuberg worked on the geometry of the triangle, discovering many interesting new details but no large new theory. Pelseneer writes, "The considerable body of his work is scattered among a large number of articles for journals; in it the influence of A. Möbius is clear." *SAU

1953 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.
Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik

1987 Andrew Paul Guinand (3 March 1912 in Renmark, South Australia, - 22 March 1987 in Peterborough, Ontario, Canada) Guinand worked on summation formulae and prime numbers, the Riemann zeta function, general Fourier type transformations, geometry and some papers on a variety of topics such as computing, air navigation, calculus of variations, the binomial theorem, determinants and special functions. In [1] W N Everitt writes,
"As a student of Titchmarsh in Oxford in the years immediately before the second world war it was natural that Guinand's research interests should be directed into the field of Fourier analysis and the Riemann zeta function. ... [In an important paper in 1948] the main application of the general result yields a deep-seated connection between the distribution of the prime numbers and the location of the zeros of the Riemann zeta function on (or near to it if the Riemann hypothesis is false) the critical line in the complex plane... Guinand was convinced that these results could lead to more information about the Riemann zeta function, and he was disappointed that he was not able to advance further in this area and that others did not take up the possibility themselves. "
*SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Tuesday, 21 March 2017

### On This Day in Math - March 21

 Fourier Series approximation of a square wave, *Mathworld

True greatness is when your name is like ampere, watt, and fourier—when it's spelled with a lower case letter.
~Richard Hamming (creator of the hamming code, with a lower case h)

The 80th day of the year; There are 80 four-digit primes which are concatenations of two-digit primes. (3137 is one example, can you find the rest?) *Prime Curios!

80 in Roman Numerals is not suitable for minors, LXXX,

The Pareto principle (sometimes called the 80-20 rule)says that, for many events, roughly 80% of the effects come from 20% of the causes, ie, $\approx 80\%$ of the accidents are caused by 20% of the drivers.

$n*2^{n-1}$ gives the number of edges (segments) in a n-dimensional cube, and in the 5th dimension, (went there once in a dream) there are 80 edges,  5*24
(It also has eighty two-dimensional square faces.)

And 80 is the smallest number diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, ...) *Tanya Khovanova

EVENTS
---Commonly considered the ﬁrst day of spring, a tradition dating from the Council of Nicaea in A.D. 325. The most recent year in which this was in fact true in the U.S. was 1979, when the vernal equinox occurred at 12:22 a.m. EST. The next time the vernal equinox will be on March 21 is in 2103 when it will occur at 1:09:04 a.m. EST. This computation uses a tropical year of 365 days, 5 hours, 48 minutes, and 46 seconds. [Mathematics Magazine, 55(1982), 46–47] *VFR

1522 Copernicus read the German version of his treatise, Modus cudendi monetam (The Way to Strike Coin), before the Royal Prussian Assembly attended by King Sigismund Is envoys at Grudziądz (Graudenz). Copernicus discusses general issues related to the theory of money and formulates inter alia a law of bad money driving out good. In the second he focused on the current monetary situation in Royal Prussia and in particular on the decline in the value of Prussian coinage, and concluded his presentation with a proposal to mint three Prussian szelągi as an equivalent of one Polish grosz (groshen) and thus to equalize the value of the new Prussian coinage with that issued by the Crown. *Leszek Zygner
Nicolaus Copernicus University (Students may not know that, in addition to being a respected astronomer, Copernicus was a respected economist.)

1543 Copernicus’ De Revolutionibus published, {{{This date seems incorrect, Thony Christie sent me a note that, "in his An Annotated Census of Copernicus' De Revolutionibus Owen Gingerich writes, 'The printing was finished on 20 April 1543 when Rheticus autographed a presentation copy of the completed work. (Copernicus himself did not receive the final pages until a month later, the day on which he died.)' However I have a note from a post by Teresa Borawska of Nicolaus Copernicus University that says, "There is no information whether a copy of the book printed shortly before 21 March 1543 ever reached Warmia before the astronomers death." and gives no other publication date.}}} The book was so technically complex that only true astronomers could read through it so the 400 copies didn't even sale out. In addition Osiander had written a disclaimer (without, it seems, the dying Copernicus' permission) that readers should view it as a useful mathematical fiction with no physical reality, thereby somewhat shielding it from accusations of blasphemy. But eventually it was banned. It was placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616 as part of the Galileo "incident". [while I was researching this note I came across a nice bit of information that I am not sure where else I could use. De revolutionibus was printed in Hans Petreiuss printing shop in Nuremberg. The building of Petreiuss former printing shop at 9, Öberg Street, (located near Albrecht Durers birthplace) luckily survived the ravages of WWII. You can see in the banner an image of the shop at The Renaissance Mathematicus blog.]

1599 Tycho sends a letter to Longomontanus, in which he reports his revised theory on the movement of the moon. On January 31, During an observation of the lunar eclipse, he had discovered that his predictive theory about the movement of the Moon was wrong since the eclipse started 24 minutes before his calculations predicted.*Wik

1665-6 Hooke writes to C. Huygens to send him a paper on Gravity he has written and presented to the Royal Society.

1684 Giovanni Domenico Cassini discovered two moons of Saturn: Tethys and Dione, using a refractor telescope with an aperture of 108mm. He had previously discovered two other satellites of Saturn: Iapetus (Sep 1671) and Rhea (1672). Christiaan Huygens was the first to discover a moon of Saturn, when he viewed Titan (the largest and easiest to see) on 25 Mar 1655.*TIS

1797 Gauss makes an entry in his diary that the perimeter of the lemniscate can be divided into five equal parts by ruler and compass. Abel would show in 1827 that the division of the lemniscate with classical tools is possible for the same numbers n as the circle. This is an important theorem in elliptic functions. *John Stillwell, Mathematics and Its History

1801 Thomas Jefferson to Joseph Priestly:
DEAR SIR,

-- I learnt some time ago that you were in Philadelphia, but that it was only for a fortnight; supposed you were gone. It was not till yesterday I received information that you were still there, had been very ill, but were on the recovery. I sincerely rejoice that you are so. Yours is one of the few lives precious to mankind,  for the continuance of which every thinking man is solicitous.
*The Letters of Thomas Jefferson, http://www.let.rug.nl/

1816 John Dalton makes the first entry in the second volume of his meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816. Volume II would continue until 31 Aug, 1827

In 1925, Wolfgang Pauli published his “exclusion principle.” At the young age of 24, in an article in Zeitschrift für Physik, Pauli introduced the idea that two nearby electrons cannot be in exactly the same state at the same time. For this, now fundamental, contribution to quantum mechanics, he was awarded a Nobel Prize in 1945. *TIS

1925 The Butler Act is signed into law. A law in Tennessee prohibiting the teaching of Darwin’s theory of evolution passed the state senate on March 13, and was signed into law by Governor Austin Peay (for whom the university in Clarksville, Tennessee is named) on March 21. The Butler Act was a Tennessee law:
That it shall be unlawful for any teacher in any of the Universities, Normals and all other public schools of the State which are supported in whole or in part by the public school funds of the State, to teach any theory that denies the Story of the Divine Creation of man as taught in the Bible, and to teach instead that man has descended from a lower order of animals.
It would remain the law in Tennessee until repealed on September 1, 1967. *Wik Within a few months, John Scopes became a willing defendant in the “Scopes Monkey Trial,” which began 10 Jul 1925, and received world attention as the statute was tested. He was convicted and fined \$100, which was overturned on appeal. *TIS

1943 Joseph Needham, 43, known at that point as a brilliant biologist, arrives in China for the first time. By the time he left, he would be well on his way to being the foremost student of China in the Western World. His "Science and Civilization in China", would alter the basis and direction of math/science history. *Simon Winchester, The Man Who Loved China

1963 When this date is written in the form 3/21/63, the product of the ﬁrst two numbers is the third. This happens 212 times each century. *VFR (you have 211 left to find)

1989 NCTM released its Curriculum and Evaluation Standards for School Mathematics, a document intended to change fundamentally the way mathematics is taught. *VFR

2016 France issues stamp honoring Sophie Germain.

2016 Sphere packing for 24 dimensions is solved by Maryna Viazovska. In 1611, Kepler conjectured that there was no way to pack spheres more densly than the way we would normally stack oranges or cannonballs, with every triangle of three supporting another nestled above (and below) tangent to all of the first three. By 1831 Gauss had managed to prove the conjecture for 3d. In her paper on May 14th Viazovska proved no packing of unit balls in Euclidean space R8 has density greater than that of the E8-lattice packing. One week later, (March 21) building on her work, with collaboration of four others, they were able to prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions, and that it is the unique optimal periodic packing. *arxiv.

BIRTHS

1768 Baron Jean-Baptiste-Joseph Fourier (21 Mar 1768; 16 May 1830 at age 62) French mathematician, Egyptologist and administrator who exerted strong influence on mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat). He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS His work on heat was termed by Maxwell, “a great mathematical poem.” He traveled to Egypt with Napoleon and became convinced that desert heat was ideal for good health. Consequently, he wore many layers of garments and lived in rooms of unbearably high heat. This hastened his death, by heart disease, so that he died, thoroughly cooked. [Eves, History of Mathematics, 362] *VFR

1866 Antonia Coetana de Paiva Pereira Maury (21 Mar 1866; 8 Jan 1952 at age 85) was an American astronomer and ornithologist whose painstaking classifications of stars by their spectra included elaborate work on 681 bright stars of the northern skies published in Annals of Harvard College Observatory (1896), a significant early catalog. Yet she was unappreciated by her observatory director, Edward C. Pickering. Her work was important in Ejnar Hertzsprung's verification of the distinction between dwarf stars and giant stars, as now seen in the Hertzsprung-Russell diagram. After Pickering discovered the first spectroscopic binary star, Mizar, she was first to measure its period, 104 days. In 1889, she identified the second such star, Beta Aurigae, with a period of about 4 days. Antonia was the niece of astronomer Henry Draper, and the granddaughter of John William Draper who pioneered in the use of photography in astronomy.*TIS
In 1897, having examined 4,800 photographs, she published her findings on 681 bright northern stars in the Annals of the Harvard College Observatory. It was the first Harvard observatory publication credited to a woman, which she had insisted on, writing to Pickering, “I worked out the theory at the cost of much thought and elaborate comparison and I think that I should have full credit for my theory of the relations of the star spectra.” *Time

1884 George David Birkhoff (21 Mar 1884, 12 Nov 1944) American mathematician, foremost of the early 20th century, who formulated the ergodic theorem. As the first American dynamicist, Birkhoff picked up where Poincaré left off, gaining distinction in 1913 with his proof of Poincaré's Last Geometric Theorem, a special case of the 3-body problem. Although primarily a geometer, he discovered new symbolic methods. He saw beyond the theory of oscillations, created a rigorous theory of ergodic behavior, and foresaw dynamical models for chaos. His ergodic theorem transformed the Maxwell- Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. He also produced a mathematical model of gravity. *TIS

1909 Founder of ACM Edmund Berkeley Is Born:
Edmund Berkeley, founder of the Association of Computing Machinery, is born. A graduate of Harvard University, Berkeley participated in the development of Harvard's Mark II while enlisted in the Navy during World War II. In addition to co-founding the ACM in 1947, he wrote one of the first books on computers intended for a general audience, "Giant Brains, or Machines that Think." *CHM

1920 John Michael Hammersley (21 March 1920 in Helensburgh, Dunbartonshire, Scotland - 2 May 2004 in Oxford, England) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. (Wikipedia) when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)
During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, On the enfeeblement of mathematical skills by Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. *from his Independent obituary

1927 Halton Christian Arp (21 Mar 1927, ) American astronomer noted for challenging the theory that red shifts of quasars indicate their great distance. Arp is one of the key actors in the contemporary debate on the origin and evolution of galaxies in the universe. His landmark compilation of peculiar galaxies led him to challenge the fundamental assumption of modern cosmology, that redshift is a uniform indicator of distance. Astronomers have debated Arp's assertion that quasars are related to peculiar galaxies since the late 1960's. Most astronomers believe that quasars are unrelated to the peculiar galaxies. Yet, no one has been able to explain why the quasars seem to be more numerous around the peculiar galaxies. *TIS

1951 David Nualart (21 March 1951 - ) is a Spanish mathematician working in the field of probability theory, in particular on aspects of stochastic processes and stochastic analysis.
He obtained his PhD titled "Contribución al estudio de la integral estocástica" in 1975 at the University of Barcelona under the supervision of Francesc d'Assís Sales Vallès. After positions at the University of Barcelona and the Polytechnique University of Barcelona he took up a professorship at Kansas University and is currently the Black-Babcock Distinguished Professor in its Mathematics Department.
He published hundreds of scientific articles in his field, served on several scientific committees, has been an associate editor of many journals and from 2006 to 2008 was the Chief Editor of Electronic Communications in Probability.
He has been elected a Fellow of the Institute of Mathematical Statistics in 1997. He received a Doctor Honoris Causa by the University Blaise Pascal of Clermond-Ferrand in 1998. He received the Prize IBERDROLA de Ciencia y Tecnologia in 1999. He has been a Corresponding Member of the Real Academia de Ciencias Exactas Fisicas y Naturales of Madrid since 2003. He has been a member of the Reial Academia de Ciencies i Arts of Barcelona since 2003. He received the Research Prize of the Real Academia de Ciencias de Madrid in 1991.
In March 2011 the International Conference on Malliavin Calculus and Stochastic Analysis in honor of David Nualart took place at University of Kansas. *Wik

DEATHS
1699 Erhard Weigel (December 16, 1625 – March 21, 1699) was a German mathematician, astronomer and philosopher. He earned his Ph.D. from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. *Wik
A post at the Renaissance Mathematicus about Weigel and some of his lesser known students (most student's would be "lesser known" compared to Leibniz) also pointed out that "Another Weigel innovation in celestial cartography was his eclipse map from 1654. An eclipse map is a map that shows the path on the surface of the earth from which a solar eclipse will be visible. Weigel’s was the first such printed map ever produced. This honor is usually falsely accredited to Edmund Halley for his 1715 eclipse map."
For religious reasons, he wanted to rename all the constellations, and made several globes of the sky with his renamed constellations.

1762 Abbé Nicolas Louis de Lacaille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS

1822 D'Amondans Charles de Tinseau (19 April 1748 in Besançon, France - 21 March 1822 in Montpellier, France) wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes that Tinseau's works, "... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space."
Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites. He also wrote Solution de quelques questions d'astronomie on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics. *SAU

1864 Luke Howard, FRS (28 November 1772 – 21 March 1864) was a British manufacturing chemist and an amateur meteorologist with broad interests in science. His lasting contribution to science is a nomenclature system for clouds, which he proposed in an 1802 presentation to the Askesian Society.
He has been called "the father of meteorology" because of his comprehensive recordings of weather in the London area from 1801 to 1841 and his writings, which transformed the science of meteorology. *Wik

1915 Frederick Winslow Taylor (20 Mar 1856, 21 Mar 1915 at age 58) was an American engineer and inventor who is known as the father of scientific management. His system of industrial management has influenced the development of virtually every country enjoying the benefits of modern industry. He introduced a scientific approach (1881) to “time and motion study” while chief engineer at Midvale Steel Company, Philadelphia, Pa. Taylor and his associates used stop-watches to time the laborers as they performed various tasks, counted the number of shovel-loads they each moved, and the load per shovel. Thus he was able to determine an optimum shovel size and length. Such careful observations, aimed at recognizing wasted effort and minimizing time used, increased the efficiency of actions of factory workers.*TIS

1928 Edward Walter Maunder (12 Apr 1851, 21 Mar 1928 at age 76) English astronomer who was the first to take the British Civil Service Commission examination for the post of photographic and spectroscopic assistant at the Royal Observatory, Greenwich. For the next forty years that he worked there, he made extensive measurements of sunspots. Checking historical records, he found a period from 1645 to 1715 that had a remarkable lack of reports on sunspots. Although he might have questioned the accuracy of the reporting, he instead attributed the shortage of report to an actual dearth of sunspots during that period. Although his suggestion was not generally accepted at first, accumulating research has since indicated there are indeed decades-long times when the sun has notably few sunspots. These periods are now known as Maunder minima.*TIS

1933 Enrico D'Ovidio (11 Aug 1842 in Campobasso, Italy - 21 March 1933 in Turin, Italy) D'Ovidio was to work for 46 years in the University of Turin. He was chairman of the Faculty of Science in 1879-80 and rector of the University between 1880 and 1885. Another spell as chairman of the Faculty of Science between 1893 and 1907 ended when he was appointed Commissioner of the Polytechnic of Turin.
Euclidean and noneuclidean geometry were the areas of special interest to D'Ovidio. He built on the geometric ideas which had been introduced by Lobachevsky, Bolyai, Riemann and Cayley. D'Ovidio's most important work is probably his paper of 1877 The fundamental metric functions in spaces of arbitrarily many dimensions with constant curvature.
D'Ovidio also worked on binary forms, conics and quadrics. He had two famous assistants, Peano (1880-83) and Corrado Segre (1883-84). D'Ovidio and Corrado Segre built an important school of geometry at Turin. *SAU

1934 Thomas Muir (25 Aug 1844 in Stonebyres, Falls of Clyde, Lanarkshire, Scotland
- 21 March 1934 in Rondebosch, South Africa) He is noted for a four volume work on the history of determinants. *VFR He also proved an important lemma about determinants of skew symmetric matrices

1960 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

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