## Tuesday, 24 April 2018

### On This Day in Math - April 24

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

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

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

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

EVENTS

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

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

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

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

1800 The Library of Congress established . $5000 was appropriated for the purchase of such books as may be necessary for the use of Congress at the said city of Washington and for filling up a suitable apartment for containing them and for placing them therein." The first catalog, dated April 1802, listed 964 volumes and 9 maps. *VFR 1897 The Chicago Section of the American Mathematical Society held its organizational meeting in Chicago under the chairmanship of E. H. Moore. It was the first section of the AMS. [Cajori, Historical Introduction to the Mathematical Literature, p. 34] *VFR In 1925, Darwin's theory of evolution was reputed to be taught in Dayton, Tennessee, by teacher John Scopes, who used the high school textbook, Civic Biology by George Hunter. For this, Scopes, 24, was prosecuted under the Butler Act, a state law enacted in the previous month, on 21 Mar 1925. It prohibited the teaching of evolution in public schools. The trial , which began 10 Jul 1925) was used as a platform to challenge the legality of the statute. Scopes was supported by the American Civil Liberties Union. At its end, on 21 Jul 1925, Scopes was convicted and fined$100. On appeal, the state supreme court upheld the constitutionality of the 1925 law but acquitted Scopes on the technicality that he had been fined excessively. The law was not repealed until 17 May 1967. *TIS

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Monday, 23 April 2018

### On This Day in Math - April 23

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

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

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

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

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

EVENTS

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

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

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

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

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

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

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

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

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

BIRTHS

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

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

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

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

1910 Sheila Scott Macintyre (née Sheila Scott, April 23, 1910 - March 21, 1960) was a Scottish mathematician well known for her work on the Whittaker constant.(The constant isn't actually a known constant, but is known to be in a small interval.  Macintyre lowered the upper bound and reduced the interval of uncertainty by about 10%).  Macintyre is also well known for creating a multilingual scientific dictionary: written in English, German, and Russian; at the time of her death, she was working on Japanese.*Wik

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

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

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

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

DEATHS

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

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

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

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

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

## Sunday, 22 April 2018

### On This Day in Math - April 22

It can be of no practical use to know
that π is irrational,
but if we can know,
it surely would be intolerable not to know.
~ Edward Titchmarsh

The 112th day of the year; 112 is a practical number (aka panarithmetic numbers), any smaller number can be formed with distinct divisors of 112.  Student's might explore the patterns of such numbers.

112 is the side of the square that can be tiled with the the fewest
number of distinct integer-sided squares, discovered by A. J. W. Duijvestijn in 1976

112 is the only 3-digit number such that its factorial raised to the sum of its digits and increased by one is prime. I.e., 112!(1+1+2)+1 is prime.
112 = 11 + 13 + 17 + 19 + 23 + 29 (sum of consecutive primes) and
= 1x2 + 2x3 + 3x4 + 4x5 + 5x6 + 6x7 (sum of oblong or pronic numbers)

EVENTS

1056, the supernova in the Crab nebula was last seen by the naked eye. The creation of the Crab Nebula corresponds to the bright SN 1054 supernova that was independently recorded by Indian, Arabic, Chinese and Japanese astronomers in 1054 AD. The Crab Nebula itself was first observed in 1731 by John Bevis. The nebula was independently rediscovered in 1758 by Charles Messier as he was observing a bright comet. Messier catalogued it as the first entry in his catalogue of comet-like objects. The Earl of Rosse observed the nebula at Birr Castle in 1848, and referred to the object as the Crab Nebula because a drawing he made of it looked like a crab.*Wik

???? In the century and a half between 1725 and 1875, the French fought and won a certain battle on 22 April of one year, and 4382 days later, also on 22 April, they gained another victory. The sum of the digits of the years is 40. Find the years of the battles. For a solution see Ball’s Mathematical Recreations and Essays, 11th edition, p. 27. *VFR (or see this blog)

1715   A total solar eclipse was observed in England from Cornwall in the south-west to Lincolnshire and Norfolk in the east. This eclipse is known as Halley's Eclipse, after Edmund Halley (1656–1742) who predicted this eclipse to within 4 minutes accuracy. Halley observed the eclipse from London where the city of London enjoyed 3 minutes 33 seconds of totality. He also drew a predictive map showing the path of totality across England. The original map was about 30 km off the observed eclipse path. After the eclipse, he corrected the eclipse path, and added the path and description of the 1724 total solar eclipse.Note: Great Britain didn't adopt the Gregorian calendar until 1752, so the date was considered 22 April 1715. (Under the modern calendar this would be May 3.) *Wik… The Royal Society reports: Edmund Halley, a Fellow of the Royal Society, is most famous for his work on the orbits of comets, predicting when the one that now bears his name would be seen; however, his interests were more widespread. In 1715 the first total solar eclipse for 500 years took place over England and Wales. Halley, a talented mathematician, realized that such an event would generate a general curiosity and requested that the ‘curious’ across the country should observe ‘what they could’ and make a record of the time and duration of the eclipse. At the time, there were only two universities in England and their astronomy professors did not have much luck in observing the event: ‘the Reverend Mr Cotes at Cambridge had the misfortune to be oppressed by too much company’ and ‘Dr John Keill by reason of clouds, saw nothing distinctly at Oxford but the end’. The event did indeed capture the imagination of the nation and the timings collected allowed Halley to work out the shape of the eclipse shadow and the speed at which it passed over the Earth (29 miles per minute). Halley's map of the path of the eclipse is here.

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

1937 "The Law of Anomalous numbers" is read before the American Philosophical Society. This paper described the mathematical idea that is now more commonly called Benford's Law. The paper seems to be available online at the time of this writing.

1939 Frederic Joliot and his group publish their work on the secondary neutrons released in nuclear fission. This was the first demonstration that a chain reaction is indeed possible. Joliot was one of the scientists mentioned in Albert Einstein's letter to President Roosevelt as one of the leading scientists on the course to chain reactions. *Atomic Heritage Foundation

In 1970, the first nationwide Earth Day was celebrated in the U.S. as an environmental awareness event celebrated by millions of Americans with marches, educational programs, and rallies. (A local Earth Day celebration had occurred on 21 Mar 1970, in San Francisco, Cal.). Later the same year, President Nixon created the Environmental Protection Agency, or EPA, on 2 Dec 1970 to address America's severe pollution problem. Its mission is to safeguard the nation's water, air and soil from pollution. The agency conducts research, sets standards, monitors activities and helps to enforce environmental protection laws*TIS   This stamp was issued in honor of the first celebration of , which took place in 1970.

2012 A rare daytime meteor was seen and heard streaking over northern Nevada and parts of California on Sunday, just after the peak of an annual meteor shower.
Observers in the Reno-Sparks area of Nevada reported seeing a fireball at about 8 a.m. local time, accompanied or followed by a thunderous clap that experts said could have been a sonic boom from the meteor or the sound of it breaking up high over the Earth. While meteors visible at night typically range in size from a pebble to a grain of sand, a meteor large enough to be seen during daylight hours would presumably be as big as a baseball or softball.*Reuters US
 A meteor in the sky above Reno, Nevada on April 22, 2012. Image credit: Lisa Warren

Bill Cooke of the Meteoroid Environments Office at NASA’s Marshall Space Flight Center in Huntsville, Ala., estimates the object was about the size of a minivan, weighed in at around 154,300 pounds (70 metric tons) and at the time of disintegration released energy equivalent to a 5-kiloton explosion. *NASA

BIRTHS

1592 Wilhelm Shickard (22 April 1592 – 24 October 1635) He invented and built a working model of the ﬁrst modern mechanical calculator. *VFR
Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables.
In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize thedesigns or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed thecalculator based upon Schickard's original plans; it is still on display there today.
He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.

1724 Immanuel Kant  in Konigsberg, Germany. German philosopher, trained as a mathematician and physicist, who published his General History of Nature and theory of the Heavens in 1755. This physical view of the universe contained three anticipations of importance to astronomers. 1) He made the nebula hypothesis ahead of Laplace. 2) He described the Milky Way as a lens-shaped collection of stars that represented only one of many "island universes," later shown by Herschel. 3) He suggested that friction from tides slowed the rotation of the earth, which was confirmed a century later. In 1770 he became a professor of mathematics, but turned to metaphysics and logic in 1797, the field in which he is best known. *TIS

1807 Luigi Palmieri (April 22, 1807 – September 9, 1896) was an Italian physicist and meteorologist. He was famous for his scientific studies of the eruptions of Mount Vesuvius, for his researches on earthquakes and meteorological phenomena and for improving the seismographer of the time. Using a modified Peltier electrometer, he also carried out research in the field of atmospheric electricity. Other scientific contributions included the development of a modified Morse telegraph, and improvements to the anemometer and pluviometer. *Wik

1811 Ludwig Otto Hesse (22 April 1811 in Königsberg, Prussia (now Kaliningrad, Russia)- 4 Aug 1874 in Munich, Germany)Hesse worked on the development of the theory algebraic functions and the theory of invariants. He is remembered particularly for introducing the Hessian (matrix)determinant. *SAU The Hessian matrix is a square matrix of second-order partial derivatives of a function; that is, it describes the local curvature of a function of many variables.*Wik

1816 The French general, Charles Denis Sauter Bourbaki was born. There is a statue of him in Nancy, France, where Jean Dieudonn´e once taught. The polycephalic mathematician Nicolas Bourbaki was named after him. See Joong Fang, Bourbaki, Paideia Press, 1970, p. 24.*VFR

1830 Thomas Archer Hirst FRS (22 April 1830 – 16 February 1892) was a 19th century mathematician, specialising in geometry. He was awarded the Royal Society's Royal Medal in 1883.Hirst was a projective geometer in the style of Poncelet and Steiner. He was not an adherent of the algebraic geometry approach of Cayley and Sylvester, despite being a personal friend of theirs. His speciality was Cremona transformations.*Wik

1884 David Enskog (April 22, 1884, Västra Ämtervik, Sunne – June 1, 1947,Stockholm) was a Swedish mathematical physicist. Enskog helped develop the kinetic theory of gases by extending the Maxwell–Boltzmann equations.*Wik

1887 Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and football player. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was a member of the Danish national team for the 1908 Summer Olympics, where he won a silver medal.*Wik (Is there another prominent mathematician who has won an Olympic medal?)

1891 Sir Harold Jeffreys (22 Apr 1891, 18 Mar 1989 at age 97)English astronomer, geophysicist and mathematician who had diverse scientific interests. In astronomy he proposed models for the structures of the outer planets, and studied the origin of the solar system. He calculated the surface temperatures of gas at less than -100°C, contradicting then accepted views of red-hot temperatures, but Jeffreys was shown to be correct when direct observations were made. In geophysics he researched the circulation of the atmosphere and earthquakes. Analyzing earthquake waves (1926), he became the first to claim that the core of the Earth is molten fluid. Jeffreys also contributed to the general theory of dynamics, aerodynamics, relativity theory and plant ecology.*TIS

1903 Taro Morishima (22 April 1903 in Wakayama, Japan - 8 Aug 1989 in Tokyo, Japan) a Japanese mathematician specializing in algebra who attended University of Tokyo in Japan. Morishima published at least thirteen papers, including his work on Fermat's Last Theorem, and a collected works volume published in 1990 after his death. He also corresponded several times with American mathematician H. S. Vandiver.
Morishima's Theorem on FLT:
Let m be a prime number not exceeding 31. Let p be prime, and let x, y, z be integers such that xp + yp + zp = 0. Assume that p does not divide the product xyz. Then, p2 must divide mp − 1-1. *Wik

1904 J(ulius) Robert Oppenheimer was a U.S. theoretical physicist and science administrator, noted as director of the Los Alamos laboratory during development of the atomic bomb (1943-45) and as director of the Institute for Advanced Study, Princeton (1947-66). Accusations as to his loyalty and reliability as a security risk led to a government hearing that resulted the loss of his security clearance and of his position as adviser to the highest echelons of the U.S. government. The case became a cause célèbre in the world of science because of its implications concerning political and moral issues relating to the role of scientists in government. *TIS

1910 Norman Earl Steenrod (April 22, 1910 – October 14, 1971) was a preeminent mathematician most widely known for his contributions to the field of algebraic topology. He was born in Dayton, Ohio, and educated at Miami University and University of Michigan (A.B. 1932). After receiving a master's degree from Harvard University in 1934, he enrolled at Princeton University. He completed his Ph.D. under the direction of Solomon Lefschetz, with a thesis titled Universal homology groups. He held positions at the University of Chicago from 1939 to 1942, and the University of Michigan from 1942 to 1947. He moved to Princeton University in 1947, and remained on the Faculty there for the rest of his career. He died in Princeton.
Thanks to Lefschetz and others, the cup product structure of cohomology was understood by the early 1940s. Steenrod was able to define operations from one cohomology group to another (the so-called Steenrod squares) that generalized the cup product. The additional structure made cohomology a finer invariant. The Steenrod cohomology operations form a (non-commutative) algebra under composition, known as the Steenrod algebra.
His book The Topology of Fiber Bundles is a standard reference. In collaboration with Samuel Eilenberg, he was a founder of the axiomatic approach to homology theory. *Wik

1929 Sir Michael Francis Atiyah, OM, FRS, FRSE (22 April 1929, ) is a British mathematician working in geometry.
was awarded the Fields Medal in 1966 for his work in developing K-theory, a generalized Lefschetz fixed-point theorem and the Atiyah–Singer theorem, for which he also won the Abel Prize jointly with Isadore Singer in 2004. Atiyah received a knighthood in 1983 and the Order of Merit in 1992. He also served as president of the Royal Society (1990-95). *TIS *Wik

1946 Paul Charles William Davies, AM (22 April 1946, ) is an English physicist, writer and broadcaster, currently a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science. He has held previous academic appointments at the University of Cambridge, University of London, University of Newcastle upon Tyne, University of Adelaide and Macquarie University. His research interests are in the fields of cosmology, quantum field theory, and astrobiology. He has proposed that a one-way trip to Mars could be a viable option.*Wik

DEATHS

1945 Wilhelm Cauer (June 24, 1900 – April 22, 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter. *Wik
By the end of World War II, he was, like millions of less-distinguished countrymen and -women, merely a person in the way of a terrible conflagration.
Cauer succeeded in evacuating his family west, where the American and not the Soviet army would overtake it — but for reasons unclear he then returned himself to Berlin. His son Emil remembered the sad result.
The last time I saw my father was two days before the American Forces occupied the small town of Witzenhausen in Hesse, about 30 km from Gottingen. We children were staying there with relatives in order to protect us from air raids. Because rail travel was already impossible, my father was using a bicycle. Military Police was patrolling the streets stopping people and checking their documents. By that time, all men over 16 were forbidden to leave towns without a permit, and on the mere suspicion of being deserters, many were hung summarily in the market places. Given this atmosphere of terror and the terrible outrages which Germans had inflicted on the peoples of the Soviet Union, I passionately tried to persuade my father to hide rather than return to Berlin, since it was understandable that the Red Army would take its revenge. But he decided to go back, perhaps out of solidarity with his colleagues still in Berlin, or just due to his sense of duty, or out of sheer determination to carry out what he had decided to do.
Seven months after the ending of that war, my mother succeeded in reaching Berlin and found the ruins of our house in a southern suburb of the city. None of the neighbors knew about my father’s fate. But someone gave identification papers to my mother which were found in a garden of the neighborhood. The track led to a mass grave with eight bodies where my mother could identify her husband and another man who used to live in our house. By April 22, 1945, the Red Army had crossed the city limits of Berlin at several points. Although he was a civilian and not a member of the Nazi Party, my father and other civilians were executed by soldiers of the Red Army. The people who witnessed the executions were taken into Soviet captivity, and it was not possible to obtain details of the exact circumstances of my father’s death.
*ExecutedToday.com

1948 Herbert William Richmond (17 July 1863 Tottenham, England – 22 April 1948 Cambridge, England) was a mathematician who studied the Cremona–Richmond configuration. He was elected a Fellow of the Royal Society in 1911. T
The Cremona–Richmond configuration is a configuration of 15 lines and 15 points, having 3 points on each line and 3 lines through each point, and containing no triangles.*Wik

1989 Emilio Gino Segrè (1 Feb 1905; 22 Apr 1989) was an Italian-born American physicist who was co-winner, with Owen Chamberlain of the United States, of the Nobel Prize for Physics in 1959 for the discovery of the antiproton, an antiparticle having the same mass as a proton but opposite in electrical charge. He also created atoms of the man-made new element technetium (1937) and astatine (1940). Technetium occupied a hitherto unfilled space in the body of the Periodic Table, and was the first man-made element not found in nature. Astatine exists naturally only in exceedly small quantities because as a decay product of larger atoms, and having a half-life of only a few days, it quickly disappears by radioactively decay to become atoms of another element.*TIS

2002 Victor Frederick Weisskopf (September 19, 1908 – April 22, 2002) was an Austrian-born American theoretical physicist. He did postdoctoral work with Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli and Niels Bohr. During World War II he worked at Los Alamos on the Manhattan Project to develop the atomic bomb, and later campaigned against the proliferation of nuclear weapons.
His brilliance in physics led to work with the great physicists exploring the atom, especially Niels Bohr, who mentored Weisskopf at his institute in Copenhagen. By the late 1930s, he realized that, as a Jew, he needed to get out of Europe. Bohr helped him find a position in the U.S.
In the 1930s and 1940s, 'Viki', as everyone called him, made major contributions to the development of quantum theory, especially in the area of Quantum Electrodynamics.[3] One of his few regrets was that his insecurity about his mathematical abilities may have cost him a Nobel prize when he did not publish results (which turned out to be correct) about what is now known as the Lamb shift. *Wik

2008 Derek Thomas "Tom" Whiteside FBA (23 July 1932 – 22 April 2008) was a British historian of mathematics. He was the foremost authority on the work of Isaac Newton and editor of The Mathematical Papers of Isaac Newton. From 1987 to his retirement in 1999, he was the Professor of History of Mathematics and Exact Sciences at Cambridge University. *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

## Saturday, 21 April 2018

### On This Day in Math - April 21

A drunk man will find his way home,
but a drunk bird may get lost forever.

From Colloquial catchy statements encoding serious mathematics at Math Overflow.[ The serious math...A 2-dimensional random walk is recurrent (appropriately defined for either the discrete or continuous case) whereas in higher dimensions random walks are not. More details can be found for instance in this enjoyable blog post by Michael Lugo.  "This particular saying, by the way, is usually attributed to Shizuo Kakutani. (I don't want anybody thinking I came up with it!)"  ]

The 111th day of the year; 111 would be the magic constant for the smallest magic square composed only of prime numbers if 1 were counted as a prime (and we often used to)
It seems that Henry Ernest Dudeney may have been the first person to explore the use of primes to create a magic square. He gave the problem of constructing a magic in The Weekly Dispatch, 22nd July and 5th August 1900. At that time, 1 was sometimes (often?) considered as a prime number. His magic square gives the lowest possible sum for a 3x3 using primes (assuming one is prime)

The smallest magic square with true primes (not using one) has a magic constant of 177. Good luck.

A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111.
*Tanya Khovanova, Number Gossip

numbers like 111 that appear the same under 180o rotations are called strobograms. For numbers like the recent 109 which appears as a different number under rotation, but is still a number, I have created the term ambinumerals.

If you concatenated three copies of 111 and then squared the result, you get (111,111,111)2 = 12,345,678,987,654,321 *Cliff Pickover@pickover

Lagrange's theorem tells us that each positive integer can be written as a sum of squares with no more than four squares needed. Most numbers don't require the maximum four, but there are 58 year dates that can not be done with less than four. 111 and 112 are the smallest consecutive pair that both require the maximum. There is one other pair of consecutive year dates that also require four, seek them my children.

EVENTS

1547 In a dispute over the priority for solving cubics, Tartaglia sent Ferrari 31 challenge problems. They were no harder than those in Luca Pacioli’s Summa (1494). *VFR
[Here is the poem in which Niccolo Fontana (Tartaglia is a nickname meaning "stutterer") revealed the secret of solving the cubic to Cardan]
When the cube and the things together
Are equal to some discrete number, 10
Find two other numbers differing in this one.
Then you will keep this as a habit
That their product shall always be equal
Exactly to the cube of a third of the things. 2)
The remainder then as a general rule
Of their cube roots subtracted
Will be equal to your principal thing. 3)
1 [Solve x3 + cx = d]
2 [Find u, v such that u - v = d and uv = (c/3)3 ]
3 [Then x = 3√u - 3√v ]
*SAU
The Math DL site has digital copies of pages from Cardano's classic Practica Arithmetice.

1702 "Early in the morning (about 2 a.m.) ..... my wife, as I slept, ...found a comet in the sky, at which time she woke me..." thus Gottfried Kirch describes the first discovery of a comet by a woman, Maria Winkelmann. The official report would list Kirch as the discoverer, but eventually Winkelmann's credit would become known. Leibniz was an admirer of Winkelmann's talent with "quadrant and telescope." *Lisa Jardine, Ingenious Pursuits, pg 335

1692 David Gregory delivered his inaugural lecture as Savilian professor of astronomy at Oxford. He received his post on the recommendation of Newton. *VFR

1791 Benjamin Bannaker, the outstanding Black self-taught mathematical-astronomer, completed the outline of the boundaries of the federal district, Washington D. C. *VFR

1826 Thomas Jefferson spent his last years actively engaged in managing the University of Virginia. On this day he writes to Charles Bonnycastle, Professor of Natl Philosophy (later mathematics) . "I omitted, in conversn with you yesterday to observe on the arrangement of the Elliptical lecturing room that one third of the whole Area may be saved by the use of lap boards for writing on instead of tables, the room will hold half as many again, and the expence & lumber of tables be spared. a bit of thin board 12. I. square covered or not with cloth to every person is really a more convenient way of writing than a table I am now writing on such an one, and often use it of preference it may be left always on the sitting bench so as to be ready at hand when wanted. a bit of pasteboard, if preferred, might be furnished. I pray you to think on this for the economy of room, and as equivalent to the enlargemt of the room by one half. I salute you with frdshp & esteem *Letters of Thomas Jefferson, http://etext.lib.virginia.edu

1910 Halley’s comet passed perihelion. *VFR The New York Times reported, “Observatories report comet closer; is visible to naked eye in Curacao.” It would reach its maximum viewing brillance in May, with rooftop parties and predictions of doom.

2011 April 21st is when computers take over the world in Terminator. *@imranghory on Twitter

2012 The Lyrid meteor shower is expected to reach maximum intensity overnight from Saturday to Sunday. Meteor showers are generated when Earth plows through streams of debris shed by comets on their path around the sun. These icy, dusty chunks burn up in our planet's atmosphere, leaving behind bright streaks in the sky to commemorate their passing.
The Lyrids' parent comet is called C/1861 G1 Thatcher (Comet Thatcher for short). The Lyrids take their name from the constellation Lyra (The Lyre), because they appear to emanate from this part of the sky. Lyra is a northern constellation, so skywatchers in the Northern Hemisphere generally get much better looks at the Lyrids every year than do folks who live south of the equator. *Mike Wall, SPACE.com

BIRTHS

1652 Michel Rolle (April 21, 1652 – November 8, 1719) was a French mathematician. He is best known for Rolle's theorem (1691), and he deserves to be known as the co-inventor in Europe of Gaussian elimination (1690).*Wik His favorite area of research was the theory of equations. He introduced the symbol we use for nth roots. *VFR (famous to Calculus I students for Rolle's Theorem... and I always tell my students he had a daughter named Tootsie) .

1759 William Farish (baptized on 21 April 1758 {1759 NS}–1837) was a British scientist who was a professor of Chemistry and Natural Philosophy at the University of Cambridge, known for the development of the method of isometric projection and development of the first written university examination.
Farish's father was the Reverend James Farish (1714–1783), vicar of Stanwix near Carlisle. Farish himself was educated at Carlisle Grammar School, entered Magdalene College, Cambridge, as a sizar in 1774, and graduated Senior Wrangler and first in Smith's Prize in 1778. As tutor in 1792, Farish developed the concept of grading students' work quantitatively.
He was Professor of Chemistry at Cambridge from 1794 to 1813, lecturing on chemistry's practical application. Farish's lectures as professor of chemistry, which were oriented towards natural philosophy while the professor of natural and experimental philosophy F. J. H. Wollaston (1762–1828) gave very chemically oriented lectures.
From 1813 to 1837 Farish was Jacksonian Professor of Natural Philosophy. In 1819 Professor Farish became the first president of the Cambridge Philosophical Society.
Farish was also Vicar of St. Giles' and St. Peter from 1800 to 1837.
At Cambridge University, according to Hilkens (1967), Farish was "the first man to teach the construction of machines as a subject in its own right instead of merely using mechanisms as examples to illustrate the principles of theoretical physics or applied mathematics." He further became "famous for his work in applying chemistry and mechanical science to arts and manufactures".
In his lectures on the mechanical principles of machinery used in manufacturing industries, Farish often used models to illustrated particular principles. This models were often especially assembled for these lectures and disassembled for storage afterwards. In order to explain how these models were to be assembled he had developed a drawing technique, which he called "Isometrical Perspective".
Although the concept of an isometric had existed in a rough way for centuries, Farish is generally regarded as the first to provide rules for isometric drawing. In the 1822 paper "On Isometrical Perspective" Farish recognized the "need for accurate technical working drawings free of optical distortion. This would lead him to formulate isometry. Isometry means "equal measures" because the same scale is used for height, width, and depth".
From the middle of the 19th century, according to Jan Krikke (2006) isometry became an "invaluable tool for engineers, and soon thereafter axonometry and isometry were incorporated in the curriculum of architectural training courses in Europe and the U.S. The popular acceptance of axonometry came in the 1920s, when modernist architects from the Bauhaus and De Stijl embraced it". De Stijl architects like Theo van Doesburg used "axonometry for their architectural designs, which caused a sensation when exhibited in Paris in 1923". *Wik

1774 Jean-Baptiste Biot (21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who established the reality of meteorites, made an early balloon flight, and studied the polarization of light.*Wik He co-developed the Biot-Savart law, that the intensity of the magnetic field produced by current flow through a wire varies inversely with the distance from the wire. He did work in astronomy, elasticity, heat, optics, electricity and magnetism. In pure mathematics, he contibuted to geometry. In 1804 he made a 13,000-feet (5-km) high hot-air balloon ascent with Joseph Gay-Lussac to investigate the atmosphere. In 1806, he accompanied Arago to Spain to complete earlier work there to measure of the arc of the meridian. Biot discovered optical activity in 1815, the ability of a substance to rotate the plane of polarization of light, which laid the basis for saccharimetry, a useful technique of analyzing sugar solutions. *TIS

1882 Percy Williams Bridgman (21 Apr 1882; 20 Aug 1961 at age 79) was an American experimental physicist noted for his studies of materials at high temperatures and pressures. He was awarded the Nobel Prize for Physics in 1946 for his “invention of an apparatus to produce extremely high pressures, and for the discoveries he made therewith in the field of high pressure physics.” He was the first Harvard physicist to receive a Nobel Prize in Physics. In 1908, he began his first experimental work with static high pressures of about 6,500 atmospheres. Eventually, he reached about 400,000 atmospheres. During studies of the phase changes of solids under pressure, he discovered several high-pressure forms of ice. Bridgman also wrote eloquently on matters of general interest in the physics of his day. *TIS

1882 Maurice Kraitchik (April 21, 1882, Minsk - August 19, 1957, Bruxelles) was a Belgian mathematician, author, and game designer. His main interests were the theory of numbers and recreational mathematics.
He is famous for having inspired the two envelopes problem in 1953, with the following puzzle in La mathématique des jeux:
Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets. The game is as follows: whoever has the least money receives the contents of the wallet of the other (in the case where the amounts are equal, nothing happens). One of the two men can reason: "Suppose that I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favorable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair. Where is the mistake in the reasoning of each man?

Kraitchik wrote several books on number theory during 1922-1930 and after the war, and from 1931 to 1939 edited Sphinx, a periodical devoted to recreational mathematics.

During World War II, Kraïtchik emigrated to the United States, where he taught a course at the New School for Social Research in New York City on the general topic of "mathematical recreations." *Wik

1951 Michael H. Freedman (21 April 1951 in Los Angeles, California, ). In 1986 he received a Fields Medal for his proof of the four-dimensional Poincar´e conjecture. *VFR [The Poincaré conjecture, one of the famous problems of 20th-century mathematics, asserts that a simply connected closed 3-dimensional manifold is a 3-dimensional sphere. The higher dimensional Poincaré conjecture claims that any closed n-manifold which is homotopy equivalent to the n-sphere must be the n-sphere. When n = 3 this is equivalent to the Poincaré conjecture. Smale proved the higher dimensional Poincaré conjecture in 1961 for n at least 5. Freedman proved the conjecture for n = 4 in 1982 but the original conjecture remained open until settled by G Perelman who was offered the 2006 Fields medal for his proof. ] *Wik

DEATHS
1142 Peter Abelard (Petrus Abaelardus or Abailard) (1079 – April 21, 1142) was a medieval French scholastic philosopher, theologian and preeminent logician. The story of his affair with and love for Héloïse has become legendary. The Chambers Biographical Dictionary describes him as "the keenest thinker and boldest theologian of the 12th Century" *Wik

1552 Petrus Apianus (16 April 1495 – 21 April 1552), also known as Peter Apian, was a German humanist, known for his works in mathematics, astronomy and cartography.*Wik His Instrumentum sinuum sivi primi mobilis (1534),  gave tables of his calculations of sines for every minute, with a decimal division of the radius.*Tis  He published important popular works on astronomy and geography. *SAU [His arithmetic is shown in "The Ambasadors" by the younger Hans Holbein]

The book is the one closed on a ruler near the front left leg of the table as shown in the close-up.

1793 John Michell (? 1724, 21 Apr 1793). British geologist and astronomer who was first to devise a realistic estimate of the distance to the stars, discovered physical double stars, and is considered the father of seismology. After the Lisbon earthquake of 1755 (which killed 70,000 people), he suggested that earthquakes set up wave motion in the earth. He noted the increased frequency of earthquakes in volcanic areas. Michell realized that by comparing the time at which earthquakes are felt, the epicentre could be calculated. He invented a torsion balance, a device to measure very small forces, though died before carrying out its purpose to determine the density of the Earth. His rebuilt apparatus was used by Cavendish to make that measurement, which also gives the gravitational constant).*TIS

1825 Johann Friedrich Pfaff (22 December 1765,Stuttgart, - 21 April 1825,Halle) German mathematician who proposed the first general method of integrating partial differential equations of the first order. Pfaff did important work on special functions and the theory of series. He developed Taylor's Theorem using the form with remainder as given by Lagrange. In 1810 he contributed to the solution of a problem due to Gauss concerning the ellipse of greatest area which could be drawn inside a given quadrilateral. His most important work on Pfaffian forms was published in 1815 when he was nearly 50, but its importance was not recognised until 1827 when Jacobi published a paper on Pfaff's method. *TIS

1946 John Maynard Keynes, 1st Baron Keynes was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments. He greatly refined earlier work on the causes of business cycles, and advocated the use of fiscal and monetary measures to mitigate the adverse effects of economic recessions and depressions. His ideas are the basis for the school of thought known as Keynesian economics, as well as its various offshoots. (WIkipedia) He once said, "The avoidance of taxes is the only intellectual pursuit that carries any reward. " (John A Paulos on twitter)

1954 Emil Leon Post (February 11, 1897, Augustów – April 21, 1954, New York City) was a mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. In 1936, Post developed, independently of Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewriting and developed by Post in the 1920s but first published in 1943. Post's rewrite technique is now ubiquitous in programming language specification and design, and so with Church's lambda-calculus is a salient influence of classical modern logic on practical computing. Post devised a method of 'auxiliary symbols' by which he could canonically represent any Post-generative language, and indeed any computable function or set at all.
The unsolvability of his Post correspondence problem turned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages.
In an influential address to the American Mathematical Society in 1944, he raised the question of the existence of an uncomputable recursively enumerable set whose Turing degree is less than that of the halting problem. This question, which became known as Post's problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
Post made a fundamental and still influential contribution to the theory of polyadic, or n-ary, groups in a long paper published in 1940. His major theorem showed that a polyadic group is the iterated multiplication of elements of a normal subgroup of a group, such that the quotient group is cyclic of order n − 1. He also demonstrated that a polyadic group operation on a set can be expressed in terms of a group operation on the same set. The paper contains many other important results.*Wik

1965 Sir Edward Victor Appleton (6 Sep 1892, 21 Apr 1965 at age 72) was an English physicist who won the 1947 Nobel Prize for Physics for his discovery of the Appleton layer of the ionosphere. From 1919, he devoted himself to scientific problems in atmospheric physics, using mainly radio techniques. He proved the existence of the ionosphere, and found a layer 60 miles above the ground that reflected radio waves. In 1926, he found another layer 150 miles above ground, higher than the Heaviside Layer, electrically stronger, and able to reflect short waves round the earth. This Appleton layer is a dependable reflector of radio waves and more useful in communication than other ionospheric layers that reflect radio waves sporadically, depending upon temperature and time of day. *TIS

1967 André-Louis Danjon (6 Apr 1890, 21 Apr 1967 at age 76) French astronomer who devised a now standard five-point scale for rating the darkness and colour of a total lunar eclipse, which is known as the Danjon Luminosity Scale. He studied Earth's rotation, and developed astronomical instruments, including a photometer to measure Earthshine - the brightness of a dark moon due to light reflected from Earth. It consisted of a telescope in which a prism split the Moon's image into two identical side-by-side images. By adjusting a diaphragm to dim one of the images until the sunlit portion had the same apparent brightness as the earthlit portion on the unadjusted image, he could quantify the diaphragm adjustment, and thus had a real measurement for the brightness of Earthshine.*TIS

1990 Richard Bevan Braithwaite (15 Jan 1900, 21 Apr 1990 at age 90) was an English philosopher who trained in physics and mathematics, but turned to the philosophy of science. He examined the logical features common to all the sciences. Each science proceeds by inventing general principles from which are deduced the consequences to be tested by observation and experiment. Braithwaite was concerned with the impact of science on our beliefs about the world and the responses appropriate to that. He wrote on the statistical sciences, theories of belief and of probability, decision theory and games theory. He was interested in particular with the laws of probability as they apply to the physical and biological sciences. *TIS

2005 William H Kruskal (October 10, 1919 – April 21, 2005) was an American mathematician and statistician. He is best known for having formulated the Kruskal–Wallis one-way analysis of variance (together with W. Allen Wallis), a widely-used nonparametric statistical method. *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