Thursday, 15 April 2021

On This Day in Math - April 15

Duomo Santa Maria del Fiore, *Wik


For since the fabric of the universe is most perfect and the work of a most wise creator, nothing at all takes place in the universe in which some rule of the maximum or minimum does not appear.
~Leonhard Euler

The 105th day of the year, Paul Erdős conjectured that this is the largest number n such that the positive values of n - 2k are all prime. *Prime Curios

105 is the first degree for which the cyclotomic polynomial factors are not all 1, 0 or -1.

105 is the sum of consecutive integers in seven distinct ways. 105 =
1 + 2 + 3 + … + 13 + 14 =
6 + 7 + 8 + … + 14 + 15 =
12 + 13 + … + 17 + 18 =
15 + 16 + 17 + 18 + 19 + 20 =
19 + 20 + 21 + 22 + 23 =
34 + 35 + 36 =
52 + 53

105 is the largest composite number for which all the odd numbers less than it either are prime,  or share a factor with it.




EVENTS

1566 Early Tycho Brahe in 1566 he left Denmark for the second time, and arrived at Wittenberg on the 15 th April. The University of Wittenberg had been founded in 1502, and had then for nearly fifty years been one of the most renowned in Europe. He Studied under Caspar Peucer, distinguished as a mathematician, a physician, and a historian. Tycho, however, did not profit very much from Peucer's instruction, as the plague broke out at Wittenberg, so that he was induced to leave it on the 16th September, after a stay of only five months. *TYCHO BRAHE, A PICTURE OF SCIENTIFIC LIFE AND WORK IN THE
SIXTEENTH CENTURY BY J. L. E. DREYER

1726, writer William Stukeley held a conversation with Isaac Newton in Kensington during which Newton recalled “when formerly, the notion of gravitation came into his mind.” Later, Stukeley writing in his Memoirs of Sir Isaac Newton's Life, recorded that Newton said, “It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre.” *TIS The story was also related to John Conduitt who was Newton's assistant at the Royal mint, and the husband of Newton's niece. The idea that the apple hit Newton on the head seems to date from the early 20th Century. A copy of the page of Stukeley's manuscript where he tells this story is available on-line at the Royal Society.

1747 Euler, writing in response to a now lost letter from D'Alembert, that he opposed the suggestion that logarithms of negative numbers could exist and in particular that \(e^1\) could have both a positive and a negative value. He adds that as soon as the value of e, in \( y = e^x \) is defined, then the logarithm of all values are also assigned.
In the same letter he continues his argument by giving a new definition, now popular, of \( e^x\) as \(e^x = 1 + x + \frac{x^2}{1*2} \dots \) and hence the idea of a negative logarithm is impossible. *L E Dickson, History of the Exponential and Logarithmic Concept. Am Math Monthly Mar, 1913

1770, Dr. Joseph Priestley made the first mention in English that a piece of a rubber substance could erase marks from black-lead pencils. At the end of the Preface to his work, Familiar Introduction to the Theory and Practice of Perspective, he described it: "Since this Work was printed off, I have seen a substance excellently adapted to the purpose of wiping from paper the mark of a black-lead-pencil. It must, therefore, be of singular use to those who practise drawing. It is sold by Mr Nairne, Mathematical Instrument Maker, opposite the Royal Exchange. He sells a cubical piece of about half an inch for three shillings; and he says it will last several years." *TIS

1831 Gauss introduces the term "complex" for a+bi. Most of the 17th and 18th century writers spoke of a + bi as an imaginary quantity. Gauss saw the desirability of having different names for ai and a + bi, so he gave to the latter the Latin expression numeros integros complexos. *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

1869 W.S. Gilman Jr (of the Naval Observatory, I think{help})to Prof Elias Loomis of Yale, sends an account of an Aurora viewed from Brooklyn, NY. He ranks the aurora "inferior in brightness to... one I Witnessed ... on 15th September" (1868) *American Journal of Science

In 1895, a mathematical relationship between the frequencies of the hydrogen light spectrum was reported by a Swiss school teacher, Johann Balmer, in Annalen der Physik. Its significance was overlooked until Niels Bohr realized this showed a structure of energy levels of the electron in the hydrogen atom. *TIS

1904 term "discrete mathematics was introduced in The Twelfth Annual Report of the Ohio State Academy of Science “The new mathematics...has triumphed for its own domain in cases where the continuity methods were wholly inapplicable, where arithmology, discrete mathematics was called-for and victorious. *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

In 1570 in Sir Henry Billingsley's translation of Euclid's Elements he described discrete numbers, but not a discrete mathematics : "Two contrary kynds of quantity; quantity discrete or number, and quantity continual or magnitude"

In 1912, the fourth dimension was spoken of by Albert Einstein as time. *TIS

1949 Even though the paper on pp 1208 through 1226 of the 15 April 1949 issue of The Physical Review looks like any other, it is today seen as revolutionary. The entry for "Physical Principles Involved in Transistor Action" by John Bardeen (two-time Nobel in physics) and Walter Brattain (Nobel '72) was the defining technical publication on the transistor, which was the first massive step towards microminiaturization and the explosive new growth in the computer, *JF Ptak Science Books

1952 The first bank credit card was issued by Franklin National Bank, Franklin Square, New York. Purchases were charged to the bank, which made the payments, and then billed the card holders. *FFF

In 1966, the first X-ray three-dimensional stereo fluoroscopic system was installed for use in heart catherization by Richard J Kuhn. The $30,000 machine, developed by Joseph Quinn was put into use at the University of Oregon Medical Center, Portland, Oregon, U.S. The X-ray tube had one anode but two cathodes, an image intensifier with polarizers, and a synchronized analyzer. This produced a 3D image that could be seen through a viewing mirror without the use of special glasses. *TIS

1977 First West Coast Computer Faire Begins:
The first West Coast Computer Faire begins, featuring the debut of the Apple II from Apple Computer. The new machine includes innovations such as built-in high-resolution color graphics. For about $1,300, buyers receive a machine and built-in keyboard, 16 kilobytes of memory, BASIC, and eight expansion slots.*CHM

The 1981 Pulitzer prize winner The Soul of a New Machine describes the development of their ECLIPSE computer. *VFR


BIRTHS

1452 Leonardo da Vinci (15 Apr 1452; 2 May 1519 at age 67) Italian painter, draftsman, sculptor, architect, and engineer. Da Vinci was a great engineer and inventor who designed buildings, bridges, canals, forts and war machines. He kept huge notebooks sketching his ideas. Among these, he was fascinated by birds and flying and his sketches include such fantastic designs as flying machines. These drawings demonstrate a genius for mechanical invention and insight into scientific inquiry, truly centuries ahead of their time. His greater fame lies in being one of the greatest painters of all times, best known for such paintings as the Mona Lisa and The Last Supper.*TIS In an interesting blog Thony Christie pointed out that "... Leonardo played absolutely no role what so ever in the history of science and or technology because none of his voluminous writings on those subjects saw the light of day before the 19th century when they were nothing more than a historic curiosity, admittedly a fascinating curiosity but nothing more than that.. " *Renaissance Mathematicus

1548 Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate. Cataldi discovered (actually re-discovered, see bottom of article) the sixth and seventh primes later to acquire the designation Mersenne primes by 1588. His discovery of the 6th, that corresponding to p=17 in the formula Mp=2p-1, exploded a many-times repeated number-theoretical myth (Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim in L.E.Dickson's History of the Theory of Numbers--with a few more repeating this afterward) that the perfect numbers had units digits that invariably alternated between 6 and 8; and that of the 7th (for p=19) held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered that 231 - 1 was the eighth Mersenne prime. Although Cataldi also claimed that p=23, 29, 31 and 37 all also generate Mersenne primes (and perfect numbers), his text's clear demonstration shows that he had genuinely established the fact through p=19.. *Wik In 1613 he published an important early work on continued fractions. The term “continued fraction” was coined by John Wallis in 1655. [DSB 3, 125]
(earlier discoverers of 5th-7th perfect numbers: Ismail ibn Ibrahim ibn Fallus (1194-1239) who wrote a treatise based on the Introduction to arithmetic by Nicomachus. Ibn Fallus gave, in his treatise, a table of ten numbers which were claimed to be perfect, the first seven are correct and are in fact the first seven perfect numbers, the remaining three numbers are incorrect.

The fifth perfect number has been discovered again (after the unknown results of the Arabs) and written down in a manuscript dated 1461. It is also in a manuscript which was written by Regiomontanus during his stay at the University of Vienna, which he left in 1461, see . It has also been found in a manuscript written around 1458, while both the fifth and sixth perfect numbers have been found in another manuscript written by the same author probably shortly after 1460. All that is known of this author is that he lived in Florence and was a student of Domenico d'Agostino Vaiaio.

In 1536, Hudalrichus Regius made the first breakthrough which was to become common knowledge to later mathematicians, when he published Utriusque Arithmetices in which he gave the factorisation 211 - 1 = 2047 = 23 . 89. With this he had found the first prime p such that (2p-1)(2p - 1) is not a perfect number. He also showed that 213 - 1 = 8191 is prime so he had discovered (and made his discovery known) the fifth perfect number \(2^12(2^13 - 1) = 33550336. \)

J Scheybl gave the sixth perfect number in 1555 in his commentary to a translation of Euclid's Elements. This was not noticed until 1977 and therefore did not influence progress on perfect numbers. *SAU

1541 "The discovery that comets are in fact supralunar entities has long been attributed to Tycho Brahe. Yet in a letter from Rheticus’ confidant Paul Eber to Melanchthon we learn that Copernicus and Rheticus had considered the matter long before Brahe:
Magister Rheticus wrote from Prussia, as he is expecting the completion of the work of his praeceptor he will not be able to return in the coming months, but rather in autumn. They have already discovered in those lands that Comets do not arise in the region of the elements, but rather in that of the ether above the lunar sphere. ..." April 15, 1541

1707 Leonhard Euler (15 Apr 1707, 18 Sep 1783) Swiss mathematician and physicist, one of the founders of pure mathematics. He not only made decisive and formative contributions to the subjects of geometry, calculus, mechanics, and number theory but also developed methods for solving problems in observational astronomy and demonstrated useful applications of mathematics in technology. At age 28, he blinded one eye by staring at the sun while working to invent a new way of measuring time. *TIS (Students who have not, should read Dunham's "Euler, The Master of us All")


He was the most productive mathematician of all times; his still only partly published collected works comprise over 75 large volumes. *VFR

1793 Friedrich Georg Wilhelm von Struve (15 Apr 1793, 23 Nov 1864) German-Russian astronomer, one of the greatest 19th-century astronomers and the first in a line of four generations of distinguished astronomers. He founded the modern study of binary (double) stars. In 1817, he became director of the Dorpat Observatory, which he equipped with a 9.5-inch (24-cm) refractor that he used in a massive survey of binary stars from the north celestial pole to 15°S. He measured 3112 binaries - discovering well over 2000 - and cataloged his results in Stellarum Duplicium Mensurae Micrometricae (1837). In 1835, Czar Nicholas I persuaded Struve to set up a new observatory at Pulkovo, near St. Petersburg. There in 1840 Struve became, with Friedrich Bessel and Thomas Henderson, one of the first astronomers to detect parallax. *TIS

1809 Hermann Günther Grassmann (15 Apr 1809, 26 Sep 1877) German mathematician chiefly remembered for his development of a general calculus of vectors in Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844; "The Theory of Linear Extension, a New Branch of Mathematics"). *TIS One of the many examinations for which Grassmann sat, required that he submit an essay on the theory of the tides. In 1840, he did so, taking the basic theory from Laplace's Mécanique céleste and from Lagrange's Mécanique analytique, but expositing this theory making use of the vector methods he had been mulling over since 1832. This essay, first published in the Collected Works of 1894-1911, contains the first known appearance of what are now called linear algebra and the notion of a vector space. He went on to develop those methods in the book mentioned above. In spite of publishing the idea somewhat early in his career, it seems his work went largely unnoticed until the last decade of his life.*Wik

1874 Johannes Stark (15 Apr 1874; 21 Jun 1957 at age 83) German physicist who won the 1919 Nobel Prize for Physics for his discovery in 1913 that an electric field would cause splitting of the lines in the spectrum of light emitted by a luminous substance; the phenomenon is called the Stark effect. *TIS

1927 Robert L. Mills (15 Apr 1927; 27 Oct 1999 at age 72) American physicist who shared the 1980 Rumford Premium Prize with his colleague Chen Ning Yang for their “development of a generalized gauge invariant field theory” in 1954. They proposed a tensor equation for what are now called Yang-Mills fields. Their mathematical work was aimed at understanding the strong interaction holding together nucleons in atomic nuclei. They constructed a more generalized view of electromagnetism, thus Maxwell's Equations can be derived as a special case from their tensor equation. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories.*TIS

1929 Thomas Brooke Benjamin​, FRS (15 April 1929 – 16 August 1995) was an English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations. *Wik

1934 Professor James "Jim" Wiegold (15 April 1934 – 4 August 2009) was a Welsh mathematician. He earned a PhD at the University of Manchester in 1958, studying under Bernhard Neumann, and is most notable for his contributions to group theory.*Wik

DEATHS
1446 Filippo Brunelleschi (1377 in Florence, Italy - 15 April 1446 in Florence, Italy) Brunelleschi's most important achievement in mathematics came around 1415 when he rediscovered the principles of linear perspective using mirrors. He understood that there should be a single vanishing point to which all parallel lines in a plane, other than the plane of the canvas, converge. Also important was his understanding of scale, and he correctly computed the relation between the actual length of an object and its length in the picture depending on its distance behind the plane of the canvas. Using these mathematical principles, he drew various scenes of Florence with correct perspective. These perspective drawings by Brunelleschi have since been lost but a "Trinity" fresco by Masaccio still exists which uses Brunelleschi's mathematical principles. He is best known for best known for his construction of the dome of Florence's cathedral, the Duomo Santa Maria del Fiore.*SAU

1704 Johan van Waveren Hudde (23 Apr 1628, 15 Apr 1704 at age 76) Dutch mathematician and statesman who, after an education in law, became interested in mathematics, though for a limited time (1654-63). 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

1754 Jacopo Francesco Riccati (28 May 1676 in Venice, Venetian Republic (now Italy) - 15 April 1754 in Treviso, Venetian Republic (now Italy)) His work had a wide influence on leading mathematicians such as Daniel Bernoulli, who studied the equation in his Exercitationes quaedam mathematicae, and Leonard Euler who extended Riccati's ideas to integration of non-homogeneous linear differential equations of any order. Riccati also worked on cycloidal pendulums, the laws of resistance in a fluid and differential geometry. *SAU

1764 Peder [Nielsen] Horrebow (Horrebov) (14 May 1679; Løgstør, Jutland – 15 April 1764; Copenhagen) From 1703 to 1707, he served as an assistant to Ole Rømer and lived in Rømer's home. He worked as a household tutor from 1707 to 1711 to a Danish baron, and entered the governmental bureaucracy as an excise writer in 1711.
After repeatedly petitioning King Frederick IV, Horrebow became professor of mathematics at the University of Copenhagen in 1714. He also became director of the university's observatory (called the Rundetårn, "the Round Tower"). His son Christian succeeded him in this position. Horrebow and his wife, Anne Margrethe Rossing, had a total of 20 children.
In 1728, the great fire of Copenhagen destroyed all of the papers and observations made by Rømer, who had died in 1710. Horrebow wrote the Basis Astronomiae (1734–35), which describes the scientific achievements made by Rømer. Horrebow's own papers and instruments were destroyed in the same fire. Horrebow was given a special grant from the government to repair the observatory and instruments. Horrebow received further support from a wealthy patron.
Horrebow invented a way to determine a place's latitude from the stars. The method fixed latitude by observing differences of zenith distances of stars culminating within a short time of each other, and at nearly the same altitude, on opposite sides of the zenith. The method was soon forgotten despite its value until it was rediscovered by the American Andrew Talcott in 1833. It is now called the Horrebow-Talcott Method.
He wrote on navigation and determined the sun parallax, 9", an approximative solution to the Kepler equation. Horrebow also learned how to correct inherent flaws in instruments. This preceded Tobias Mayer's theory of correction of 1756.
Horrebow was a member of a number of scientific societies, including the Académie des Sciences (from 1746). He also worked as a medical doctor and as an academic notary (from 1720). *Wik

1873 Christopher Hansteen (26 Sep 1784, 15 Apr 1873 at age 88) Norwegian astronomer and physicist who is noted for his research in geomagnetism. In 1701, Edmond Halley had already published a map of magnetic declinations, and the subject was studied by Humboldt, de Borda, and Gay-Lussac, among others. Hansteen collected available data and also mounted an expedition to Siberia, where he took many measurements for an atlas of magnetic strength and declination. *TIS

1993 John Tuzo Wilson, CC, OBE, FRS, FRSC, FRSE (October 24, 1908 – April 15, 1993) the world-renowned Canadian geophysicist, served as Director General of the Ontario Science Centre from 1974 to 1985. He was instrumental in developing the theory of Plate Tetonics in the 1960s. This theory describes the formation, motion and destruction of the Earth's crust, the origin of volcanic eruptions and earthquakes, and the growth of mountains. Dr. Wilson's signficant contributions to this theory revolutionized Earth Sciences. He proposed the existence of transform faults to explain the numerous narrow fracture zones and earthquakes along oceanic ridges. He also showed that rising magma plumes beneath the Earth's crust could create stationary hot spots, leading to the formation of mid-plate volcanic chains like the Hawaiian Islands.
The first graduate of geophysics from the University of Toronto in 1930, Dr. Wilson went on to study at Cambridge and Princeton, earning his doctorate in 1936. After spending two years with the Geological Survey of Canada and almost a decade with the Canadian Military Engineers, he accepted the position of Professor of Geophysics at the University of Toronto in 1946. Internationally recognized for his major contributions as a research scientist, educator and visionary, Dr. Wilson received many prestigious
awards, including the Vetlesen Prize, the Earth Sciences equivalent of the Nobel Prize.*THE HISTORICAL
MARKER DATABASE





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, 14 April 2021

On This Day in Math - April 14


Can  you guess what joke about Topology this was supposed to represent?  

The 'control of nature' is a phrase conceived in arrogance, born of the Neanderthal age of biology and the convenience of man.
~Rachel Carson


The 104th day of the year; 104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex. *What's Special About This Number

104 is the sum of eight consecutive even numbers, 104 = 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20

13 straight lines through an annulus can produce a maximum of 104 pieces (students might try to create the maximum for smaller numbers of lines, the sequence is 2, 5, 9, 14, 20,... https://oeis.org/A000096 the differences give a clue to the complete pattern.)


*************** Lots of additional math facts for days 91-120 at https://mathdaypballew.blogspot.com/


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

1561 One of the earliest recorded citations of UFO's:
At sunrise on the 14th April 1561, the citizens of Nuremberg beheld "A very frightful spectacle." The sky appeared to fill with cylindrical objects from which red, black, orange and blue white disks and globes emerged. Crosses and tubes resembling cannon barrels also appeared whereupon the objects promptly "began to fight one another." This event is depicted in a famous 16th century woodcut by Hans Glaser.
*UFO Evidence Org

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


1685 It's easy for students of Math History to get the impression that John Wallis was totally immersed in mathematics, but a perusal of his writing on religion, or  his many varied contributions to the Royal Society paint the picture of a polymath.

“A Relation Concerning the Late Earthquake Neer Oxford: Together with Some Observations of the Sealed Weatherglass, and the Barometer Both upon That Phænomenon, and in General,” Phil Trans 1 (1665-1666):
166-171; Wallis, “A Discourse concerning the Air’s Gravity, Observd in the Baroscope, Occasioned by That of Dr. Garden: Presented to the Phil. Soc. of Oxford, by the Reverend Dr. Wallis, President of That Society. April, 14, 1685,” Phil Trans 15 (1685): 1002-1014; WC II, 282; WC III, 281-287.
This is almost certainly concerning the earthquake of 6 Oct, 1683 at Derbyshire. This earthquake also has the distinction of being the first British earthquake surveyed by the British Geological Survey.

1790 Mathurin Jacques Brisson (1723–1806) proposed to the Paris Academy the establishment of a system of measurement resting on a natural unit of length. The general idea of decimal subdivision was obtained from a work of Thomas Williams, London, 1788. *F Cajori, History of Mathematics

1822 In a letter to Gauss, Bessell recommends his student, Heinrich Ferdinand Scherk. Gauss considered Scherk one of the best students he ever had. Scherk would go on to great educational success and Kummer was one of his students. * Dunnington, Gray, & Dohse , Carl Friedrich Gauss: Titan of Science

1855 The first chess problem of Sam Loyd, age fourteen, was published in the New York Saturday Courier. Within a few years he was recognized as the nation’s foremost composer of chess problems. Once he announced that he had discovered a way to mate a lone king in the center of the board with a knight and two rooks. Readers were first furious, afterwards amused, by his preposterous solution: line them up in the order knight, rook, king, rook. [Mathematical Puzzles of Sam Loyd, edited by Martin Gardner, Dover 1959, p. xi-xii]

1860 A printed article on the Four Color theorem (perhaps only the second public statement about it, see June 10, 1854) was printed on this date and spread knowledge of the problem to America. In the unusual form of an Atheaneum book review of The Philosophy of Discovery by William Whewell, the unsigned, but almost surely written by DeMorgan, review launched in to a discussion of the Four Color problem. The review treats the four color necessity as obvious to cartographers, and makes no mention of either Guthrie, since he most surely knew the mathematical community in England were aware of his contribution from DeMorgan's own letters.
The review of Whewell's book came to the attention of American Philosopher/Logician C. S. Peirce, son of Harvard Professor Benjamin Peirce, and became a lifelong fascination. He immediately crafted a proof, which is still unknown, to my knowledge. He wrote later that it had been the Atheanenum review which first ignited his interest, and that his own proof was never printed. Shortly before DeMorgan's death in 1871, he was visited by Peirce, but no record is known of what they talked.

1914 Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras. He arrived in London on 14 April, with E. H. Neville waiting for him with a car. I received a tweet from @amanicdroid who pointed out that, "this was significant for him culturally as a high-caste Hindu as crossing the ocean was taboo. "

1931 The first issue of the review journal Zentralblatt f¨ur Mathematik was published by Springer. Otto Neugebauer, then a young professor at G¨ottingen, conceived the idea of a journal that would publish the reviews of
articles as soon as possible after the papers had appeared and persuaded the publishing house of J. Springer to publish such a journal. The first issue of Zentralblatt f¨ur Mathematik und ihre Grenzgebiete, as the new journal was called, dated April 14, 1931, had Neugebauer as its editor. It also had a very distinguished and international editorial committee (consisting of P. Alexandroff, J. Bartels, W. Blaschke, R. Courant, H. Hahn, G. H. Hardy, F. Hund, G. Julia, O. Kellogg, H. Kienle, T.Levi-Civita, R. Nevanlinna, H. Thirring and B. L. van der Waerden). The first volume consisted of seven issues plus an index, in 466 pages. (The very first item reviewed was the second edition
of Methoden der mathematischen Physik, by Courant and Hilbert.) The classification system used was very similar to the scheme used by Jahrbuch.
Mathematical Reviews. Zentralblatt flourished under Neugebauer’s direction and became the primary reviewing journal in mathematics. Jahrbuch valiantly continued until issue number 4 of its Volume 68, for the year 1942, ceasing publication in mid-1944, but it had already lost its prominence in the research community. But, just asWorldWar I damaged Jahrbuch, serious harm was done to Zentralblatt soon after its founding by political conditions beyond its control. The anti-Semitic and anti-Soviet policies of the Nazi regime generated pressures on the editorial policies of Zentralblatt concerning the use of Jewish and Russian reviewers. Although Neugebauer left G¨ottingen for the University of Copenhagen in 1934, he had continued to edit Zentralblatt. But by 1938 the intrusion of politics had become intolerable and he and other members of the editorial board resigned. Despite these difficulties Zentralblatt continued its operation and, except for a brief suspension of publication from November 1944 until June 1948, has continued to publish to the present day.

1943 In 1943, a proposal for an electronic computer was submitted to colleagues at the U.S. Army's Ballistics Research Laboratory by John Grist Brainerd, director of research at the University of Pennsylvania's Moore School, where the proposal was written by John Mauchly. In May 1943, the Army contracted the Moore School to build ENIAC, the first electronic computer. Although ENIAC was not finished until after the war had ended, it nevertheless marked a major step forward in computing. *TIS

1995 Chinese Government Works to Purge Its Agencies of Illegal Software:
The Chinese government launches widespread efforts to purge governmental agencies of illegally copied software, a practice that had been costing U.S. software publishers millions of dollars. The plan calls for allotting more money to purchase software while giving an enforcement agency the power to prosecute anyone bootlegging software. The announcement follows a March meeting at which China had signed an accord with the United States vowing to crackdown on piracy.*CHM

2014 A total Lunar eclipse visible in most of North and South America on this night. The total eclipse will begin around 3am EDT and last for about 80 minutes. More information is here. *Michael Zeiler

BIRTHS

1629 Christiaan Huygens (14 Apr 1629; 8 Jul 1695 at age 66) Dutch physicist and astronomer who founded the wave theory of light, discovered the true shape of the rings of Saturn, and contributed to the science of dynamics - the study of the action of forces on bodies. Using a lens he ground for himself, on 25 Mar 1655, he discovered the first moon of Saturn, later named Titan. In 1656, he patented the first pendulum clock, which he developed to enable exact time measurement while observing the heavens. Cristiaan Huygens studied the relation of the length of a pendulum to its period of oscillation (1673) and stated theories on centrifugal force in circular motion which influenced Sir Isaac Newton in formulating his Law of Gravity. Huygens also studied and drew the first maps of Mars. On 14 Jan 2005, a NASA space probe, named after Huygens, landed on Titan. *TIS
Amazon has the Kindle version of his Treatise on Light for free.



1898 Harold Stephen Black (14 Apr 1898; 11 Dec 1983 at age 85) American electrical engineer who discovered and developed the negative-feedback principle, in which amplification output is fed back into the input, thus producing nearly distortionless and steady amplification. In 1921, Black joined the forerunner of Bell Labs, in New York City, working on elimination of distortion. After six years of persistence, Black conceived his negative feedback amplifier in a flash commuting to work aboard the ferry. Basically, the concept involved feeding systems output back to the input as a method of system control. The principle has found widespread applications in electronics, including industrial, military, and consumer electronics, weaponry, analog computers, and such biomechanical devices as pacemakers. *TIS

1917 Nathan Saul Mendelsohn, CM, FRSC (April 14, 1917 – July 4, 2006) was an American-born mathematician who lived and worked in Canada. Mendelsohn was a researcher in several areas of discrete mathematics, including group theory and combinatorics.*Wik

DEATHS

1792 Maximilian Hell (May 15, 1720 – April 14, 1792) was a Slovak astronomer and an ordained Jesuit priest from the Kingdom of Hungary.
Born as Rudolf Maximilian Höll in Selmecbánya, Kingdom of Hungary (present-day Banská Štiavnica, Slovakia)., but later changed his surname to Hell. He was the third son from the second marriage of his father Matthias Cornelius Hell (Matthäus Kornelius Hell) and his mother Julianna Staindl. The couple had a total of 22 children. Registry entries indicate that the family was of German descent, while Maximilian Hell later in life (ca 1750) is known to declare himself as Hungarian.
Hell became the director of the Vienna Observatory in 1756. He published the astronomical tables Ephemerides astronomicae ad meridianum Vindobonemsem ("Ephemerides for the Meridian of Vienna"). He and his assistant János Sajnovics went to Vardø in the far north of Norway (then part of Denmark-Norway) to observe the 1769 transit of Venus. He was elected as a foreign member of the Royal Danish Academy of Sciences and Letters on October 13, 1769. This society also funded the publication of his 1770 account of the Venus passage Observatio transitus Veneris ante discum Solis die 3. Junii anno 1769 (Copenhagen, 1770).
There was some controversy about Hell's observations of the transit of Venus because he stayed in Norway for eight months, collecting non-astronomical scientific data about the arctic regions for a planned encyclopedia (which never appeared, in part due to the suppression of the Jesuit order). The publication of his results was delayed, and some (notably Joseph Johann Littrow) accused Hell posthumously of falsifying his results. However, Simon Newcomb carefully studied Hell's notebooks and exonerated him a century after his death in Vienna.
Besides astronomy, Hell also had an interest in magnet therapy (the alleged healing power of magnets), although it was Franz Anton Mesmer who went further with this and received most of the credit.
In 1771, Hell was elected a foreign member of the Royal Swedish Academy of Sciences.
The crater Hell on the Moon is named after him. *Wik

1935 Amalie Emmy Noether (23 Mar 1882, 14 Apr 1935 at age 53) was a 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 Emmy Noether’s house in Erlangen is shown in a blog at The Renaissance Mathematicus

1964 Tatyana Alexeyevna Afanasyeva (Kiev, 19 November 1876 – Leiden, 14 April 1964) (also known as Tatiana Ehrenfest-Afanaseva) was a Russian/Dutch mathematician. On 21 December 1904 she was married to Paul Ehrenfest (1880–1933) an Austrian physicist. They had two daughters and two sons: one daughter, Tatyana Pavlovna Ehrenfest, also became a mathematician.
Afanasyeva was born in Kiev, Ukraine, then part of the Russian Empire. After her father died she was brought up by an uncle in St Petersburg, Russia, where she attended a women's pedagogical school and a Women's College. In 1902 she transferred to Göttingen, where she met Ehrenfest. The couple got married in 1904, and in 1907 they returned to St Petersburg. In 1912 they moved to Leiden, where Paul Ehrenfest was appointed to succeed H.A. Lorentz as professor at the University of Leiden.
Tatyana collaborated closely with her husband, most famously on their classic review of the statistical mechanics of Boltzmann. She published many papers on various topics such as randomness and entropy, and teaching geometry to children. *Wik

1964 Rachel Louise Carson (27 May 1907, 14 Apr 1964 at age 56) was an American marine biologist, conservationist and writer well known for her writings on environmental pollution and the natural history of the sea. Embedded within all of Carson's writing was the view that human beings were but one part of nature distinguished primarily by their power to alter it, in some cases irreversibly. Disturbed by the profligate use of synthetic chemical pesticides after World War II, Carson reluctantly changed her focus in order to warn the public about the long term effects of misusing


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, 13 April 2021

On This Day in Math - April 13

Double False Position from Gemma Frisius  Arithmeticae Practicae Methodus Facilis (1540) *MAA

"I endeavor to keep their attention fixed on the main objects of all science, the freedom & happiness of man. so that coming to bear a share in the councils and government of their country, they will keep ever in view the sole objects of all legitimate government."
A plaque with this quotation, with the first phrase omitted, is in the stairwell of the pedestal of the Statue of Liberty.
~Thomas Jefferson, in  a Letter to Tadeusz Kosciuszko, 26 February 1810

The 103rd day of the year; there are 103 geometrical forms of magic knight's tour of the chessboard.

103 is the reverse of 301. The same is true of their squares: 1032 = 10609 and 3012 = 90601. *Jim Wilder

The smallest prime whose reciprocal contains a period that is exactly 1/3 of the maximum length. (The period of the reciprocal of a prime p is always a divisor of p-1, so for 103 the period is 102/3 = 34. )

Using a standard dartboard, 103 is the smallest possible prime that cannot be scored with two darts.

*************** Lots of additional math facts for days 91-120 at https://mathdaypballew.blogspot.com/


EVENTS

In 1625, the word "microscope" was coined as a suggested term in a letter written by Johannes Faber of Bamberg, Germany, to Federigo Cesi, Duke of Aquasparata and founder of Italy's Accademia dei Lincei (Academy of the Lynx). This Academy, possibly the world's first scientific society took its name after the animal for its exceptional vision. *TIS

1668 Lord Brouncker, President of the Royal Society, publishes "the fist mathematical result to be published in a mathematical journal" in the Philosophical transactions of the Royal Society. His demonstration of the method of quadrature of the rectangular hyperbola, y= x-1 extended the work of Wallis in Arithmetica infinitorium. Brouncker had been working with Wallis on extending the work of Torricelli's Opera geometrica hoping to apply the methods to the long-sought quadrature of the circle.
The rectangular hyperbola had eluded Fermat, and only been partially solved by de Saint Vincent by 1625. It was a fellow Jesuit of Saint Vincent, Alphonse Antonio de Sarasa he may have been the first to recognize that certain areas under the hyperbola are related to each other in the same was as logarithms. *Jacqueline Stedall, Mathematics Emerging, 2008.

1672 After presenting his paper on the composition of light as a, “heterogeneous mixture of differently refrangible rays” on 19 Feb, several critics emerged, most notably Robert Hooke. Newton responded to the critiques with a letter to the Royal Society, "Some Experiments propos'd in relation to Mr. Newtons Theory of light, printed in Numb. 80; together with the Observations made thereupon by the Author of that Theory; communicated in a Letter of his from Cambridge, April 13. 1672." Newton had performed a series of experiments to validate his theory, and here described the results. See the letter here.

Halley's Comet, March 8, 1986
1759  Halley’s comet returns, as he predicted in 1682. The comet last reached perihelion on 9 February 1986, and will next reach it again on 28 July 2061 *Wik   Halley's prediction that it would return in 1758 was incorrect, and observations and calculations led to a correct prediction and perihelion occurred on April 13, 1759.  It was sighted in 1758, the year he predicted  on 25 December, when it was observed by German farmer, and armature astronomer, Johan Palitsch. *HT to @RMathematicus


1791 Legendre is named one of the French Academy’s three commissioners for the astronomical operations and triangulations necessary for determining the standard meter. The others were Mechain and Cassini IV. [DSB 8, 136]*VFR


BIRTHS

953 Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji (13 April 953 in Baghdad (now in Iraq) - died about 1029) Al-Karaji was an Islamic mathematician who wrote about the work of earlier mathematicians and who can be regarded as the first person to free algebra from geometrical operations and replace them with the type of operations which are at the core of algebra today. *SAU

1728 Paolo Frisi (13 Apr 1728; 22 Nov 1784 at age 56) Italian mathematician, astronomer, and physicist who is best known for his work in hydraulics (he designed a canal between Milan and Pavia). He was, however, the first to introduce the lightning conductor into Italy. His most significant contributions to science, however, were in the compilation, interpretation, and dissemination of the work of other scientists, such as Galileo Galilei and Sir Isaac Newton. His work on astronomy was based on Newton's theory of gravitation, studying the motion of the earth (De moto diurno terrae). He also studied the physical causes for the shape and the size of the earth using the theory of gravity (Disquisitio mathematica, 1751) and tackled the difficult problem of the motion of the moon. *TIS

1743 Thomas Jefferson, American President and Mathematical enthusiast, was born.
"Thomas Jefferson had four main accomplishments in mathematics. First, he took mathematics from the ranks of a secondary subject and raised it to such a prominence in the curriculum of the University of Virginia that it was not seen at any other college in the United States at the time. Through Jefferson’s influence, men like J.J. Sylvester, in 1841 (though unsuccessful), were recruited to build up the mathematics courses at the University of Virginia....David Eugene Smith sums it best in the following passage:
It is apparent that Jefferson was not a mathematician but that he was a man who appreciated the beauties, the grandeur, the values, the classics, and the uses of mathematics and did much to give to the science a recognized standing as a university subject. "
From an online article by Ajaz Siddiqui, See the short article here.

1802 George Palmer Williams (Woodstock, Vermont, April 13, 1802-Ann Arbor, September 4, 1881) Hegraduated Bachelor of Arts from the University of Vermont in 1825, and then studied about two years in the Theological Seminary at Andover, Massachusetts. He did not complete the course, but took up teaching, which proved to be his life work.
He was Principal of the Preparatory School at Kenyon College, Ohio, from 1827 to 1831. In 1831 he was elected to the chair of Ancient Languages in the Western University of Pennsylvania, but after two years he returned to Kenyon College, where he remained until called, in 1837, to the branch of the incipient University of Michigan at Pontiac.
In 1841, when the College proper was opened at Ann Arbor, he was made Professor of Natural Philosophy. In 1854 he was transferred to the chair of Mathematics and in 1863 to the chair of Physics. From 1875 to 1881 he was Emeritus Professor of Physics.
He received the degree of Doctor of Laws from Kenyon College in 1849. The University Senate in a memorandum relative to his death declared that: "Dr. Williams welcomed the first student that came to Ann Arbor for instruction; as President of the Faculty he gave diplomas to the first class that graduated, and from the day of his appointment to the hour of his death his official connection with the University was never broken."
In 1846 he was ordained to the ministry of the Protestant Episcopal Church; but he did no regular parish work, except for a short time in Ann Arbor. He was first and last a teacher, beloved by his colleagues and pupils and universally respected and honored.
Some years before his death the alumni raised a considerable fund, the proceeds of which were to be paid to him during his lifetime and after his death were to be used for maintaining a professorship named in honor of his memory. *Hinsdale and Demmon, History of the University of Michigan 221

1813 Duncan Farquharson Gregory (13 April 1813 in Edinburgh, Scotland - 23 Feb 1844 in Edinburgh, Scotland) Scottish mathematician who was one of the first to investigate modern ideas of abstract algebra.In this work Gregory built on the foundations of Peacock but went far further towards modern algebra. Gregory, in his turn, had a major influence on Boole and it was through his influence that Boole set out on his innovative research. *SAU

1869 Ada Isabel Maddison (April 12, 1869 - October 22, 1950) born in Cumberland, England. She attended Girton College, Cambridge, in the same class with Grace Chisholm Young and they attended lectures of Cayley. Then she came to Bryn Mawr, where she earned her Ph.D. in 1895. She continued there until retirement, involved mostly in administrative work. *WM

1879 Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematicianborn in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables. He became the effective leader of the Italian school of algebraic geometry. Together with Federigo Enriques, he won the Bordin prize from the French Academy of Sciences.
He contributed in a major way to birational geometry, the theory of algebraic surfaces, in particular of the curves lying on them, the theory of moduli spaces and the theory of functions of several complex variables. He wrote prolifically, and some of his work has subsequently been shown to be not rigorous according to the then new standards set in particular by Oscar Zariski and David Mumford. At the personal level, according to Roth (1963) he was easily offended, and he was involved in a number of controversies. He died in Rome of cancer.*Wik

1889 Herbert Osborne Yardley American cryptographer who organized and directed the U.S. government's first formal code-breaking efforts during and after World War I. He began his career as a code clerk in the State Department. During WW I, he served as a cryptologic officer with the American Expeditionary Forces in France during WWI. In the 1920s, when he was chief of MI-8, the first U.S. peacetime cryptanalytic organization, he and a team of cryptanalysts exploited nearly two dozen foreign diplomatic cipher systems. MI-8 was disbanded in 1929 when the State Department withdrew funding. Jobless, Yardley caused a sensation in 1931 by publishing his memoirs of MI-8, The American Black Chamber, which caused new security laws to be enacted.*TIS


1905 Bruno Rossi (13 Apr 1905, 21 Nov 1993)Italian pioneer in the study of cosmic radiation. In the 1930s, his experimental investigations of cosmic rays and their interactions with matter laid the foundation for high energy particle physics. Cosmic rays are atomic particles that enter earth's atmosphere from outer space at speeds approaching that of light, bombarding atmospheric atoms to produce mesons as well as secondary particles possessing some of the original energy. He was one of the first to use rockets to study cosmic rays above the Earth's atmosphere. Finding X-rays from space he became the grandfather of high energy astrophysics, being largely responsible for starting X-ray astronomy, as well as the study of interplanetary plasma. *TIS

1909 Stanislaw M. Ulam (13 Apr 1909; 13 May 1984 at age 75) Polish-American mathematician who played a major role in the development of the hydrogen bomb at Los Alamos. He solved the problem of how to initiate fusion in the hydrogen bomb by suggesting that compression was essential to explosion and that shock waves from a fission bomb could produce the compression needed. He further suggested that careful design could focus mechanical shock waves in such a way that they would promote rapid burning of the fusion fuel. Ulam, with J.C. Everett, also proposed the "Orion" plan for nuclear propulsion of space vehicles. While Ulam was at Los Alamos, he developed "Monte-Carlo method" which searched for solutions to mathematical problems using a statistical sampling method with random numbers. *TIS He is buried in Santa Fe National Cemetery in Santa Fe, New Mexico, USA

DEATHS

1728 Samuel Molyneux (18 Jul 1689, 13 Apr 1728 at age 38)British astronomer (Royal Observatory at Kew) and politician. Together with assistant James Bradley, he made measurements of abberation - the diversion of light from stars. They made observations of the star  Draconis with a vertical telescope. Starting in 1725 they had the proof of the movement of the earth giving support to the Copernican model of the earth revolving around the sun. The star oscillated with an excursion of 39 arcsecs between its lowest declination in May and its the highest point of its oscillation in September. He was unfortunate to fall ill in 1728 and into the care of the Anatomist to the Royal Family, Dr Nathaniel St Andre, whose qualifications were as a dancing master. Molyneux died shortly thereafter. *TIS

1906 Walter Frank Raphael Weldon DSc FRS (Highgate, London, 15 March 1860 – Oxford, 13 April 1906) generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of Biometrika, with Francis Galton and Karl Pearson.*Wik Pearson said of him, "He was by nature a poet, and these give the best to science, for they give ideas." *SAU

1941 Annie Jump Cannon (11 Dec 1863; 13 Apr 1941) American, deaf astronomer who specialized in the classification of stellar spectra. In 1896 she was hired at the Harvard College Observatory, remaining there for her entire career. The Harvard spectral classification system had been first developed by Edward C. Pickering, Director of the Observatory, around the turn of the century using objective prism spectra taken on improved photographic plates. In conjunction with Pickering Cannon was to further develop, refine, and implement the Harvard system. She reorganized the classification of stars in terms of surface temperature in spectral classes O, B, A, F, G, K, M, and cataloged over 225,000 stars for the monumental Henry Draper Catalog of stellar spectra, (1918-24).*TIS

2004 David Herbert Fowler (April 28, 1937 – April 13, 2004) was a historian of Greek mathematics who published work on pre-Eudoxian ratio theory (using the process he called anthyphaeresis). He disputed the standard story of Greek mathematical discovery, in which the discovery of the phenomenon of incommensurability came as a shock.
His thesis was that, not having the real numbers, nor division, the Greeks faced difficulties in defining rigorously the notion of ratio. They called ratio 'logos'. Euclid Book V is an exposition of Eudoxus's theory of proportion, which Eudoxus discovered about 350BC, and which has been described as the jewel in the crown of Greek mathematics. Eudoxus showed by a form of abstract algebra how to handle rigorously the case when two ratios are equal, without actually having to define them. His theory was so successful that, in effect, it killed off perfectly good earlier theories of ratio, and Fowler's aim had been to find the evidence for the rediscovery of these previous theories.
In particular Thaetetus (c 414-369BC) introduced a definition of ratio using a procedure called anthyphairesis, based on the Euclidean subtraction algorithm. Fowler developed his ideas in a series of papers, culminating in the book The Mathematics of Plato's Academy: A New Reconstruction, which was published in 1987. This book is based on a study of the primary sources and on their assimilation and transformation.*Wik

2008 John Archibald Wheeler (9 Jul 1911, 13 Apr 2008 at age 96) was the first American physicist involved in the theoretical development of the atomic bomb. He also originated a novel approach to the unified field theory. Wheeler was awarded the 1997 Wolf Prize "for his seminal contributions to black hole physics, to quantum gravity, and to the theories of nuclear scattering and nuclear fission." After recognizing that any large


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, 12 April 2021

On This Day in Math - April 12





"If equations are trains threading the landscape of numbers,
then no train stops at pi. "
~Richard Preston


The 102nd day of the year; I wrote that the number 102 may be the most singularly uninteresting number so far this year, but was corrected. Within an hour David Brooks sent me a list of items about 102. I really liked, and don't know how I missed, that "The sum of the cubes of the first 102 prime numbers is a prime number." Thanks David. It might be interesting for students to examine for which n is the cube of the first n primes also a prime.) He also included that 102 is the name of a river in the state of Missouri. To French explorers the native American name for the river sounded like cent deux, the French words for 102. ( It is near the Iowa border, a tributary of the Platte River of Missouri that is approximately 80 miles long) ******* see math facts on every year day (1-365) at  https://mathdaypballew.blogspot.com/ **************


EVENTS

In 1633 Galileo Galilei’s investigation by the Roman Inquisition began. At its conclusion, his belief that the Earth was not the center of the Universe was pronounced heretical.*Thony Christie, *TIS

1749 Euler succeeded in proving Fermat's theorem on sums of two squares in 1749, when he was forty-two years old. He communicated this in a letter to Goldbach #OTD.
Fermat's theorem on sums of two squares asserts that an odd prime number can be expressed as

p = x^2 + y^2

with integer x and y if and only if p is congruent to 1 (mod 4).   Euler add The statement was announced by Fermat in 1640, but he supplied no proof.  Fermat's famous Last Theorem, this one was written in the margin of Bachet's translation of Diophantos.   *Wik   *Oystein Ore

1803 A letter from Dalton to "Respected Friend" describes his theory that "If a quantity of water thus freed from air be agitated in any kind of gas, not chemically uniting with water, it will absorb its bulk of the gas, or otherwise a part of it equal to some one of the following fractions, namely, 1/8, 1/27, 1/64, 1/125, &c. these being the cubes of the reciprocals of the natural numbers " He then goes on to add that " I am just upon the point of discovering something superior to any of those already published, & which may be of as much importance to science as that of Gravitation itself. I mean the nature of Heat & all its combinations with substances." This may be the earliest note by Dalton of his atomic theory as it precedes his first lab notebook entry of 6 September by five months. This would be the basis for a paper read to the Literary and Philosophical Society of Manchester on Oct. 21, 1803.

1804 Gauss is made a fellow of the Royal Society of  London

1888, a French newspaper mistakenly published an obituary for Alfred Nobel, inventor of dynamite, calling him “"a merchant of death.” The mistake was that it was actually Alfred's brother, Ludwig Nobel, who had just died (at age 56, due to heart trouble). However, shocked by the newspaper's report,  Nobel began to seek a change in public opinion, which led to his decision to establish the Nobel Prizes.*TIS

1898 In 1898, Marie Curie observed a meeting of the French Academy of Sciences, where one of her teachers, Prof. Gabriel Lippmann announced her discovery of substances much more radioactive than uranium. Working since Dec 1897, she had verified that the radiant activity of various compounds was directly related to the amount of uranium present, whether solid, powdered, or in a wet state. She proposed the radiant activity was an atomic property, for it was independent of physical or chemical state. She announced that in pitchblende and charcolite she had discovered compounds even more active than uranium. (She had not, in fact, found a new element, but was the first to identify thorium's powerful radioactivity.*TIS

1842 The first mutual life insurance company in the U.S. was chartered. Since such companies must employee many actuaries, this provides a good source of jobs for individuals with a knowledge of mathematics. *FFF

In 1954, the American Atomic Energy Commission (AEC) began hearings to revoke Robert Oppenheimer's security clearance, thereby severing him from the commission's work. Although he had led the scientists making the atomic bombs during the WW II Manhattan Project, he had been affected by the bombs' death toll and chilling descriptions of radiation sickness. When the Soviet Union detonated an atom bomb in 1949, Edward Teller and Ernest Lawrence lobbied feverishly to develop the hydrogen bomb. Oppenheimer chaired the General Advisory Committee AEC, repudiated the hydrogen bomb as a weapon of “genocide.” In May 1953, when Lewis Strauss accepted the chair of the AEC, he regarded Oppenheimer as a security risk, and wanted him to be dismissed. *TIS
In his testimony, Isador Rabi would say in Oppenheimer's defense: "there he was; he is a consultant, and if you don't want to consult the guy, you don't consult him, period. Why you have to then proceed to suspend clearance and go through all this sort of thing,...We have an A-bomb and a whole series of it, and what more do you want, mermaids? This is just a tremendous achievement. If the end of that road is this kind of hearing, which can't help but be humiliating, I thought it was a pretty bad show. I still think so." *atomicarchive

1961 In Syracuse, Italy, the scientific festivities began to celebrate the memory of Archimedes who was born in the city in 287 BC and was killed there in 212 BC by a Roman soldier. His last words, according to Livy, were “Nolitangere circulos meos” (Don’t touch my circles). [Scripta Mathematica, 26(1961), 143] *VFR

1961 Yuri Gagarin became the first man in space, orbiting the earth in 108 minutes in the Soviet spacecraft Vostok. (or did he... )

1977 Fiji issued a stamp showing a world map in sinusoidal projection. [Scott #374] *VFR
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson-Flamsteed or the Mercator equal-area projection. It is defined by:

x = \left(\lambda - \lambda_0\right) \cos \phi
y = \phi\,
where \phi\, is the latitude, \lambda\, is the longitude, and \lambda_0\, is the central meridian.
The north-south scale is the same everywhere at the central meridian, and the east-west scale is throughout the map the same as that; correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude; thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian or the equator.  *Wik

1981 HP-41 calculator used in space:
HP-41 calculator used on board NASA's first space shuttle flight. The HP-41 allowed astronauts to calculate the exact angle at which they needed to re-enter the Earth's atmosphere. *CHM

1994, the first Internet spamming program was used by an attorney in Arizona. Laurence Canter created the software program, a simple Perl script, that flooded Usenet message board readers with a notice for the "Green Card Lottery" to solicit business for his law firm of Canter & Siegel (with wife, Martha Siegel.) The reaction from the online community was vigorously critical, condemning such a form of advertising. Thousands of recipients complained, but a new, burgeoning business of unsolicited mass Internet advertising had been spawned. The term "spam" was coined from a sketch in the "Monty Python's Flying Circus" BBC television show in which a waitress offered a menu full of variations of spam to an unwilling patron. *TIS
The Monty Python skit is here.

BIRTHS

1794 Germinal Pierre Dandelin (12 April 1794 – 15 February 1847) was a mathematician, soldier, and professor of engineering. He was born near Paris to a French father and Belgian mother, studying first at Ghent then returning to Paris to study at the École Polytechnique. He was wounded fighting under Napoleon. He worked for the Ministry of the Interior under Lazare Carnot. Later he became a citizen of the Netherlands, a professor of mining engineering in Belgium, and then a member of the Belgian army.
He is the eponym of the Dandelin spheres, of Dandelin's theorem in geometry (for an account of that theorem, see Dandelin spheres), and of the Dandelin–Gräffe numerical method of solution of algebraic equations. He also published on the stereographic projection, algebra, and probability theory.*Wik

1851 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

1852 Carl Louis Ferdinand von Lindemann(12 Apr 1852; 6 Mar 1939 at age 86) He showed π is transcendental (not the root of any algebraic equation with rational coefficients), consequently the circle cannot be squared  (constructing a square with the same area as a given circle using ruler and compasses alone.) In 1873, Lindemann visited Hermite in Paris and discussed the methods which Hermite had used in his proof that e, the base of natural logarithms, is transcendental. Following this visit, Lindemann was able to extend Hermite's results to show that  was also transcendental.  *TIS
(the image is of his tombstone.... note the square and  circle with Pi inside.)

1903 Jan Tinbergen (April 12, 1903 – June 9, 1994), was a Dutch economist. He was awarded the first Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1969, which he shared with Ragnar Frisch for having developed and applied dynamic models for the analysis of economic processes. Tinbergen was a founding trustee of Economists for Peace and Security.
Tinbergen became known for his 'Tinbergen Norm', which is the principle that, if the difference between the least and greatest income in a company exceeds a rate of 1:5, that will not help the company and may be counterproductive.*Wik

DEATHS

1817 Charles Messier (26 Jun 1730, 12 Apr 1817 at age 86)French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.*TIS

1919 Friedrich Otto Rudolf Sturm (6 Jan 1841 in Breslau, Germany (now Wrocław, Poland) -12 April 1919 in Breslau, Germany (now Wrocław, Poland)) Sturm wrote extensively on geometry and, other than the teaching textbook on descriptive geometry and graphical statics which we mentioned above and one other teaching text Maxima und Minima in der elementaren Geometrie which he published in 1910, all his work was on synthetic geometry.
He wrote a three volume work on line geometry published between 1892 and 1896, and a four volume work on projective geometry, algebraic geometry and Schubert's enumerative geometry the first two volumes of which he published in 1908 and the second two volumes in 1909. These two multi-volume works collect together most of his life's research. *SAU

1971  Wolfgang Krull proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring.

1971 Igor Yevgenyevich Tamm (8 Jul 1895, 12 Apr 1971 at age 75)Soviet physicist who shared the 1958 Nobel Prize for Physics with Pavel A. Cherenkov and Ilya M. Frank for his efforts in explaining Cherenkov radiation. Tamm was an outstanding theoretical physicist, after early researches in crystallo-optics, he evolved a method for interpreting the interaction of nuclear particles. Together with I. M. Frank, he developed the theoretical interpretation of the radiation of electrons moving through matter faster than the speed of light (the Cerenkov effect), and the theory of showers in cosmic rays. He has also contributed towards methods for the control of thermonuclear reactions. *TIS George Gamow tells an interesting story about Tamm's unusual math encounter during the Ukraine revolution.


2000 David George Crighton FRS (15 November 1942, Llandudno, Wales - 12 April 2000, Cambridge) was a British mathematician and physicist. In his first paper, Crighton studied the sound wave associated with turbulent flow over a discontinuous surface formed by two semi-infinite flexible planes.
Over the years he worked broadly in the fields of acoustics, equation theory and quasi-diabatic systems including solitons. This included on the generalized Burgers' equation and inverse scattering theory. *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

Sunday, 11 April 2021

On This Day in Math - April 11

Bayeux Tapestry with Halley's Comet *Heraldic Times.org


I will stop here.
Concluding the lecture in which he claimed to have proved the Taniyama-Weil Conjecture for a class of examples, including those necessary to prove Fermat's Last Theorem. (1993)
~Andrew Wiles

The 101st day of the year; 101 is the sum of five consecutive primes, but even more exciting, 101 = 5! - 4! + 3! - 2! + 1! (What would be the next number created in a sequence like this?)

101 is the largest known prime of the form 10n + 1.

There are 101 digits in the product of the 39 successive primes produced by the formula n2 + n + 41, where n = 1 to 39. This formula was used by Charles Babbage to demonstrate the capabilities of his Difference Engine (1819-1822). *Prime Curios

and The last five digits of 101101 are 10101.


Wonowon, British Columbia i so named because it is at Mile Marker 101 on Highway 97, the Alaska Highway.

More Math facts on 101, about Bourbon and repdigits and palindromes and more... here


EVENTS
1594, the twenty-two-year-old Kepler arrived in southern Austria to take up his duties as teacher and as provincial mathematician. In the first year he had few pupils in mathematical astronomy and in the second year none, so he was asked to teach Vergil and rhetoric as well as arithmetic. But the young Kepler made his mark in another way; soon after coming to Graz, he issued a calendar and prognostication for 1595, which contained predictions of bitter cold, peasant uprisings, and invasions by the Turks. All were fulfilled, to the great enhancement of his local reputation. Five more calendars followed in annual succession, and later in Prague he issued prognostications for 1602 to 1606. These ephemeral items are now extremely rare, some surviving in unique copies; and all the copies of nearly half the editions are totally lost. *encyclopedia.com

In 1751, Ebenezer Kinnersley advertised in the Pennsylvania Gazette that he was to give a lecture on "The Newly Discovered Electrical Fire." His lectures were the first of the kind in America or Europe. The announcement read: "Notice is hereby given to the Curious, that Wednesday next, Mr. Kinnersley proposes to begin a course of experiments on the newly discovered Electrical Fire, containing not only the most curious of those that have been made and published in Europe, but a considerable number of new ones lately made in this city, to be accompanied with methodical Lectures on the nature and properties of that wonderful element." Thus, Kinnersley was one of the earliest popularizers of science. *TIS

1816 Gauss writes to Gerling from Goettingen. Gerling had written to Gauss in March about Legendre’s theory of parallels in the book elemens de geom. Gauss responded that Legendre’s argument does not carry the weight of proof for him, and then comments on what happens if Euclidean geometry is not correct.
It is easy to show that if Euclid’s geometry is not the true one then there are no similar figures: the angles in an equilateral triangle depend on the size of the edges, in which I do not find anything absurd. Then the angle is a function of the side, and the side a function of the angle, naturally such a function in which a linear constant appears. It seems somewhat paradoxical that a linear constant can be a priori possible; but I don’t find anything contradictory in this. It would be even desirable that Euclid’s geometry is not true, for then we would have a general measure a priori, for example, one could assume as the unit of space the side of the equilateral triangle whose angle = 59o 59’ 59’’.99999….
*Stan Burris, Notes on Euclidean Geometry

Lambert wrote his Theorie der Parallellinien in an attempt to prove, by contradiction, the parallel postulate. He deduced remarkable consequences including this one, from the negation of that postulate. These consequences make his memoir one of the closest (probably the closest) text to hyperbolic geometry, among those that preceded the writings of Lobachevsky, Bolyai and Gauss. His conclusions include (6) below, and preceded Gauss' by about 50 years:

"(1) The angle sum in an arbitrary triangle is less than 180◦.
(2) The area of triangles is proportional to angle defect, that is, the
difference between 180◦
and the angle sum.
(3) There exist two coplanar disjoint lines having a common perpendicular
and which diverge from each other on both sides of
the perpendicular.
(4) Given two lines coplanar d1 and d2 having a common perpendicular,
if we elevate in the same plane a perpendicular d3 to
d1 at a point which is far enough from the foot of the common
perpendicular, then d3 does not meet d2.
(5) Suppose we start from a given point in a plane the construction
of a regular polygon, putting side by side segments having the
same length and making at the junctions equal angles having a
certain value between 0 and 180◦
(see Figure 2 below). Then,
the set of vertices of these polygons is not necessarily on a circle.
Equivalently, the perpendicular bisectors of the segment do not
necessarily intersect.
(6) There exist canonical measures for length and area."
*HYPERBOLIC GEOMETRY IN THE WORK OF J. H. LAMBERT; ATHANASE PAPADOPOULOS AND GUILLAUME THERET

1936 Zuse patent filed for automatic execution of calculations. German computer pioneer Konrad Zuse files for a patent for the automatic execution of calculations, a process he invents while working on what would become the Z-1, Germany's first computer. In the patent application, Zuse offers the first discussion of programmable memory, using the term ""combination memory"" to describe breaking programs down into bit combinations for storage. This is the first device to calculate in binary with translation to decimal. Zuse goes on to build a series of computers. *CHM (Christopher Sears sent a comment last year to tell me that, "There was a character in Tron: Legacy named "Zuse". I thought is was "Zeus" during the movie, but I saw it was spelled differently in the credits . Now I know where the reference came from.")

1970 France issued a stamp honoring the physicist Maurice de Broglie (1875–1960). He is pictured with a spectrograph. [Scott #B439] *VFR He made advances in the study of X-ray diffraction and spectroscopy. In 1971, the government of Nicaragua issued a series of stamps entitled "Ten Equations That Changed the Face of the World".  De Broglie's famous equation, \( \lambda = \frac{h}{mv} \) was one of them.

1970 Apollo 13 lifted off, an on-board computer and large computers on Earth performed the critical guidance and navigation calculations necessary for a successful journey. In addition, crews carried a slide rule for more routine calculations. NASA chose a 5-inch, metal rule, model "N600-ES," manufactured by the Pickett Company for their use. It was a model that was popular among engineers, scientists and students at the time. No modifications were needed for use in space.

This rule used by the crew of Apollo 13, in April 1970 was transferred from NASA to the National Air and Space Museum in 1984. *airandspace.si.edu


1986, Halley's Comet made its closest approach to Earth this trip, 63 million kilometers (39 million mi), on its outbound journey. Many observers were disappointed because the famous comet was barely visible to the naked eye. Some years are simply better than others, as in 1066 when the comet was so bright that it terrified millions of Europeans. Comet Halley isn't officially scheduled to visit Earth again until 2061 when it returns on its 76-year orbit. This comet's closest known approach to the Earth was 3 million miles on 10 Apr 837 AD). Its perihelion (the closest point to the Sun) occurred earlier in the year, on 9 Feb 1986, when it was 88 million km (55 million mi) from the Sun, between the orbits of Mercury and Venus. *TIS


BIRTHS
1798 Macedonio Melloni (11 Apr 1798; 11 Aug 1854 at age 56) Italian physicist who was the firstst to extensively research infrared radiation. Sir William Frederick Herschel discovered infrared radiation in 1800, but research stalled until the invention of a thermopile in 1830. That instrument was a series of strips of two different metals that produced electric current when one end was heated. Melloni improved the thermopile and used it to detect infrared radiation. In 1846, from an observation point high on Mount Vesuvius, he measured the slight heating effect of moonlight. He showed also that rock salt, being transparent to infrared, made suitable lenses and prisms to demonstrate the reflection, refraction, polarization and interference of infrared in the same manner as visible light.*TIS

1829 Alexander Buchan (11 Apr 1829; 13 May 1907 at age 78) British meteorologist, eminent in his field, who first noticed what became known as Buchan spells - departures from the normally expected temperature occurring during certain seasons. They are now believed by meteorologists to be more or less random. Buchan is credited with establishing the weather map as the basis of weather forecasting as a result of his tracing (1868) the path of a storm across North America and the Atlantic into northern Europe. *TIS

1862 William Wallace Campbell (11 Apr 1862 near Findlay in Hancock county, Ohio; 14 Jun 1938 at age 76) American astronomer known particularly for his spectrographic determinations of the radial velocities of stars--i.e., their motions toward the Earth or away from it. In addition, he discovered many spectroscopic binary stars, and in 1924 he published a catalog listing more than 1,000 of them.*TIS

1894 Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician.
Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger. Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox. *Wik

1901 Donald Howard Menzel (11 Apr 1901 in Florence, Colorado; 14 Dec 1976 at age 75) was an American astronomer who was best known for his arguments against the existence of extraterrestrial UFO's. Menzel was one of the first practitioners of theoretical astrophysics in the United States and pioneered the application of quantum mechanics to astronomical spectroscopy. An authority on the sun's chromosphere, he discovered with J. C. Boyce (1933) that the sun's corona contains oxygen. With W. W. Salisbury he made (1941) the first of the calculations that led to radio contact with the moon in 1946. He supervised the assignment of names to newly discovered lunar features. *TIS

1904 Phillip Hall (11 April 1904, Hampstead, London, England – 30 December 1982, Cambridge,England) was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him. *SAU

1914 Dorothy Lewis Bernstein (April 11, 1914 – February 5, 1988) was an American mathematician known for her work in applied mathematics, statistics, computer programming, and her research on the Laplace transform.
Dorothy Bernstein was born in Chicago, the daughter of Russian immigrants to the US. She was a member of the American Mathematical Society and the first woman elected president of the Mathematical Association of America. Due in great part to Bernstein's ability to get grants from the National Science Foundation, Goucher College (where she taught for decades) was the first women's university to use computers in mathematics instruction in the 1960s.*Wik

1921 Leo Moser (April 11, 1921, Vienna—February 9, 1970, Edmonton) was an Austrian-Canadian mathematician, best known for his polygon notation.
A native of Vienna, Leo Moser immigrated with his parents to Canada at the age of three. He received his Bachelor of Science degree from the University of Manitoba in 1943, and a Master of Science from the University of Toronto in 1945. After two years of teaching he went to the University of North Carolina to complete a Ph.D., supervised by Alfred Brauer. There, in 1950, he began suffering recurrent heart problems. He took a position at Texas Technical College for one year, and joined the faculty of the University of Alberta in 1951, where he remained until his death at the age of 48. *Wik In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. It is an extension of Steinhaus’s polygon notation.
n in a triangle a number n in a triangle means nn.
n in a square a number n in a square is equivalent with "the number n inside n triangles, which are all nested."
n in a pentagon a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested."
*Wik 

1953 Sir Andrew John Wiles, KBE, FRS (born 11 April 1953)[1] is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory. He is most famous for proving Fermat's Last Theorem in 1995 (and my proof was nearly complete, ;-{


DEATHS
1626 Marino Ghetaldi (2 Oct 1568 in Ragusa, Dalmatia (now Dubrovnik, Croatia)- 11 April 1626 in Ragusa, Dalmatia (now Dubrovnik, Croatia)) Marino Ghetaldi was a Croatian mathematician who published work with early applications of algebra to geometry.*SAU

1734 Thomas Fantet de Lagny (7 Nov 1660 in Lyon, France - 11 April 1734 in Paris, France was a French mathematician who is well known for his contributions to computational mathematics, calculating π to 120 places. [V F Rickey has this as the 12th of April.... and shares], using Gregory’s series, Maupertius was called to de Lagny’s deathbed, and finding the poor man unconscious, asked him for the square of 12. Like an automaton, de Lagny rose in bed, gave the answer, and immediately passed away. [Eves, Circles, 238◦ and Allen Debus, World Who’s Who in Science] *VFR

1875 Samuel Heinrich Schwabe (25 Oct 1789, 11 Apr 1875 at age 85) Amateur German astronomer who discovered the 10-year sunspot activity cycle. Schwabe had been looking for possible intramercurial planets. From 11 Oct 1825, for 42 years, he observed the Sun virtually every day that the weather allowed. In doing so he accumulated volumes of sunspot drawings, the idea being to detect his hypothetical planet as it passed across the solar disk, without confusion with small sunspots. Schwabe did not discover any new planet. Instead, he published his results in 1842 that his 17 years of nearly continuous sunspot observations revealed a 10-year periodicity in the number of sunspots visible on the solar disk. Schwabe also made (1831) the first known detailed drawing of the Great Red Spot on Jupiter. *TIS

1907 Christian Gustav Adolph Mayer (February 15, 1839 – April 11, 1907) was a German mathematician. Mayer studied at Heidelberg, and submitted his habilitation thesis to the University of Heidelberg. He gained the permission to teach at universities in 1866. He taught mathematics at the University of Heidelberg for the rest of his life. He did research on differential equations, the calculus of variations and mechanics. His research on the integration of partial differential equations and a search to determine maxima and minima using variational methods brought him close to the investigations which Sophus Lie was carrying out around the same time.
Several letters were exchanged between Mayer and mathematician Felix Klein from 1871 to 1907. Those letters provide insights into the scientific and personal relations among Felix Klein, Mayer and Lie over the period.
Mayer's students included : Friedrich Engel, Felix Hausdorff and Gerhard Kowalewski. *Wik

1974 Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics. *Wik He is the creator of non-standard analysis.

1989 Emil Grosswald (December 15, 1912 – April 11, 1989) was a Romanian-American mathematician who worked primarily in number theory. His career is closely associated with that of his teacher, Hans Rademacher. Grosswald completed some works of his teacher Hans Rademacher, who died in 1969. Rademacher had prepared notes for an Earle Raymond Hedrick Lecture in Boulder, Colorado in 1963 on Dedekind sums, but fell ill, and Grosswald gave the lecture for him. After Rademacher's death, Grosswald edited and completed the notes and published them in the Carus Mathematical Monographs series as Dedekind Sums. He also edited for publication Rademacher's posthumous textbook Topics in Analytic Number Theory.*Wik

2020 John Horton Conway ceases to play the game of life.
John Horton Conway (born 26 December 1937, died  April 11, 2020 ) was a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971),[1] was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.*Wik
Conway was known for his sense of humor, and the last proof in his "On Numbers and Games" is this:
Theorem 100; This is the last Theorem in this book.
The Proof is Obvious.
 2020 John H Conway ceases to play the game of life. Conway was exposed to the corona virus and took a fever around the 8th of April.  He had suffered from ill health for an extended time, and in three days, on April 11, 2020 he died at his home in New Jersey.

I really enjoyed Siobhan Roberts biography of Conway.  You may, too.



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