Friday, 15 May 2026

On This Day in Math - May 15

  



The Moving Finger writes; and, having writ,
Moves on : nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
 
The Rubaiyat by Omar Khayyam


The 135th day of the year; 135 = 11 + 32 + 53. *What's So Special About This Number 

135 is the smallest non-trivial SP (sum times product) number. If you take the sum of the digits of a number, and also the product of the digits, and then multiply the two outcomes, there are only three positive numbers for which you will get the original value. One works, trivially. The other two are 135 and 144.  135-> (1+3+5)*(1*3*5) = 9*15=135.   144->(1+4+4)*(1*4*4)= 9 * 16 = 144.
A Good exercise for students is to take the SP product in a iteration to find out if it goes to zero, or repeats some pattern, or lands eventually on one of these three fixed points. (Try it with your students). 23->5*6 = 30.  30-> 3*0 = 0.... fixed point.

\(135 \equiv 3 (\mod 6)\) and so 135 is expressible as the difference of two squares, using bases three apart.  The two bases must sum to 135 / 3 = 45.  So 21 and 24 should work, and 24² - 21² = 135  


Both 1!+3!+5!= 127 is prime; and 1!!+3!!+5!! is prime if the double factorial n!! means n (n-2)(n-4).... (the same symbol is sometimes used for the factorial of n! ).

135 is a "partition number", the number of ways to partition 14. We still do not know if there are an infinite number of "partition numbers" which are divisible by 3, although we do know there are an infinite number divisible by 2

Quick! How many primes from 1000 to 2000?    135, of course!




EVENTS


1618 Kepler Writes his third law of planetary motion. He was teaching at the Landschaftsschule in Linz (1612 - 1630) and also continuing to be Court Mathematician. During this period, he married Susanna Reuttinger while he was here (1613) and produced Harmonices Mundi, (1618) giving his third law.[Kepler's third law says that the square of the time it takes a planet to travel its path around the sun is proportional to the cube of the average distance from the sun] He also became acquainted with the techniques of measuring wine casks here, a practical art for the 17th century as barrels were not uniform in design. He wrote "Stereometria Doliorum Vinariorum” in 1615 and gave the dimensions of the “ideal” cask. 
He attempted to explain proportions and geometry in planetary motions by relating them to musical scales and intervals (an extension of what Pythagoras had described as the "harmony of the spheres".) Kepler said each planet produces musical tones during its revolution about the sun, and the pitch of the tones varies with the angular velocities of those planets as measured from the sun.  The Earth sings Mi, Fa, Mi. At very rare intervals all planets would sing in perfect concord. Kepler proposed that this may have happened only once in history, perhaps at the time of creation. (assorted sources). For more detail, including Kepler's own announcement of his third law, see   "The Renaissance Mathematicus"





1718 James Puckle, a London lawyer, patents the world's first machine gun. The Puckle gun (also known as the defence gun) was a primitive crew-served, manually-operated flintlock revolver patented in 1718 by James Puckle (1667–1724), a British inventor, lawyer and writer. It was one of the earliest weapons to be referred to as a "machine gun", being called such in a 1722 shipping manifest, though its operation does not match the modern use of the term. It was never used during any combat operation or war. Production was highly limited and may have been as few as two guns.*Wik



1817 John Herschel in a letter to Charles Babbage sent a mysterious doodle that still seem to be much of a mystery. Herschel said: "Interpret this hieroglyphic, it contains a great discovery." The figure at the center is described as: "Dionysius the God of Functions, alias the genius of numerical magnitude." The God of Functions is suspected to refer to Dionysius Lardner who taught Mathematics at Trinity College at that time.Many of the symbols seem to have no relevance to mathematics of the period. They may have been ideas tossed around between the two men in their attempts to modernize British Mathematics


1834 After first rejecting Whewell's suggestions on May 3, Faraday writes, "I have taken your advice, and the names used are anode cathode anions cations and ions; the last I shall have but little occasion for. I had some hot objections made to them here and found myself very much in the condition of the man with his son and ass who tried to please every body; but when I held up the shield of your authority, it was wonderful to observe how the tone of objection melted away." *Frank James (ed.), The Correspondence of Michael Faraday (1993), Vol. 2, 186.






1836 Francis Baily observed "Baily's Beads" during an annular solar eclipse. His vivid description aroused new interest in the study of eclipses. Baily's Beads are the bright points of light, that appear around the edge of the moon during a solar eclipse. The beads are created by sunlight passing through the moon's valleys. The last bead is the brightest, resembling a diamond on a brilliant ring. After retiring from a successful business career (1825), Baily turned to science. He revised several star catalogs, repeated Henry Cavendish's experiments to determine the density of the Earth, and measured its elliptical shape. His protests regarding the British Nautical Almanac, then notorious for its errors, were instrumental in bringing about its reform.





1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this.
May 15: (Sunday edition) – Speculation on probability of Earth passing through comet’s tail. Article on those still living who remember Halley’s Comet visit of 75 years ago. *Joseph M. Laufer, Halley's Comet Society - USA


1921 First record of Aurora Borealis observation during day time? Aurora seen in New Zealand and surrounding islands. NASA Eclipse Calendar   The first recorded observation is in late Babylonian astronomical texts, discovered at the site of Babylon (32.5°N, 44.4°E) more than a century ago, contain what is probably the earliest reliable account of the aurora borealis. A clay tablet recording numerous celestial observations made by the official astronomers during the 37th year of King Nebuchadnezzar II (568/567 BC) describes an unusual “red glow” in the sky at night; the exact date of this observation corresponds to the night of 12/13 March in 567 BC. 

 Later on, Henry Cavendish recorded the first scientific observations.) of the northern lights in 1790. Using triangulation, the French-born English scientist determined the aurora borealis occurred approximately 60 miles above the Earth’s surface. It was British astronomer Richard Carrington, in 1859, who linked the aurora borealis with the sun.

Aurora viewed from space




1935, at the Franklin Institute, Philadelphia, Albert Einstein was awarded the Benjamin Franklin Medal for his outstanding fundamental contributions to theoretical physics, especially his relativity theory. According to Time magazine, "A throng of scientists and dignitaries was assembled to hear what the medalist had to say. Einstein genially informed the chairman that he had nothing to say, that inspiration which he had awaited until the last moment had failed him. The chairman, much more embarrassed than the medalist, conveyed this information to the audience." In atonement, Einstein wrote a 44-page essay entitled "Physics and Reality," published in the Mar 1936 issue of their Journal of the Franklin Institute. *TIS




1948 The independent State of Israel established. In 1952 the Israeli government asked Einstein, who had labored for the creation of the State, to accept the presidency of the country. He sadly declined the honor, insisting that he was not fitted for such a position. *VFR


1961, the first computer in Argentina began operating at the University of Buenos Aires. It was a Ferranti Mercury computer called Clementina because it had been programmed to play the song Oh My Darling, Clementine. Cecilia Berdichevsky was one of the mathematicians who worked on it.





1971 Nicaragua issued a series of stamps showing “mathematical equations which changed the world.” They range from 1 + 1 = 2 (Egyptians counting on their fingers) to Napier’s law of logarithms and the Pythagorean Theorem. On the back of each stamp is a descriptive paragraph. [Scott #877–881, C761–5] all ten are here



1985 At a Columbia University graduation Benoit B. Mandelbrot received the Barnard Medal for Meritorious Service to Science, an award made every five years. He is noted for his work on fractals.*VFR   Here is a nice link to a web page showing the Mandelbrot set as a “catalogue\ of Julia Sets”.   Mandelbrot has been at the IBM research institute in Yorktown Heights since 1958.  He is now emeritus and also holds a professorship at Yale since 2000.




2004 Josh Findley discovered the 41st Mersenne prime, 224,036,583 - 1. He found it using a 2.4-GHz Pentium 4 computer. A Mersenne prime number is one less than a power of two expressed as Mn = 2n - 1. For this to be true, the exponent n must also be prime. Mersenne primes have a close connection to perfect numbers, which are equal to the sum of their proper divisors. The study of Mersenne primes was motivated by this connection. In the 4th century B.C. Euclid demonstrated that if M is a Mersenne prime, then M(M+1)/2 is a perfect number. In the 18th century, Leonhard Euler proved that all even perfect numbers have this form. No odd perfect numbers are known and it is suspected that none exist. It is currently unknown whether an infinite number of Mersenne primes exist. *CHM 

Mersenne primes take their name from the 17th-century French scholar Marin Mersenne, who compiled what was supposed to be a list of Mersenne primes with exponents up to 257. The exponents listed by Mersenne in 1644 were as follows:

2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257.

His list replicated the known primes of his time with exponents up to 19. His next entry, 31, was correct, but the list then became largely incorrect, as Mersenne mistakenly included M67 and M257 (which are composite) and omitted M61, M89, and M107 (which are prime). Mersenne gave little indication of how he came up with his list.

Édouard Lucas (Creator of the towers of Hanoi puzzle) proved in 1876 that M127 is indeed prime, as Mersenne claimed. This was the largest known prime number for 75 years until 1951,





BIRTHS

1048 Omar Khayyam (15 May, 1048 - 1131)
mathematician and poet, He was the first to claim cubic equations—and hence angle trisection—could not be solved with straightedge and compass. P. Wantzel gave a proof in 1837. *VFR Omar Khayyám (1048–1131; Persian: ‏عمر خیام‎) was a Persian polymath: philosopher, mathematician, astronomer and poet. He also wrote treatises on mechanics, geography, mineralogy, music, climatology and Islamic theology.
Born in Nishapur, at a young age he moved to Samarkand and obtained his education there, afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. He also contributed to a calendar reform.*Wik
Khayyam , produced a work on algebra that was used as a textbook in Persia until this century. In geometry, he studied generalities of Euclid and contributed to the theory of parallel lines. Around 1074, he set up an observatory and led work on compiling astronomical tables, and also contributed to the reform of the Persian calendar. His contributions to other fields of science included developing methods for the accurate determination of specific gravity. He is known to English-speaking readers for his "quatrains" as The Rubáiyát of Omar Khayyám, published in 1859 by Edward Fitzgerald, though it is now regarded as an anthology of which little or nothing may be by Omar. *TIS


Cubic equation and intersection of conic sections" the first page of two-chaptered manuscript kept in Tehran University *Wik


1615 Frans van Schooten (1615 in Leiden – 29 May 1660 in Leiden) was a Dutch mathematician who was one of the main people to promote the spread of Cartesian geometry. *Wikipedia  His group of students extended Descartes work and created a calculus without limits. Hudde in particular was highly rated by Leibniz; "Leibniz in particular was impressed with Hudde’s work, and when Johann Bernoulli proposed the brachistochrone problem, Leibniz lamented: If Huygens lived and was healthy, the man would rest, except to solve your problem. Now there is no one to expect a quick solution from, except for the Marquis de l’Hopital, your brother [Jacob Bernoulli], and Newton, and to this list we might add Hudde, the Mayor of Amsterdam, except that some time ago he put aside these pursuits ."





1637 Valentin Heins (May 15th 1637 in Hamburg - November 17 1704 ) was a German arithmetician (Reckoner)
The son of a linen weaver, the source of his education is unknown. From 1651 Heins was licensed to provide instruction in commercial computing (accounting, bookkeeping, arithmetic, etc). In the years 1658 and 1659 Heins studied theology for several semesters at the universities of Jena and Leipzig , but then returned to Hamburg. There he married and had a vicariate (financial endoument) in 1661 at the Cathedral. Whether Heins performed for a service is not known.
In 1670 he became writing and arithmetic master of the German Church School St. Michaelis . He was also from 1663-1672 accountant of the Guinean-African Company.
He wrote several textbooks, which made him known beyond national boundaries. They were reprinted up to the beginning of the 19th Century. Particularly popular was his tyrocinium mercatorio arithmeticum, a commercial arithmetic and accounting book.
Heins founded in 1690, with the calculation of the parish school master of St. Jacobi Henry Meissner , the art-loving Societät billing. This later became the Mathematical Society of Hamburg, the worlds oldest existing mathematical society. *Wik




1689 Lady Mary Wortley Montagu (15 May 1689 – 21 August 1762) was an English aristocrat, writer, and poet.  She is listed in this blog because during her life in Turkey with her diplomat husband, she realized that the Turkish people almost never suffered the scars of smallpox.  Investigating, she found that mothers would take a scab from a smallpox sufferer and open their children's veins in several places and plant the scabs there.   She did the same to her own children and when she returned to England she shared the idea with her friends and tried to make its use more broad.  She persuaded the Princess of Wales to test the treatment and seven prisoners' awaiting execution were offered the treatment in exchange for clemency.  All survived, and were released. Catherine the Great and her son Paul were both inoculated.  When Lady Mary Montagu died in 21 August of 1762, Edward Jenner was thirteen years old.  HT @drSueMoss




1720 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




1801 Joseph Ludwig Raabe (15 May 1801 in Brody, Galicia – 22 January 1859 in Zürich, Switzerland) was a Swiss mathematician. He began to study mathematics in 1820 at the Polytechnicum in Vienna, Austria. In the autumn of 1831, he moved to Zürich, where he became professor of mathematics in 1833. In 1855, he became professor at the newly founded Swiss Polytechnicum.

He is best known for Raabe's ratio test, an extension of d'Alembert's ratio test. Raabe's test serves to determine the convergence or divergence of an infinite series, in some cases. He is also known for the Raabe integral of the gamma function:




1835 Émile Léonard Mathieu (May 15, 1835, Metz – October 19, 1890, Nancy) is remembered especially for his discovery (in 1860 and 1873) of five sporadic simple groups named after him*SAU The Mathieu group is related to the solutions of the fifteen puzzle, and the more recent Rubix Cube.



1857 Hermann Ludwig Gustav Wiener (15 May 1857 in Karlsruhe, Germany - 13 June 1939 in Darmstadt, Germany) was a German mathematician who worked on the foundations of geometry. Although Wiener is not explicitly credited with influencing Hilbert in his championing of the axiomatic method, it is still worth noting that he gave the talk Über Grundlagen und Aufbau der Geometrie to the German Mathematical Society which was published in the first volume of the Jahresberichte der Deutschen Mathematiker vereinigung (1892). Wiener proposed that geometry be studied without using visual images, but rather by abstract axiomatic methods. He also joined his father in the creation of mathematical models of geometric surfaces, constructed from plaster and wire. *SAU




1857  Williamina Paton Stevens Fleming (May 15, 1857 – May 21, 1911) Scottish-born American astronomer who pioneered in the classification of stellar spectra and the first to discover stars called "white dwarfs." She emigrated to Boston at age 21. Prof. Edward Pickering, director of the Harvard Observatory first employed Fleming as a maid, but in 1881 hired her to do clerical work and some mathematical calculations at the Observatory. She further proved capable of doing science. After devising her system of classifying stars by their spectra, she cataloged over 10,000 stars within the next nine years. Her duties were expanded and she was put in charge of dozens of young women hired to do mathematical computations (as now done by computers).*TIS




1859 Pierre Curie (French: [15 May 1859 – 19 April 1906) was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity and radioactivity. In 1903 he received the Nobel Prize in Physics with his wife, Marie Skłodowska Curie, and Henri Becquerel, "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel". *Wik

When awarded the 1903 Nobel Prize in Physics, Pierre Curie rejected the prize unless he could share it with his wife Marie. In his response, Pierre was adamant that awarding their research on radioactivity without recognising Marie's essential contribution would be unjust. *The Nobel Prize




1863 Frank Hornby (15 May 1863; 21 Sep 1936 at age 73) English inventor and manufacturer who patented the Meccano construction set in 1901. This toy used perforated metal strips, wheels, roods, brackets, clips and assembly nuts and bolts to build unlimited numbers of models. His original sets, marketed as "Mechanics Made Easy" produced in a rented room, were initially sold at only one Liverpool toy shop. By 1908, he had formed his company, Meccano Ltd., and within five more years had established manufacturing in France, Germany, Spain and the U.S. He introduced Hornby model trains in 1920, originally clockwork and eventually electrically powered with tracks and scale replicas of associated buildings. The "Dinky" range of miniature cars and other motor vehicles was added in 1933. *TIS



1865  Alice Everett (15 May 1865 – 21 July 1949) was a British astronomer and engineer who grew up in Belfast. Everett is best known for being the first woman to be paid for astronomical work at the Royal Observatory, Greenwich, when she began her employment at the observatory January 1890. In 1903 she was the first woman to have a paper published by the Physical Society of London. She also contributed to the fields of optics and early television.



1899  Joseph Berkson,  (15 May, 1899 - 12 Sep, 1982) Dr. Berkson became Head of Biometry and Medical Statistics at the renowned Mayo Clinic in 1933, which he held until his retirement in 1964.
His research interests covered all aspects of medical statistics, resulting in 118 scientific papers from 1928 to 1980. He was involved in a number of controversies, particularly that involving the rate of cigarette smoking in lung cancer.
Two well-known coinages of Berkson that became common in Statistics are from two of his articles: “Rao-Blackwellization” (1955 article in JASA) and “logit” (1944 article in JASA).
Also, a 1946 paper by Berkson introduced what later became known as “Berkson’s Fallacy”, which is now part of Biostat 101 courses.
[Note: Berkson's Fallacy would make for a good post-APStatExam lesson as it involves a common chi-square test in a Simpson's Paradox-like setting...] *David Bee

An example of Berkson's paradox:

In figure 1, assume that talent and attractiveness are uncorrelated in the population.

In figure 2, someone sampling the population using celebrities may wrongly infer that talent is negatively correlated with attractiveness, as people who are neither talented nor attractive do not typically become celebrities.




1903 Maria Reiche ( 15 May 1903 - 8 June, 1998) German-born Peruvian mathematician and archaeologist who was the self-appointed keeper of the Nazca Lines, a series of desert ground drawings over 1,000 years old, near Nazcain in southern Peru. For 50 years the "Lady of the Lines" studied and protected these etchings of animals and geometric patterns in 60 km (35 mi) of desert. Protected by a lack of wind and rain, the figures are hundreds of feet long best seen from the air. She investigated the Nazca lines from a mathematical point of view. Death at age 95 interrupted her new mathematical calculations: the possibility that the lines predicted cyclical natural phenomena like El Nino, a weather system that for centuries has periodically caused disastrous flooding along the Peruvian coast. *TIS


1939 Brian Hartley (15 May 1939-8 October 1994) was a British Mathematician specialising in group theory.
Hartley's Ph.D. thesis was completed in 1964 at the University of Cambridge under Philip Hall's supervision. He spent a year at the University of Chicago, and another at MIT before being appointed as a lecturer at the newly established University of Warwick in 1966, and was promoted to reader in 1973. He moved to a chair at Manchester in 1977 where he served as head of the Mathematics department between 1982 and 1984.
He published more than 100 papers, mostly on group theory, and collaborated widely with other mathematicians. His main interest was locally finite groups where he used his wide knowledge of finite groups to prove properties of infinite groups which shared some of the features of finite groups. One recurrent theme appearing in his work was the relationship between the structure of groups and their subgroups consisting of elements fixed by particular automorphisms.
Hartley is perhaps best known by undergraduates for his book Rings Modules and Linear Algebra, with Trevor Hawkes (ISBN 9780412098109).
Hartley was a keen hill walker, and it was while descending Helvellyn in the English Lake District that he collapsed with a heart attack and died.
The 'Brian Hartley Room' at the School of Mathematics at Manchester is named in his honour.
*Wik




1942 Arthur Taylor Winfree (May 15, 1942 – November 5, 2002) was a theoretical biologist at the University of Arizona. He was born in St. Petersburg, Florida, United States.
Winfree was noted for his work on the mathematical modeling of biological phenomena: from cardiac arrhythmia and circadian rhythms to the self-organization of slime mold colonies and the Belousov–Zhabotinsky reaction. Winfree was a MacArthur Fellow from 1984 to 1989 and shared the 2000 Norbert Wiener Prize in Applied Mathematics with Alexandre Chorin. *Wik
Among numerous awards he was a Westinghouse Science Talent Search Finalist in 1960, a John Simon Guggenheim Memorial Fellowship awardee in 1982, and shared the AMS-SIAM Norbert Wiener Prize in Applied Mathematics with A. Chorin in 2000. His obituary in Siam began: "When Art Winfree died in Tucson on November 5, 2002, at the age of 60, the world lost one of its most creative scientists. I think he would have liked that simple description: scientist. After all, he made it nearly impossible to categorize him any more precisely than that. He started out as an engineering physics major at Cornell (1965), but then swerved into biology, receiving his PhD from Princeton in 1970. Later, he held faculty positions in theoretical biology (Chicago, 1969-72), in the biological sciences (Purdue, 1972-1986), and in ecology and evolutionary biology (University of Arizona, from 1986 until his death). " *SIAM
He was the father of Erik Winfree, another MacArthur Fellow and currently a professor at the California Institute of Technology, and Rachael Winfree, currently an Assistant Professor in the Department of Entomology at Rutgers University.




1964 Sijue Wu (May 15, 1964 - ) She received her B.S. (1983) and M.S. (1986) from Beijing University, Beijing, China, and her Ph.D. (1990) [Abstract] from Yale University. Since then she has held the following position: Courant Instructor at Courant Institute, New York University (2 years); assistant professor at Northwestern University (4 years); and assistant, then associate professor at the University of Iowa (2 years). She was also a member at the Institute for Advanced Study in the fall of 1992 and during the year 1996-97. She has been as associate professor at the University of Maryland, College Park, since 1998.
Sijue Wu was awarded the 2001 Ruth Lyttle Satter Prize by the American Mathematics Society. This prize is awarded every two years to recognize an outstanding contribution to mathematics research by a woman in the previous five years. Following is the selection committee's citation:
The Ruth Lyttle Satter Prize in Mathematics is awarded to Sijue Wu for her work on a long-standing problem in the water wave equation, in particular for the results in her papers (1) "Well-posedness in Sovolev spaces of the full water wave problem in 2-D", Invent. Math. 130 (1997), 39-72; and (2) "Well-posedness in Sobolev spaces of the full water wave problem in 3-D", J. Amer. Math. Soc. 12, no. 2 (1999), 445-495. By applying tools from harmonic analysis (singular integrals and Clifford algebra), she proves that the Taylor sign condition always holds and that there exists a unique solution to the water wave equations for a finite time interval when the initial wave profile is a Jordon surface. *Women Mathematicians, Agnes Scott College




DEATHS


1751  John Bonnycastle (baptized 29 December 1751 in Hardwick or Whitchurch, England – 15 May 1821 in Woolwich, England) was an English teacher of mathematics and author.
John Bonnycastle was born in Buckinghamshire, in about 1750. Nothing is known of his family or early life, but he went to London where he established an Academy. He became a tutor to the two sons of the Earl of Pontefract at Easton in Northumberland. Between 1782 and 1785, he was appointed Professor of Mathematics at the Royal Military Academy, Woolwich, where he remained until his death on 15 May 1821.
He was a prolific writer, and wrote for the early volumes of Rees's Cyclopædia, about algebra, analysis and astronomy.
On Oct.7th, 1786 he married Brigette Newell with whom he had six children Charlotte, William, Mary, Sir Richard (Royal Engineer/Author), Humphrey and Charles.
His son Richard Henry Bonnycastle settled in Canada, where the family became quite well known in Winnipeg and Calgary.
His son, Charles Bonnycastle (1796-1840) became Professor of Mathematics at the University of Virginia.



1833 Bewick Bridge (1767, Linton, Cambridgeshire – 15 May 1833, Cherry Hinton) was an English vicar and mathematical author.
In 1786, he was admitted as a sizar to study mathematics Peterhouse, Cambridge University, where he graduated as senior wrangler and won the Smith's Prize in 1790.
In October 1790, he was ordained a deacon at Ely, and became a priest in 1792; in the same year he became a Fellow at Peterhouse, during which he spent time as both as college moderator and as proctor. From 1806 until 1816, he was Professor of Mathematics at the East India Company College, Haileybury. He wrote a number of mathematical texts: his Algebra achieved international circulation. He became a Fellow of the Royal Society in 1812.
From 1816 until 1833, he was vicar of Cherry Hinton in Cambridge, where in 1818 he built the vicarage, and he founded the village school in 1832 (now a Church of England PrimarySchool). He died on 15 May 1833, aged 66. In September 2011 the Cherry Hinton Community Junior School was named after Bewick, becoming Bewick Bridge Community Primary School. *Wik


1907  Anne Lucy Bosworth Focke (September 29, 1868 – May 15, 1907) was an American mathematician who became the first mathematics professor at what is now the University of Rhode Island, and later became the first female doctoral student of David Hilbert.

Bosworth attended Woonsocket High School, and graduated from Wellesley College in 1890.  At Wellesley, her classmates included mathematicians Grace Andrews and Clara Latimer Bacon.

She worked for two years as a teacher at Amesbury High School in Massachusetts, and was appointed as an instructor of mathematics at the Rhode Island College of Agriculture and Mechanic Arts (later to become the University of Rhode Island) in early 1892, the first year the school became a college. One month later she became its professor of mathematics and physics.

While continuing to work at the college, Bosworth earned a master's degree at the University of Chicago from 1894 through 1896 through summer study with E. H. Moore and Oskar Bolza.

In 1898, taking a leave from her work for the college, Bosworth traveled to the University of Göttingen in Germany, where she worked under the supervision of David Hilbert. She defended her dissertation there in 1899, and was awarded the Ph.D. in 1900. Her dissertation was Begründung einer vom Parallelenaxiome unabhängigen Streckenrechnung, and concerned non-Euclidean geometry. She was David Hilbert's first female doctoral student, part of a group that later included Nadeschda Gernet (1902), Vera Myller (1906), Margarete Kahn (1909), Klara Löbenstein (1910), and Eva Koehler (1912).  *Wik



1923  Arthur Gordon Webster (November 28, 1863 - May 15, 1923) was the founder of the American Physical Society.  A group of twenty physicists, invited by Webster, founded the American Physical Society at a meeting at Fayerweather Hall in Columbia University on 20 May 1899. In 1903, Webster became president of the American Physical Society and was elected to the National Academy of Sciences.
Webster committed suicide in 1923, following the closure of the mathematics department at Clark, after it was rumored that the physics department would be the next to be closed by the new president. With a revolver he had bought a few hours before, Webster shot himself twice in the head in his private office while a class waited for him next door. He left a note to his son which read;
Dear Gordon: This is the only way. For years I have been a failure - my research is worth nothing. Everyone else knows it, and S.N. physics has got away from me and I cannot come back. Everything I have started has stalled. Students will not come and they will put me out. Your mother will not see. She will get over this. Take care of her. I am sorry for the trouble I have caused you. Am sorry to make so much trouble. Do your best and tell the truth. With my best love, "Papa"*Wik (with thanks to Arjen Dijksman).




1975 Taira Honda (本田 平 Honda Taira?, 2 June 1932 Fukui, Japan – 15 May 1975 Osaka, Japan) was a Japanese mathematician working on number theory who proved the Honda–Tate theorem classifying abelian varieties over finite fields. *Wik His mathematical research was mainly devoted to the investigation of the arithmetic properties of commutative formal groups. A brilliant career was cut short when he took his own life.*SAU




1991 Andreas Floer (23 Aug 1956 in Duisburg, Germany - 15 May 1991 in Bochum, Germany) was a German mathematician who made seminal contributions to the areas of geometry, topology, and mathematical physics, in particular the invention of Floer homology.

Floer's first pivotal contribution was a solution of a special case of Arnold's conjecture on fixed points of a symplectomorphism. Because of his work on Arnold's conjecture and his development of instanton homology, he achieved wide recognition and was invited as a plenary speaker for the International Congress of Mathematicians held in Kyoto in August 1990. He received a Sloan Fellowship in 1989.*Wik



2008 Willis Eugene Lamb, Jr (July 12, 1913 – May 15, 2008) was an American physicist and joint winner, with Polykarp Kusch, of the Nobel Prize for Physics in 1955 "for his discoveries concerning the fine structure of the hydrogen spectrum." His experimental work spurred refinements in the quantum theories of electromagnetic phenomena.*TIS The Lamb shift was an energy difference between the 2S½ and 2P½ energy levels of the hydrogen atom. According to the current theory, these two levels should have the same amount of energy, but when the electrons were exposed to a magnetic field, the energy level of 2S½ was slightly different. This discovery led to the renormalization theory of quantum electrodynamics. *This Day in Science History





2019  Dionisio Gallarati (May 8, 1923 – May 13, 2019) was an Italian mathematician, who specialised in algebraic geometry. He was a major influence on the development of algebra and geometry at the University of Genova.

 Gallarati joined the University of Pisa in 1941. His studies being interrupted by the war, he received his first degree from Genova.


He started his research career at l'Istituto Nazionale di Alta Matematica in Rome, where he was taught by Giacomo Albanese, Leonard Roth, Leonida Tonelli, E. G. Togliatti, Beniamino Segre and Francesco Severi.

He took a post at Genova in 1947, where he stayed until he retired in 1987.

Gallarati published 64 papers between 1951 and 1996.

Important among his research was the study of surfaces in P3 with multiple isolated singularities. His lower bounds for maximal number of nodes of surfaces of degree n stood for a long time, and exact solutions for large n were still unknown in 2001.

In Grassmannian geometry he extended Segre's bound "for the number of linearly independent complexes containing the curve in the Grassmannian corresponding to the tangent lines of a nondegen *Wikerate projective curve."[3] He extended the results to arbitrarily dimensioned varieties' tangent spaces, to higher degree complexes, and to arbitrary curves in Grassmannians corresponding to degenerate scrolls. *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

Thursday, 14 May 2026

Don't Write the Law of Sines Upside Down, Please!

Mostly I'm a teach and let teach kind of guy... you do what you think is important, and let me do the same... but sometimes when I see people teach the law of sines... I wonder... DO THEY KNOW?????

The ideas behind the law of sines, like those of the law of cosines, predate the word sine by over a thousand years. Theorems in Euclid on lengths of chords are essentially the same ideas we now call the law of sines. The law of sines for plane triangles was known to Ptolemy and by the tenth century Abu'l Wefa had clearly expounded the spherical law of sines (in 2014 Thony Christie sent a note telling me that "Glen van Brummelen in his "Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry" says the spherical law of sines was discovered either by Abū al-Wafā or Abu Nasr Mansur .  It seems that the term "law of sines" was applied sometime near 1850, but I am unsure of the origin of the phrase (and if you have a reference, please advise).


A simple proof of the law of sines begins with a triangle, ABC, inscribed in a circle with radius R. A diameter is drawn with one endpoint at A terminating at D and the right triangle ADC is created. Using the right triangle definitions of Sine, we see that sin (ADC)=AC/AD.


Because Angles ABC and ADC are both inscribed angles cutting the same arc, they have equal measures, and therefore equal sines. By substitution then we get sin(B)=AC/AD and since AD is a diameter equal to 2R , we may also write sin(B) =AC/2R . Now if we adopt the modern convention of calling the side AC opposite angle B, side b, we can rewrite this as sin(B)= b/2R. With one last algebraic manipulation we exchange the positions of sin(B) and 2R to get 2R= b/sin(B) . Since the choice of angle B was arbitrary, we could show that the same holds for each side and opposite angle pair, producing the typical high school textbook theorem below. 

\(\frac{a}{Sin A} =\frac{b}{Sin B} =\frac{c}{Sin C} = 2R\)

I am frequently disappointed to see this theorem presented in math texts without the "=2R" which seems to give it visual or geometric life, and even more so when the angles are in the numerator.... not wrong, but just not beautiful. It is especially curious since the property dates back to Ptolemy. 

Since the area of triangle ABC can be written as Area= a*b*c/4R ,  then \(2R = \frac {abc}{2 * Area }\)

I especially like this suggested approach from Joshua Zucker because it relates to a similar relation in spherical geometry


As a footnote, in spherical triangles it is customary to work with a sphere of unit radius, thus allowing the sides to be expressed in radian or angle measure as well as the angles. Since all great circles have length 360 degrees, we may express the length of a side by the fraction of a complete great circle it occupies. With this convention, the spherical law of sines states that in a spherical triangle with sides a, b, and c and angles A, B, and C, it is true that

\( \frac{sin a}{sin A} = \frac{sin b}{sin B} = \frac{sin c}{sin C}  = \frac {6 Vol(OABC)}{sin a sin b sin c} \)

That is the ratio of  the sine of any side to the sine of its opposite angle is the product of the sines of the sides over six times the volume of the tetrahedron formed by the center of the sphere and the points A, B, and C.


According to Ubiratàn D'Ambrosio and Helaine Selin, the spherical law of sines was discovered in the 10th century. It is variously attributed to al-Khujandi, Abul Wafa Bozjani, Nasir al-Din al-Tusi and Abu Nasr Mansur. 

Ptolemy knew the formula  for the planer law of sines and something like the angle addition formula but he expressed them in terms of chords of arcs, not sines of angle.  The half chords, or sines, were introduced by the Hindu mathematician Aryabhata around 500.

The spherical law of sines was first presented in the west by Johann Muller, also known as Regiomontus,in his De Triangulis Omnimodis in 1464. This was the first book devoted wholly to trigonometry (a word not then invented). David E. Smith suggests that the theorem was Muller's invention. The word trigonometry, by the way, seems to have been the creation of Bartholomaus Pitiscus, who used it in the title of a book, Trigonometriae sive de dimensions triangulorum libri cinque in 1595. Among other things the book includes a demonstration of the law of sines and the law of cosines. I find it highly unusual that the first use of a word would be in the title of a book.

As a second footnote, it may be of interest to teachers and students that the use of the unit circle was "unknown much before 1800". I found that out in an article on "Benjamin Banneker's Trigonometry Puzzle" by Florence Fasanelli, Graham Jagger, and Bea Lumpkin that appeared in the MAA online magazine Convergence. Unfortunately the magazine is no longer free on-line. Older trig tables gave the measurements for the sine, tangent and secant on a circle of very large radius (van Schooten used 10,000,000) rather than on a circle of radius 1, as we do today. Thus, the sin 90°, also called the “total sine” was given as 10,000,000, and the sine of 45° was 707,107 and not 0.707107, as we would use today. Anyone using these tables would use rules of proportion to make any necessary conversions. 


On This Day in Math - May 14

  




“I have found a very great number of exceedingly beautiful theorems.”
 
Pierre de Fermat


The 134th day of the year; 134 has only two prime factors (67 and 2){called a bi-prime or a semiprime, it is the 45th semiprime of the year to date.} . Note that 1342 - 672 = 13467, which is the base numbers concatenated. *Prime Curios

134 is the sum of 8C1 + 8C3 + 8C4


134 is the 19th day of the year that is the sum of three positive cubes.


And 134 is the maximal number of regions the plane can be divided with 12 circles.

It is not possible to append a single digit to 134 and produce a prime. Students, can you find the next such number?,,,, any other such number?

In this politically charged atmosphere, individuals in the military might want to be aware that, the American UCMJ; Article 134 is the catch-all article, for offences "not specifically mentioned in this chapter." Used to prosecute a wide variety of offences, from cohabitation by personnel not married to each other to statements critical of the U.S. President. Some prisoners, including Abu Ghraib were tagged with this number. Wik  (
Abu Ghraib, twenty miles west of Baghdad, was one of the world's most notorious prisons, with torture, weekly executions, and vile living conditions.  Elever US soldiers were convicted of crimes related to the abuse.) .




EVENTS


May 14, 1230 "On the 14th May, which was the Tuesday in Rogation Week, the unusual eclipse of the Sun took place very early in the morning, immediately after sunrise; and it became so dark that the labourers, who had commenced their morning's work, were obliged to leave it, and returned again to their beds to sleep; but in about an hour's time, to the astonishment of many, the Sun regained its usual brightness." Refers to the total solar eclipse of 14 May 1230. From: Rogerus de Wendover, Flores Historiarum, vol.
ii. p.235 *NASA with HT to David Dickinson ‏ @Astroguyz



1539 Georg Joachim Rheticus writes from Posen to his teacher/friend Johannes Schoener in Nuremberg to tell him he is on the way to visit Copernicus. It may well have been Schoener that urged him to visit Copernicus. No record of the letter itself exists, but it was mentioned in the dedication of the Narratio prima by Rheticus sent to Schoener in 1540 while Rheticus was still studying with Copernicus. *John W. Hessler, A Renaissance Globemaker's Toolbox

Georg Joachim de Porris, also known as Rheticus (/ˈrɛtɪkəs/; 16 February 1514 – 4 December 1574), was a mathematician, astronomer, cartographer, navigational-instrument maker, medical practitioner, and teacher. He is perhaps best known for his trigonometric tables and as Nicolaus Copernicus's sole pupil. He facilitated the publication of his master's De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres).  In 1551 Rheticus produced a tract titled Canon of the Science of Triangles, the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined).





1607 The first permanent English settlement in American was founded at Jamestown, VA. *VFR


1631 Pierre de Fermat installed at Toulouse, at age 31, as commissioner of requests. *VFR He would retain the position until his death.


1743 In a letter to Nikolaus Bernoulli in 1743, Euler writes 1 + x + x2 + ... +  xn. One of the first uses of ellipses for series.  Cajori states earlier use was most commonly "etc." or "&c." 


1755 Joseph Louis Vincens de Mauleon, governor of the principality of Orange, published his “proof” that the circle could be squared. He claimed this proof enabled him to explain the mysteries of original sin and of the Holy Trinity.Although he offered a prize of 300,000 franks to anyone who could show his proof fallacious, it is pure nonsense. *VFR




1791, the twenty-one year old Alexander von Humboldt wrote a to the Prussian minister and director of the Mining and Smelting Department (Bergwerks- und Hüttendepartment) in Berlin. In the letter he described his ‘plan’ (Entwurf) for his ‘future public life.’ Young Humboldt had manifold interests, but in spring 1791 he had made up his mind. He wanted to serve his Fatherland, not as a member of the military, but as a scientifically trained, practical mining official.
‘I am of the age,’ he stated, ‘in which I must desire to enter a certain sphere of activity, and to become useful to my Fatherland through the minor forces I sense within me.’ His wish to join von Heynitz's mining department and to ‘undergo comprehensive training’ in his department, he further explained, was motivated by ‘the decisive inclination for mineralogy [and] for the science of salt works and mining (Salz- und Bergwerkskunde)’ along with ‘the hope, one day perhaps to contribute to the large and beneficial plans’ through which von Heynitz, based on the ‘principles of state economy,’ had ‘opened new sources of national wealth. *Ursula Klein,The Prussian Mining Official Alexander von Humboldt, Annals of Science, 2012




1832 "In March 1832 a cholera epidemic swept Paris and prisoners, including Galois, were transferred to the Pension Sieur Faultrier. There he apparently fell in love with Stephanie-Felice du Motel, the daughter of the resident physician. After he was released on 29 April Galois exchanged letters with Stephanie, and it is clear that she tried to distance herself from the affair. The name Stephanie appears several times as a marginal note in one of Galois' manuscripts." *SAU On May 14, Galois received a rejection letter from Stephanie. (Am I the only one who finds it funny that he met a woman named Motel in a Pension.)




1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this. "May 14: NYC hotel roofs being used for comet parties; Professor S. A. Mitchell tells of superstitions surrounding comets through the ages in NYC speech." *Joseph M. Laufer, Halley's Comet Society - USA

Mary Proctor FRAS FRMetS (1 April 1862 – 11 September 1957) was a British-American popularizer of astronomy. While not a professional astronomer, Proctor became well known for her books and articles written for the public – particularly her children's fiction.





1953 Results of the third annual MAA Mathematics Contest for high school students were announced. Tied for fourth place was Geraldine Anne Ferraro who later became the first woman vice-presidential nominee of a major political party. *VFR

She grew up in New York City and worked as a public elementary school teacher before training as a lawyer. She joined the Queens County District Attorney's Office in 1974, heading the new Special Victims Bureau that dealt with sex crimes, child abuse, and domestic violence. In 1978 she was elected to the U.S. House of Representatives, where she rose rapidly in the party hierarchy while focusing on legislation to bring equity for women in the areas of wages, pensions, and retirement plans.

 Ferraro died at Massachusetts General Hospital in Boston on March 26, 2011.




1963  Yvonne Choquet-Bruhat became the first woman full member of the French Academy of Sciences.  She was a French mathematician and physicist who made important contributions to the general theory of relativity.

 She has made seminal contributions to the study of Einstein's general theory of relativity, by showing that the Einstein equations can be put into the form of an initial value problem which is well-posed. In 2015, her breakthrough paper was listed by the journal Classical and Quantum Gravity as one of thirteen 'milestone' results in the study of general relativity, across the hundred years in which it had been studied.




BIRTHS

1679 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




1701 William Emerson (14 May 1701 – 20 May 1782), English mathematician, was born at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school. William himself had a small estate in Weardale called Castle Gate situated not far from Eastgate where he would repair to work throughout the Summer on projects as disparate as stonemasonry and watchmaking. Unsuccessful as a teacher, he devoted himself entirely to studious retirement. Possessed of remarkable energy and forthrightness of speech, Emerson published many works which are singularly free from errata.

In The Principles of Mechanics (1754) he shows a wind-powered vehicle in which the vertically mounted propeller gives direct power to the front wheels via a system of cogs. In mechanics he never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model. He was skilled in the science of music, the theory of sounds, and the ancient and modern scales; but he never attained any excellence as a performer. He died on 20 May 1782 at his native village, where his gravestone bears epitaphs in Latin and Hebrew.

Emerson dressed in old clothes and his manners were uncouth. He wore his shirt back to front and his legs wrapped in sacking so as not to scorch them as he sat over the fire. He declined an offer to become FRS because it would cost too much after all the expense of farthing candles he had been put to in the course of his life of study. Emerson rode regularly into Darlington on a horse like Don Quixote's, led by a hired small boy. In old age, plagued by the stone, he would alternately pray and curse, wishing his soul 'could shake off the rags of mortality without such a clitter-me-clatter.' *Wik





1832 Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903)  is remembered for the "Lipschitz condition", an inequality that guarantees a unique solution to the differential equation y' = f (x, y). *SAU
Lipschitz discovered Clifford algebras in 1880, two years after William K. Clifford (1845–1879) and independently of him, and he was the first to use them in the study of orthogonal transformations. Up to 1950 people mentioned “Clifford-Lipschitz numbers” when they referred to this discovery of Lipschitz. Yet Lipschitz’s name suddenly disappeared from the publications involving Clifford algebras; for instance Claude Chevalley (1909–1984) gave the name “Clifford group” to an object that is never mentioned in Clifford’s works, but stems from Lipschitz’s. Pertti Lounesto (1945–2002) contributed greatly to recalling the importance of Lipschitz’s role. *Wik



1863 John Charles Fields (May 14, 1863 - August 9, 1932) born in Toronto, Canada. After earning his Ph.D. at Johns Hopkins in 1887, he taught at Allegheny College (1889-1892) before going to Europe for a decade to study in Paris and Berlin. In 1902 he joined the faculty at the University of Toronto, where he remained until his death on 9 August 1932. *VFR
He originated the idea, posthumously given his name - for the Fields Medal. It became the most prestigious award for mathematicians, often referred to as the equivalent of a Nobel Prize for mathematicians. As a professor at the University of Toronto, he had worked to bring the International Congress of Mathematicians to Toronto (1924). The Congress was so successful that afterward there was a surplus of about \($2,500\) which Fields, as chairman of the organizing committee, proposed be used to fund two medals to be awarded at each of future Congresses. This was approved on 24 Feb 1931. He died the following year, leaving \($47,000\) as additional funding for the medals, which have been awarded since 1936. *TIS






1875  Beppo Levi (14 May 1875 – 28 August 1961) was an Italian mathematician. He published high-level academic articles and books, not only on mathematics, but also on physics, history, philosophy, and pedagogy. Levi was a member of the Bologna Academy of Sciences and of the Accademia dei Lincei.

His early work studied singularities on algebraic curves and surfaces. In particular, he supplied a proof (questioned by some) that a procedure for resolution of singularities on algebraic surfaces terminates in finitely many steps. Later he proved some foundational results concerning Lebesgue integration, including what is commonly known as Beppo Levi's lemma.



1878  Roland George Dwight Richardson (born May 14, 1878, Dartmouth, Nova Scotia; died July 17, 1949, Antigonish, Nova Scotia) was a prominent Canadian-American mathematician chiefly known for his work building the math department at Brown University and as Secretary of the American Mathematical Society.

Richardson was the Secretary of the American Mathematical Society in 1921 and held the job until 1940. During his time, Raymond Clare Archibald wrote in his article on Richardson, "No American mathematician was more widely known among his colleagues and the careers of scores of them were notably promoted by his time-consuming activities in their behalf." He was credited with helping many European mathematicians concerned about conditions in Europe move to America during the 1930s.

At the start of World War II Richardson organized accelerated applied mathematics courses at Brown for servicemen as the "Program of Advanced Instruction and Research in Applied Mechanics", recruiting German mathematician William Prager to lead it. This led to the founding of a new "Quarterly of Applied Mathematics" edited at Brown in 1943. After the war the program was converted into a new graduate division of applied mathematics. From 1943 to 1946 he was a member of the applied mathematics panel of the National Defense Research Committee.




1917 William Thomas Tutte FRS (May 14, 1917 – May 2, 2002) was a British, later Canadian codebreaker and mathematician. During World War II he broke a major German code system, which had a significant impact on the Allied invasion of Europe. He also had a number of significant mathematical accomplishments, including foundation work in the fields of combinatorics and graph theory. *Wik;




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




DEATHS

1669 Denis de Sallo, Sieur de la Coudraye (1626 - May 14, 1669) was a French writer and lawyer from Paris, known as the founder of the first French literary and scientific journal - the Journal des sçavans.
De Sallo obtained classical education and was admitted to the Paris bar in 1652, although he later devoted himself to scholarly aspects of the law rather than active practice, serving also as a counsel in the French government. He belonged to the clique of Jean-Baptiste Colbert, minister of finance under Louis XIV, and had active contacts with other prominent European scholars.
In 1665 he published the first issue of the Journal des sçavans under the pseudonym Sieur d'Hédouville. The idea for the journal was similar in scope to an outline written by the historian François Eudes de Mézeray who also belonged to the Colbert's clique and briefly lived in the same household as de Sallo. It included recording news and inventions in the various arts and sciences, decisions of secular and ecclesiastical courts, reviews of new scholarly books and other items of broader interest to a modern scholar.
De Sallo's health deteriorated in his final years so that he was unable to walk; his condition has been attributed to diabetes. *Wik




1761 Thomas Simpson (20 August 1710 – 14 May 1761) is best remembered for his work on interpolation and numerical methods of integration. However the numerical method known today as "Simpson's rule", although it did appear in his work, was something he learned from Newton as Simpson himself acknowledged. By way of compensation, however, the Newton-Raphson method for solving the equation f (x) = 0 is, in its present form, due to Simpson. Newton described an algebraic process for solving polynomial equations which Raphson later improved. The method of approximating the roots did not use the differential calculus. The modern iterative form xn+1 = xn - f (xn) / f '(xn) is due to Simpson, who published it in 1740. *SAU





1797 Giovanni Francesco Fagnano dei Toschi (31 Jan 1715 in Sinigaglia, Italy - 14 May 1797 in Sinigaglia, Italy) He proved that the triangle which has as its vertices the bases of the altitudes of any triangle has those altitudes as its bisectors. *VFR Of all the triangles that could be inscribed in a given triangle, the one with the smallest perimeter is the orthic triangle [The triangle connecting the foot of the altitude to each leg/]. This has sometimes been called Fagnano's Problem since it was first posed and answered by Giovanni Francesco Fagnano dei Toschi. Fagnano also was the first to show that the altitudes of the original triangle are the angle bisectors of the orhtic triangle, so the incenter of the orthic triangle is the orthocenter of the original triangle.*pb





1893 Ernst Eduard Kummer (29 January 1810 – 14 May 1893)  He was professor at the University of BRESLAU (now WROCLAW, Poland) in 1842-1855 and developed his theory of ideals here. KRONECKER studied with him. Later he replaced Dirichlet at The University of Berlin. He died at age 83, after a short attack of influenza. German mathematician whose introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic to complex number fields. He worked on Function theory, and  extended Gauss's work on hypergeometric series, giving developments that are useful in the theory of differential equations. He was the first to compute the monodromy groups of these series. Later. Kummer

devoted himself to the study of the ray systems, but treated these geometrical problems algebraically. He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent planes.  *TIS and others   An oft told, and almost certianly untrue anecdote is told about Kummer: Kummer was so inept at simple arithmetic that he often asked students to help him in class. On one occasion, Kummer sought the result of a simple multiplication. "Seven times nine," he began. "Seven times nine is er - ah - ah - seven times nine is..." "Sixty-one," a mischievous student suggested and Kummer wrote the "answer" on the blackboard. "Sir," another one interjected, "it should be sixty-seven." "Come,  gentlemen, it can't be both," Kummer exclaimed. "It must be one or the other!" According to Erdos, Kumer reasoned out the answer as follows, -It can't be 61 as that is prime, as is 67, and 65 is a multiple of five, and 69 is too big, so it must be 63.


1924 Enrico Barone (December 22, 1859, Naples – May 14, 1924, Rome) Italian mathematical economist who built on the general equilibrium theory of Léon Walras and was instrumental in convincing Walras to incorporate variable production techniques - and, by extension, marginal productivity theory - into the Walras theory. Barone's greatest contribution was in getting the "Socialist Calculation" debate started with his famous 1908 article. His position was that it was indeed possible in a collectivist state for a planning agency to calculate prices for maximum efficiency. He was the first to apply indifference curve analysis to compare the relative burdens of income taxes and excise taxes (1912). He opposed "progressive" taxation schemes as based on dubious utilitarian calculations. *TIS




1935 Edwin Brant Frost II (July 16, 1866 – May 14, 1935) American astronomer, born in Brattleboro, Vermont. His father, Carlton Pennington Frost, was dean of Dartmouth Medical School.
Frost joined the staff of Yerkes Observatory in 1898 and became its director in 1905 when George Hale resigned. Frost kept the position until his retirement in 1932. He was the editor of the Astrophysical Journal from 1902 to 1932, known for his careful attention to details. In 1915 he lost the use of his right eye and in 1921, his left. Despite his blindness he continued working for eleven more years until his retirement in 1932.
Frost's research focused on the determination of radial velocity using stellar spectroscopy and spectroscopic binaries. In 1902, he discovered the strange behavior of Beta Cephei, which later became the prototype for Beta Cephei variable stars. *TIA



1985 Charles Leonard Hamblin (20 November 1922 – 14 May 1985) was an Australian philosopher, logician, and computer pioneer, as well as a professor of philosophy at the New South Wales University of Technology (now the University of New South Wales) in Sydney.
Among his most well-known achievements in the area of computer science was the introduction of Reverse Polish Notation and the use in 1957 of a push-down pop-up stack. This preceded the work of Friedrich Ludwig Bauer and Klaus Samelson on use of a push-pop stack. The stack had been invented by Alan Turing in 1946 when he introduced such a stack in his design of the ACE computer. Hamblin's most well-known contribution to philosophy is his book Fallacies, a standard work in the area of the false conclusions in logic. *Wik





2008 Arthur Burks​ (October 13, 1915 – May 14, 2008) was a principal designer of the ENIAC. Burks -- who was born in Duluth, Minn., and educated at DePauw University and the University of Michigan -- did extensive work on the ENIAC, the machine designed at the University of Pennsylvania​’s Moore School and completed in 1946. After working with J. Presper Eckert​ and John Mauchly on the ENIAC, Burks moved on to Princeton University, where he helped John von Neumann develop his computer at the Institute for Advanced Studies.*CHM



2014 Alexander Murray Macbeath (30 June 1923 Glasgow – 14 May 2014 Warwick)was a mathematician who worked on Riemann surfaces. Macbeath surfaces and Macbeath regions are named after him.

During World War II, he worked in Hut 7 of the Government Code and Cypher School at Bletchley Park, breaking ciphers used for military communications by the Japanese navy and, later, the army.

After the war he earned an M.A. (again with honours) from Clare College, Cambridge. With a Commonwealth Fund fellowship, he then attended Princeton University, where he earned his Ph.D. in 1950 under the supervision of Emil Artin.
He taught at Keele University and the University of Dundee before moving to the University of Birmingham in 1963 where he stayed until 1979 as Mason Professor, then moved back to the University of Pittsburgh in the United States until he reached their statutory retirement age of 60.

He subsequently took up a position at the University of Dundee where he remained for a number of years, before moving to Warwickshire where at the University of Warwick he held the position of Emeritus Professor of Mathematics.*Wik
Murray Macbeath (right) with Wilhelm Kaup




2021 Yuan Wang (29 April 1930 in Lanhsi, Zhejiang province, China - 14 May 2021) )Most of Wang Yuan's research has been in the area of number theory. He looked at sieve methods and applied them to the Goldbach Conjecture. He also applied circle methods to the Goldbach Conjecture. In 1956 he published (in Chinese) On the representation of large even integer as a sum of a prime and a product of at most 4 primes in which he assumed the truth of the Riemann hypothesis and with that assumption proved that every large even integer is the sum of a prime and of a product of at most 4 primes. He also proved that there are infinitely many primes p such that p + 2 is a product of at most 4 primes. In 1957 Wang Yuan published four papers: On sieve methods and some of their applications; On some properties of integral valued polynomials; On the representation of large even number as a sum of two almost-primes; and On sieve methods and some of the related problems.*SAU



Credits :

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