## Monday 15 May 2023

### 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

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.

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

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

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

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 hte 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

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

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

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

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

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

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.*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