## Thursday 22 August 2024

### On This Day in Math - August 22

Only professional mathematicians learn anything from professors.
Other people learn from explanations.
~Ralph Boas

commented...

I thought the quote was "Only professional mathematicians learn anything from proofs..."

The 234th day of the year; There are 234 ways of grouping six children into rings of at least two children with one child at the center of each ring.

234 is the 55th abundant number.  It's proper divisors are {123691318263978117}  and their sum is greater than 234, it is  312.  There are 86 abundant numbers in a non-leap year. 234=6(39) and all multiples two or greater of a perfect number are abundant.

234 begins a string of eight consecutive digits which is a prime number, 23456789.  It is the concatenation of three primes, 23, 4567, and 89.  All the children need to know why there can not be any ordering of all nine digits , 1 to 9 that is prime. Teach one today.
Casting out nines is as old as Iamblichus, and as new as the youngest kid entering kindergarten

EVENTS

1450 Gutenberg borrowed 800 guilden in gold at 6% interest (a low rate then) to develop his invention of printing from movable metal type. The ﬁrst book produced was a 42-line Latin Bible, the famous Gutenberg Bible. [G. H. Putnam, Books and Their Makers During the Middle Ages (1896), p. 361]. *VFR
In 1455, Gutenberg completed his 42-line Bible, known as the Gutenberg Bible. About 180 copies were printed, three quarters on paper, and the rest on vellum.
Some time in 1456, there was a dispute between Gutenberg and Fust, in which Fust demanded his money back, and accused Gutenberg of misusing the funds. Gutenberg's two rounds of financing from Fust, totaling 1,600 guilders at 6% interest, now amounted to 2,026 guilders. Fust sued at the archbishop's court. A legal document, from November 1455, records that there was a partnership for a "project of the books," the funds for which Gutenberg had used for other purposes, according to Fust. The court decided in favor of Fust, giving him control over the Bible printing workshop.

Thus, Gutenberg was effectively bankrupt, but it appears he retained, or restarted, a printing shop and participated in the printing of a Bible in the town of Bamberg around 1459, for which he seems at least to have supplied the type. But since his printed books never carry his name or a date, it is difficult to be certain.

The Gutenberg Bible, now housed at the Library of Congress in Washington, D.C.

1676 Ole Rømer's conjecture that the speed of light was finite may have appeared in a presentation to the Royal Academy of Sciences in Paris on August 22, "This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit." His final calculations of 220,000 Km/sec were presented to the Academy on 22 November, but the record of that meeting has been lost. The first public notice occurred on Dec 7, 1676 in the Journal des sçavans. *Wik

1800  On this day in 1800, Georg Vega was given the hereditary title of baron, including the right to his own coat of arms.   Vega wrote about artillery but he is best remembered for his tables of logarithms and trigonometric functions.
Vega's calculating abilities, often carried on during military campaigns, is clear in his remarkable achievement of calculating π to 140 places, a record which stood for over 50 years. This appears in a paper which he published in 1789, the year he was involved in fighting the Turks. Tomaz Pisanski discusses methods for calculating decimal digits of π in . He writes about Vega's achievement:-
We mention the contribution of the Slovenian mathematician Jurij Vega ... not because he worked harder than his contemporaries, but because he had a better algorithm.
What was this better algorithm? He used two formulas, basically using one as a check against the other,

.

Logarithmisch trigonometrisches Handbuch  was published in 1793 in both German and Latin. This book of 7-figure logarithm tables contained tables of the logarithms of the natural numbers from 1 to 100,000 and the logarithms of the trigonometric functions. This remarkable work, which went through over 100 editions, contained more than just tables, for in it Vega explained the theory of logarithms in the Preface, and then went on to give useful examples of how the tables could be used. In 1794 he went to Stuttgart where he spent two months and, in the same year, he was elected to the Royal Society of Sciences and Humanities in Göttingen. The 10-figure tables Thesaurus logarithmorum completus , based on Adriaan Vlacq's tables, appeared in 1794 and again this was a remarkable work with the 90th edition appearing in 1924.  *SAU

1850 Michael Faraday in a letter to William Whewell writes, "I have been driven to assume for some time, especially in relation to the gases, a sort of conducting power for magnetism. Mere space is Zero. One substance being made to occupy a given portion of space will cause more lines of force to pass through that space than before, and another substance will cause less to pass. The former I now call Paramagnetic & the latter are the diamagnetic. The former need not of necessity assume a polarity of particles such as iron has with magnetic, and the latter do not assume any such polarity either direct or reverse. I do not say more to you just now because my own thoughts are only in the act of formation, but this I may say: that the atmosphere has an extraordinary magnetic constitution, & I hope & expect to find in it the cause of the annual & diurnal variations, but keep this to yourself until I have time to see what harvest will spring from my growing ideas." * L. P. Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 589.

1883 Sylvester writes Cayley that, "I have been recovering my theory of multiple algebras - by slow degrees." Thus begins his first sustained assault on Matrix Theory. *The Emergence of the American Mathematical Research Community, 1876-1900, Parshal & Rowe
 J J Sylvester

In 1893 "An international Congress of Mathematicians is held at the World's Columbian Exposition in Chicago, August 21-26. Felix Klein​ and E.H. Moore occupy center stage. The Committee of Ten on Secondary School Studies recommends a year of algebra, followed by two years of plane and solid geometry to be taught side by side with more algebra. The first year's course in algebra is recommended for all students."*from Milestones in (Ohio)Mathematics, by David E. Kullman
I began a search for the history of teaching of spherical geometry in America, and one of the first statementsa I found was this discouraging indictment, " Spherical geometry is not typically covered in a secondary geometry course due to time constraints and teacher knowledge (indicating the lack thereof).
 Klein

1900 It seems that Henry Ernest Dudeney may have been the first person to explore the use of primes to create a magic square. He gave the problem of constructing a prime magic square in The Weekly Dispatch, 22nd July and 5th August 1900. At that time, 1 was sometimes (often?) considered as a prime number. His magic square gives the lowest possible sum for a 3x3 using primes (assuming one is prime)
The smallest magic square with true primes (not using one) has a magic constant of 177
The left square is the 3×3 prime magic square (containing a 1) having the smallest possible magic constant, and was discovered by Dudeney in 1917 (Dudeney 1970; Gardner 1984, p. 86). The second square is the 3×3 magic square consisting of primes only having the smallest possible magic constant (Madachy 1979, p. 95; attributed to R. Ondrejka). The third square is the 3×3 prime magic square consisting of primes in arithmetic progression (199+210n) having the smallest possible magic constant of 3117 (Madachy 1979, p. 95; attributed to R. Ondrejka). The 4×4 prime magic square on the right was found by A. W. Johnson, Jr. (Dewdney 1988). *Wolfram MathWorld

1955 The first computer User Group is founded. SHARE was founded by users of IBM's Model 704 computer, ... in order for the growing community of IBM computer users (mainly aerospace companies on the U.S. West Coast) to exchange information and programs. The first meeting included scientists and engineers whose companies had ordered IBM's newest computer, the 704. Sparked by quick growth and the fact that its members were some of IBM's largest customers, the group had significant influence over IBM designs and customer support. *CHM

Aug 22-26,  1989, the first complete ring around Neptune was discovered in photographs transmitted by Voyager 2 to the Jet Propulsion Laboratory in the U.S. Dusty debris was seen to form a tenuous but complete ring about 17,000 miles above Neptune's clouds. The material in the ring appeared be distributed uniformly through the dark circle, though whether fine or large particles was undetermined. The ring lies just outside the orbit of one of the planet's small moons, designated then as 1989 N3, also newly discovered by Voyager 2. Only arcs - fragments of rings around Neptune, had previously viewed from Earth-based observations, which were also shown as arcs in photographs taken by Voyager 2 eleven days earlier.

 *NASA

On August 22, 2006, four Fields Medals were awarded at the opening ceremonies of the Inter-
national Congress of Mathematicians (ICM) in Madrid, Spain. The medalists are ANDREI O KOUNKOV, GRIGORY PERELMAN, TERENCE TAO, and WENDELIN WERNER.
During the award ceremony, John Ball, president of the International Mathematical
Union, announced that Perelman declined to accept. Tao became one of the youngest persons, the first Australian, and the first UCLA faculty member ever to be awarded a Fields Medal. *AMS Notices
Dr. Perelman, 40, is known not only for his work on the Poincaré conjecture, among the most heralded unsolved math problems, but also because he has declined previous mathematical prizes and has turned down job offers from Princeton, Stanford and other universities. He has said he wants no part of \$1 million that the Clay Mathematics Institute in Cambridge, Mass. has offered for the first published proof of the conjecture.
 *NY Times

BIRTHS

1638  Georg Christoph Eimmart, a German astronomer and artist, was born Aug. 22, 1638.  In 1678, Eimmart founded an astronomical observatory in the Vestnertorbastei, a garden area within a low wall just north of Nuremberg Castle.  Unlike Tycho Brahe's pioneer observatory at Hven in Denmark, where each instrument was protected by a conical dome, Eimmart's observatory appears to have been an open-air affair.  Several images survive of Eimmert's garden of sextants and transit circles; the one we have in our collection is an inset on a large star map that was included in Johann Doppelmayr's Atlas coelestis (1742; first image).  Doppelmayr was a Nuremberger himself and was happy to showcase Eimmart's observatory, along with those at Greenwich, Paris, and Hven.

Being an artist and engraver, Eimmart was naturally drawn to the production of stellar and lunar maps.  Most of the celestial planispheres that survive and bear his name were printed by others in the 18th century, especially by Johann Baptist Homann; there are a moderate number of these that survive.  *Linda Hall Org

1647 Denis Papin (22 Aug 1647; c1712) French-born British physicist who invented the pressure cooker (1679). He assisted Dutch physicist Christiaan Huygens with air-pump experiments, and went to London in 1675 to work with the English physicist Robert Boyle. A few years later, Papin invented his steam digester (pressure cooker), a closed vessel with a tightly fitting lid that confined the steam at a higher pressure, considerably raising the boiling point of the water. A safety valve of his own invention prevented explosions. Observing that the enclosed steam in his cooker tended to raise the lid, Papin conceived of the use of steam to drive a piston in a cylinder, the basic design for early steam engines. He never built an engine of his own, but his idea was improved by others and led to the development of the steam engine, a major contribution to the Industrial Revolution. *TIS If you are not familiar with Papin, check out this blog by The Renaissance Mathematicus.

1796 Baden Powell (22 August 1796–11 June 1860 Kensington, London) born in Stamford Hill, England. Savilian professor of geometry at Oxford from 1827 to 1854. He deserves credit for the modest reforms in mathematical education at Oxford in the 1850s. One son (he had 14 children by 3 wives) Robert Baden-Powell founded the scouting movement. *VFR He fought for the principle acknowledging scientific advances were compatible with Christian religion. Following Darwin's "Origin of Species" in 1859, he contributed one of seven essays in "Essays and Reviews," 1860. This was violently attacked, and the authors denounced as being inspired by "the Evil One himself." "There was some expectation of him becoming a Bishop, before Essays and Reviews were published" (letter from his widow to her nephew 20.8.1909). *Pinetreeweb.com

1834 Samuel Pierpont Langley, (22 Aug 1834; 27 Feb 1906)American astronomer, physicist, and aeronautics pioneer who built the first heavier-than-air flying machine to achieve sustained flight. He launched his Aerodrome No.5 on 6 May 1896 using a spring-actuated catapult mounted on top of a houseboat on the Potomac River, near Quantico, Virginia. He also researched the relationship of solar phenomena to meteorology. *TIS
Developed a bolometer (for measurements of the cosmic microwave background) and determent the value of the solar constant.*Wik

1908 Donald Harry Sadler (22 August, 1908 – 24 October, 1987 ) was an English astronomer and mathematician who developed an international reputation for his work in preparing astronomical and navigational almanacs. He worked as the Superintendent of His Majesty's Nautical Almanac Office from 1937 to 1971.
Sadler began work as an assistant at His Majesty's Nautical Almanac Office in 1930, working under the direction of the Superintendent, Leslie Comrie, when it was based at the Royal Naval College in Greenwich, London. Sadler was promoted to Deputy Superintendent of the Office in 1933.

Comrie left the Nautical Almanac Office in 1936. A decision was taken to move the Office to the Royal Observatory, Greenwich, placing it under the direction of the Astronomer Royal, and Sadler was appointed a Chief Assistant at the observatory. Sadler was appointed Comrie's successor as Superintendent of the Nautical Almanac Office in 1937. Sadler was the eighth person to occupy this post since it was created in 1818.

Sadler took on the task of consolidating projects begun by Comrie, publishing new tables for use in navigation. The Second World War soon intervened and the Nautical Almanac Office was moved temporarily out of London to the safer environment of Bath. The Office expanded in size temporarily to prepare data for military use. Sadler was awarded the OBE in 1948 in recognition of this work.

Sadler supervised the relocation of the Nautical Almanac Office in 1949 from Bath to the new home of the Royal Greenwich Observatory at Herstmonceux Castle in Sussex. He expanded the use of calculating machines in astronomical calculations. He increased international cooperation in preparing astronomical tables, particularly with the United States Naval Observatory.

In 1954 Sadler married his colleague, Flora Sadler (née McBain), in what was described as 'the astronomical romance of the decade'.

Donald Sadler oversaw the transfer of the Nautical Almanac Office within the Royal Greenwich Observatory from the control of the Admiralty to the new Science Research Council.

1915 James Hillier, OC (August 22, 1915 – January 15, 2007) was a Canadian-born scientist and inventor who designed and built, with Albert Prebus, the first successful high-resolution electron microscope in North America in 1938. *Wik
Professor Burton and grad students Hillier and Prebus developed the first practical electron microscope that focused a beam of electrons for illumination
Three years earlier, Professor E.F. Burton, Chairman of the Physics Department, was at a meeting in Berlin, Germany to discuss the useful possibilities of electron microscopy. Observed at the originator of the instrument, German scientist Ernst Ruska built an electron microscope in 1931. He had trouble with refining his design, resulting in specimens destroyed by the hot beam of the microscope. “After attending the meeting Burton became certain that, once perfected, the electron microscope would be a key tool in biological and medical research,” said Julie Stoehr in The Undiscovered Country: Development of the Electron Microscope (Quasar, University of Alberta). Burton “returned to Canada determined to construct such an instrument.”

DEATHS

1664 Maria Cunitz (1604 - August 22, 1664) was an astronomer who published simpler versions of Kepler's work. *SAU The publication of the book Urania propitia gained Cunitz a European reputation. She was acclaimed as the most learned woman since Hypatia of Alexandria. Significantly for a technical publication of that period, her book was written both in Latin and German (stating that it was to increase the accessibility to her work). Urania propitia was a simplification of the Rudolphine Tables. It provided new tables, new ephemera, and a more elegant solution to Kepler's Problem, which is to determine the position of a planet in its orbit as a function of time. Today, her book is also credited for its contribution to the development of the German scientific language. *Wik

1676 Edward Cocker (1631 – 22 August 1676) was an English scholar who was the author of an influential arithmetic text which ran to more than 100 editions. Cocker died with no money in his Poke to quote his own phrase. As Wallis writes
Subsequently he might well have suffered material loss in the Fire and have had the expense of successive removals. He may also have spent extravagantly. He possessed 'some choice Manuscripts, and a great Collection of Printed Authors in several Languages' ... In any event, he died in debt, 'within the rules' of the King's Bench Prison, which was situated in Southwark; the quoted phrase meant that the prisoner had purchased the right to live within a short distance of the prison. Cocker's move to Southwark was probably an enforced one, consequent on his committal for debt.
*SAU

For many years in the early 19th century a common expression in England was, "all according to Cocker", to indicate something done correctly.

Benjamin Franklin's autobiography makes mention that he studied ..., Cocker's Arithmetic, after he moved from his home to Pennsylvania, " And now it was that, being on some occasion made asham'd of my ignorance in figures, which I had twice failed in learning when at school, I took Cocker's book of Arithmetick, and went through the whole by myself with great ease.

1700 Siguenza y Gongora (August 14, 1645 – August 22, 1700) was a Mexican astronomer and philosopher. *SAU He was one of the first great intellectuals born in the Spanish viceroyalty of New Spain. A polymath and writer, he held many colonial government and academic positions. In 1681 Sigüenza wrote the book "Philosophical Manifest Against the Comets" in which he tried to dismiss fears of impending superstitious predictions based from astrology; in the work he takes steps to separate the fields of astrology and astronomy. The jesuit Eusebio Kino strongly criticized the texts written by Sigüenza because they were contradicting to established Catholic beliefs in the heavens. Sigüenza often cited authors like Copernicus, Galileo, Descartes, Kepler, and Brahe. In 1690 Sigüenza took an audacious move to defend his previous work by publishing "Libra Astronómica y Filosófica". *Wik

1752 William Whiston (born 9 Dec 1667, 22 Aug 1752) English Anglican priest and mathematician who sought to harmonize religion and science, and who is remembered for reviving in England the heretical views of Arianism. He attended Newton's lectures while at Cambridge and showed great promise in mathematics. Ordained in 1693. While chaplain to the bishop of Norwich (1694-98), he wrote A New Theory of the Earth (1696), in which he claimed that the biblical stories of the creation, flood and final conflagration could be explained scientifically as descriptions of events with historical bases. The Flood, he believed, was caused by a comet passing close to the Earth on 28 Nov 2349 BC. This put stress on the Earth's crust, causing it to crack and allow the water to escape and flood the Earth. After serving as vicar of Lowestoft (1698–1701), he returned to his alma mater, Cambridge University to become assistant to the mathematician Sir Isaac Newton, whom he succeeded as professor in 1703. *TIS (His translations of the works of Josephus are still in print)

1907 Platon Sergeevich Poretsky (October 3, 1846, Elisavetgrad - August 9, 1907) He published major works on methods of solution of logical equations, and on the reverse mode of mathematical logic. He applied his logic calculus to the theory of probability. Although he retired from his teaching role at Kazan in 1889 due to ill health, this did not mean that he stopped his research. He continued to undertake research into mathematical logic for the remaining eighteen years of his life. *SAU

1923 Hidehiko Yamabe (山辺 英彦, Yamabe Hidehiko, August 22, 1923, in Ashiya, Hyōgo, Japan – November 20, 1960, in Evanston, Illinois) was a Japanese mathematician. Above all, he is famous for discovering that every conformal class on a smooth compact manifold is represented by a Riemannian metric of constant scalar curvature. Other notable contributions include his definitive solution of Hilbert's fifth problem. *Wik

1940 Sir Oliver Joseph Lodge, FRS (12 June 1851 – 22 August 1940) was a British physicist and writer involved in the development of key patents in wireless telegraphy. In his 1894 Royal Institution lectures ("The Work of Hertz and Some of His Successors"), Lodge coined the term "coherer" for the device developed by French physicist Édouard Branly based on the work of Italian physicist Temistocle Calzecchi Onesti. In 1898 he was awarded the "syntonic" (or tuning) patent by the United States Patent Office. He was also credited by Lorentz (1895) with the first published description of the length contraction hypothesis, in 1893, though in fact Lodge's friend George Francis FitzGerald had first suggested the idea in print in 1889. *Wik

1974 Jacob Bronowski, (18 Jan 1908, 22 Aug 1974)Polish-born British mathematician and man of letters who eloquently presented the case for the humanistic aspects of science. He is remembered as writer and presenter of the BBC television series, The Ascent of Man. Bronowski, who had a Ph.D. in algebraic geometry, spent WW II in Operations Research, and was an official observer of the after-effects of the Nagasaki and Hiroshima bombings. After this experience, he turned to biology, to better understand the nature of violence. *TIS

1975 Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician who worked on logic and the foundations of mathematics.*SAU His son Tadeusz is also a mathematician working on differential geometry. With Krzysztof Kurdyka and Adam Parusinski, Tadeusz Mostowski solved René Thom's gradient conjecture in 2000. *Wik

1975 Lancelot Thomas Hogben FRS FRSE (9 December 1895 – 22 August 1975) was a British experimental zoologist and medical statistician. He developed the African clawed frog (Xenopus laevis) as a model organism for biological research in his early career, attacked the eugenics movement in the middle of his career, and wrote popular books on science, mathematics and language in his later career. *Wik

His 1936 Mathematics for the Million, I picked up in the middle school library in 7th grade, was one of the most influential books in shaping my love for math.  Read it, read it to your children, have them read it to their younger siblings.

1992 Harold Maile Bacon (Jan. 13, 1907, August 22, 1992) was an elder statesmen of the Stanford faculty who taught calculus to generations of Stanford undergraduates during a career that spanned more than four decades.
Bacon was widely recognized on campus as the owner of the white colonial-style Row house with the rose-lined driveway. He had ties to the house, and the University, almost since his birth.
He was an ill 6-month-old child when he first visited the campus house he would occupy for more than 60 years. Harriet Dunn, a cousin of Harold Bacon's father, Robert, and owner of the distinctive house, suggested that the child be brought to Stanford from Southern California for examination by Dr. Ray Lyman Wilbur, who lived nearby on the site now occupied by Dinkelspiel Auditorium. (Wilbur, who prescribed medicine and a better diet for young Bacon, later became the university's third president.)
In the 1920s, Harold Bacon enrolled at Stanford, following in the footsteps of his father, who graduated in 1902. Bacon lived in the two-story, six-bedroom house during part of his undergraduate years, then moved in permanently , at the invitation of Harriet Dunn, when he returned in 1930 to teach.
In 1946, Rosamond Clarke, '30, came to the house when she married the math professor. Harriet Dunn died a month later, leaving the house and renewable land-lease to the Bacons. Jane Stanford had given permission for Mrs. Dunn a nd her husband, Orrin, to build the colonial-revival house in 1899 as recompense for Harriet Dunn's earlier work building and operating a campus boarding house.
For many years, Bacon directed the undergraduate program in mathematics, according to Halsey Royden, who took classes from Bacon during his student days and later became a faculty colleague.
To students and fellow faculty members, Bacon was "the embodiment of Stanford ways and history," Royden said. At the time he retired, Bacon, through his calculus classes, probably had taught "more engineering and science undergraduates than anyone else in the history of the university," Royden said.
*Stanford Obituary
For a wonderful story describing the nature of Harold Bacon as a man and a teacher, see this cover story, The Prisoner and the Professor, from the Stanford Alumni magazine of Mar/Apr 1997

2023 Calyampudi Radhakrishna Rao FRS (10 September 1920 – 22 August 2023) was an Indian-American mathematician and statistician. He was professor emeritus at Pennsylvania State University and research professor at the University at Buffalo. Rao was honoured by numerous colloquia, honorary degrees, and festschrifts and was awarded the US National Medal of Science in 2002. The American Statistical Association has described him as "a living legend" whose work has influenced not just statistics, but has had far reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine." The Times of India listed Rao as one of the top 10 Indian scientists of all time.

In 2023, Rao was awarded the International Prize in Statistics, an award often touted as the "statistics' equivalent of the Nobel Prize". Rao was also a Senior Policy and Statistics advisor for the Indian Heart Association non-profit focused on raising South Asian cardiovascular disease awareness.

Among his best-known discoveries are the Cramér–Rao bound and the Rao–Blackwell theorem both related to the quality of estimators. *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