## Saturday 30 September 2023

### On This Day in Math - September 30

Big whirls have little whirls,
That feed on their velocity;
And little whirls have lesser whirls,
And so on to viscosity.
~Lewis Richardson

The 273rd day of the year; 273oK(to the nearest integer)is the freezing point of water, or 0oC

OOOOH wait, 273 = 13*7*3, and 1373 is also prime.. and There are only two sphenic numbers consisting of concatenation of distinct prime numbers, this is the smaller of the two.(sphenic or wedge numbers are products of three distinct primes) *Prime curios

273 is a repdigit in hexdecimal, or base 16 (111) 16^2 + 16 + 1, and in base 20(vigesimal), where it looks like a bad report card (DD)

273 = 47^2 - 44^2 and also 137^2 - 136^2

Prime Curios says that 273^10 - 10^273 is the smallest n for which this expression is prime. There are no more year days that exhibit this relationship.

Prime Curios includes this tasty factoid, the prime factors of 273 = 3 x 7 x 13, and if concatenated in reverse order, 1373, it is prime.

273 is a Palindrome in base 2(100010001). 2^8 + 2^4 + 2^0. Also a Palindrome in base 4 (10101) , 4^4 + 4^2 + 4^0.

273 is the product of two consecutive Fibonacci numbers (13 x 21) and is thus a Golden rectangle Number. Each of these have side ratios that approximate a Golden Rectangle as they grow larger . 21/13=1.615....

There are 273 distinct ways to connect 6 points with 5 straight non-crossing lines. Here they are:

Only 28 are unique up to reflection and rotation,

EVENTS

1717 Colin Maclaurin (1698–1746), age 19, was appointed to the Mathematics Chair at Marischal College, Aberdeen, Scotland. This is the youngest at which anyone has been elected chair (full professor) at a university. (Guinness) In 1725 he was made Professor at Edinburgh University on the recommendation of Newton. *VFR

At eleven, Maclaurin, a child prodigy at the time, entered the University of Glasgow. He graduated Master of Arts three years later by defending a thesis on the Power of Gravity, and remained at Glasgow to study divinity until he was 19, when he was elected professor of mathematics in a ten-day competition at Marischal College and University in Aberdeen. This record as the world's youngest professor endured until March 2008, when the record was officially given to Alia Sabur, Alia Sabur.  On 19 February 2008, at 18 years of age (3 days before her 19th birthday), she was appointed to the position of International Professor as Research Liaison with Stony Brook University by the Dept. of Advanced Technology Fusion at Konkuk University in Seoul, South Korea. The position was a temporary, one-year contract which she chose not to renew.

 Colin MacLaurin *Wik

1810 The University of Berlin opened. *VFR It is now called The Humboldt University of Berlin and is Berlin's oldest university. It was founded as the University of Berlin (Universität zu Berlin) by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt, whose university model has strongly influenced other European and Western universities.*Wik

1846 First use of either for tooth extraction by American dentist William T G Morten.  He would give a public demonstration on October 16 of his use of the anesthesia.

*Lucio Gelmini@gelminil7

1890 In his desk notes Sir George Biddell Airy writes about his disappointment on finding an error in his calculations of the moon’s motion. “ I had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.” *George Biddell Airy and Wilfrid Airy (ed.), Autobiography of Sir George Biddell Airy (1896), 350.

1893 Felix Klein visits Worlds fair in Chicago, then visits many colleges. On this day the New York Mathematical society had a special meeting to honor him. *VFR

1921 William H Schott patented the "hit-and-miss synchronizer for his clocks. The Shortt-Synchronome free pendulum clock was a complex precision electromechanical pendulum clock invented in 1921 by British railway engineer William Hamilton Shott in collaboration with horologist Frank Hope-Jones, and manufactured by the Synchronome Co., Ltd. of London, UK. They were the most accurate pendulum clocks ever commercially produced, and became the highest standard for timekeeping between the 1920s and the 1940s, after which mechanical clocks were superseded by quartz time standards. They were used worldwide in astronomical observatories, naval observatories, in scientific research, and as a primary standard for national time dissemination services. The Shortt was the first clock to be a more accurate timekeeper than the Earth itself; it was used in 1926 to detect tiny seasonal changes (nutation) in the Earth's rotation rate. *Wik

 *Wikipedia

1929
The first manned rocket-powered flight was made by German auto maker Fritz von Opel. His Sander RAK 1 was a glider powered by sixteen 50 pound thrust rockets. In it, Opel made a successful flight of 75 seconds, covering almost 2 miles near Frankfurt-am-Main, Germany. This was his final foray as a rocket pioneer, having begun by making several test runs (some in secret) of rocket propelled vehicles. He reached a speed of 238 km/h (148 mph) on the Avus track in Berlin on 23 May, 1928, with the RAK 2. Subsequently, riding the RAK 3 on rails, he pushed the world speed record up to 254 km/h (158 mph). The first glider pilot to fly under rocket power, was another German, Friedrich Staner, who flew about 3/4-mile on 11 Jun 1928.*TIS

1938  On this day in 1938, Olga Taussky married Jack Todd. 50 years later she said:-
"My life and my career would have been so different if my Irishman had not come along."
Olga Taussky-Todd was an Austrian born mathematician who worked on algebraic number theory and matrix theory.
John Todd was an Irish-born numerical analyst.

 Olga Taussky photo by Paul Erdos

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2010 The ignoble prizes, presented on this date, included an engineering for collecting Whale Snot, and a MANAGEMENT PRIZE: for demonstrating mathematically that organizations would become more efficient if they promoted people at random. See all the 2010 winners here.

BIRTHS

1550 Michael Maestlin (30 September 1550, Göppingen – 20 October 1631, Tübingen) was a German astronomer who was Kepler's teacher and who publicised the Copernican system. Perhaps his greatest achievement (other than being Kepler's teacher) is that he was the first to compute the orbit of a comet, although his method was not sound. He found, however, a sun centerd orbit for the comet of 1577 which he claimed supported Copernicus's heliocentric system. He did show that the comet was further away than the moon, which contradicted the accepted teachings of Aristotle. Although clearly believing in the system as proposed by Copernicus, he taught astronomy using his own textbook which was based on Ptolemy's system. However for the more advanced lectures he adopted the heliocentric approach - Kepler credited Mästlin with introducing him to Copernican ideas while he was a student at Tübingen (1589-94).*SAU The first known calculation of the reciprocal of the golden ratio as a decimal of "about 0.6180340" was written in 1597 by Maestlin in a letter to Kepler. He is also remembered for :
Catalogued the Pleiades cluster on 24 December 1579. Eleven stars in the cluster were recorded by Maestlin, and possibly as many as fourteen were observed.
Occultation of Mars by Venus on 13 October 1590, seen by Maestlin at Heidelberg. *Wik

1715 Étienne Bonnot de Condillac (30 Sep 1715; 3 Aug 1780) French philosopher, psychologist, logician, economist, and the leading advocate in France of the ideas of John Locke (1632-1704). In his works La Logique (1780) and La Langue des calculs (1798), Condillac emphasized the importance of language in logical reasoning, stressing the need for a scientifically designed language and for mathematical calculation as its basis. He combined elements of Locke's theory of knowledge with the scientific methodology of Newton; all knowledge springs from the senses and association of ideas. Condillac devoted careful attention to questions surrounding the origins and nature of language, and enhanced contemporary awareness of the importance of the use of language as a scientific instrument.*TIS

1774 Carl Wilhelm Scheele sent a letter to Antoine Lavoisier announcing the discovery of oxygen (O). Unfortunately the letter from the Swedish chemist was never acknowledged and Joseph Priestly published the discovery first. Scheele was trounced in the announcement of other discoveries as well, he identified molybdenum, tungsten, barium, hydrogen, and chlorine before Humphry Davy, among others. Scheele discovered organic acids tartaric, oxalic, uric, lactic, and citric, as well as hydrofluoric, hydrocyanic, and arsenic acids. (Not bad for a chemist you never heard of.) For this reason, Isaac Asimov nicknamed him “hard-luck Scheele” *rsc.org , *Wik
An interpretation of Scheele from the late 19th or early 20th century as no contemporary portraits of him are known (by xylographer Ida Amanda Maria Falander (1842-1927))

1775 Robert Adrain (30 September 1775 – 10 August 1843) . Although born in Ireland he was one of the ﬁrst creative mathematicians to work in America. *VFR Adrain was appointed as a master at Princeton Academy and remained there until 1800 when the family moved to York in Pennsylvania. In York Adrain became Principal of York County Academy. When the first mathematics journal, the Mathematical Correspondent, began publishing in 1804 under the editorship of George Baron, Adrain became one of its main contributors. One year later, in 1805, he moved again this time to Reading, also in Pennsylvania, where he was appointed Principal of the Academy.
After arriving in Reading, Adrain continued to publish in the Mathematical Correspondent and, in 1807, he became editor of the journal. One has to understand that publishing a mathematics journal in the United States at this time was not an easy task since there were only two mathematicians capable of work of international standing in the whole country, namely Adrain and Nathaniel Bowditch. Despite these problems, Adrain decided to try publishing his own mathematics journal after he had edited only one volume of the Mathematical Correspondent and, in 1808, he began editing his journal the Analyst or Mathematical Museum.
With so few creative mathematicians in the United States the journal had little chance of success and indeed it ceased publication after only one year. After the journal ceased publication, Adrain was appointed professor of mathematics at Queen's College (now Rutgers University) New Brunswick where he worked from 1809 to 1813. Despite Queen's College trying its best to keep him there, Adrain moved to Columbia College in New York in 1813. He tried to restart his mathematical journal the Analyst in 1814 but only one part appeared. In 1825, while he was still on the staff at Columbia College, Adrain made another attempt at publishing a mathematical journal. Realising that the Analyst had been too high powered for the mathematicians of the United States, he published the Mathematical Diary in 1825. This was a lower level publication which continued under the editorship of James Ryan when Adrain left Columbia College in 1826. *SAU
This is the title page of an American edition of Charles Hutton’s A Course of Mathematics for the Use of Academies as well as Private Tuition. Hutton (1737-1823) was a self taught mathematician and mathematics instructor at the British Royal Military Academy, in Woolwich, England. He wrote this text for his students and included all the mathematics he believed a military cadet of the time should know.

When the United States Military Academy formally opened at West Point in 1801, the study of this book was included for its students. Robert Adrain (1775–1843), a leading American mathematician, revised the book for an American audience in 1812. The copy shown below is the third American edition of 1818.

Eventually, the British version experienced thirteen reprints and its American counterpart went through four reprints. The text was used at West Point until 1823. *MAA Mathematical Treasures

 portrait by Charles C. Ingham *Wik

1870 Jean-Baptiste Perrin (30 Sep 1870; 17 Apr 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids, verified Albert Einstein's explanation of this phenomenon and thereby confirmed the atomic nature of matter. Using a gamboge emulsion, Perrin was able to determine by a new method, one of the most important physical constants, Avogadro's number (the number of molecules of a substance in so many grams as indicated by the molecular weight, for example, the number of molecules in two grams of hydrogen). The value obtained corresponded, within the limits of error, to that given by the kinetic theory of gases. For this achievement he was honoured with the Nobel Prize for Physics in 1926.*TIS

1882 Hans Wilhelm Geiger  (30 Sep 1882; 24 Sep 1945) was a German physicist who introduced the Geiger counter, the first successful detector of individual alpha particles and other ionizing radiations. After earning his Ph.D. at the University of Erlangen in 1906, he collaborated at the University of Manchester with Ernest Rutherford. He used the first version of his particle counter, and other detectors, in experiments that led to the identification of the alpha particle as the nucleus of the helium atom and to Rutherford's statement (1912) that the nucleus occupies a very small volume in the atom. The Geiger-Müller counter (developed with Walther Müller) had improved durability, performance and sensitivity to detect not only alpha particles but also beta particles (electrons) and ionizing electromagnetic photons. Geiger returned to Germany in 1912 and continued to investigate cosmic rays, artificial radioactivity, and nuclear fission.*TIS
A "two-piece" bench-type Geiger–Müller counter using a cylindrical end-window detector connected to an electronics module with analogue readout

1883 Ernst David Hellinger (1883 - 1950) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. *SAU

1894 Dirk Jan Struik (30 Sept 1894 , 21 Oct 2000) Dirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician and Marxian theoretician who spent most of his life in the United States.
In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time.
Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994),
Mathematics, and Marxism.
It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics.
Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.
In 1950 Stuik published his Lectures on Classical Differential Geometry.
Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.
Struik died October 21, 2000, 21 days after celebrating his 106th birthday. *Wik

1905 Sir Nevill F. Mott (30 Sep 1905; 8 Aug 1996) English physicist who shared (with P.W. Anderson and J.H. Van Vleck of the U.S.) the 1977 Nobel Prize for Physics for his independent researches on the magnetic and electrical properties of amorphous semiconductors. Whereas the electric properties of crystals are described by the Band Theory - which compares the conductivity of metals, semiconductors, and insulators - a famous exception is provided by nickel oxide. According to band theory, nickel oxide ought to be a metallic conductor but in reality is an insulator. Mott refined the theory to include electron-electron interaction and explained so-called Mott transitions, by which some metals become insulators as the electron density decreases by separating the atoms from each other in some convenient way.*TIS

1913 Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish and American mathematician born in Warsaw, Russian Empire (now in Poland) and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.
He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor was Karol Borsuk. His main interest was algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (whose names the Eilenberg–Steenrod axioms bear), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.
Eilenberg was a member of Bourbaki and with Henri Cartan, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules. Eilenberg also wrote an important book on automata theory. The X-machine, a form of automaton, was introduced by Eilenberg in 1974. *Wik

1916 Richard Kenneth Guy (born September 30, 1916, Nuneaton, Warwickshire -  March 9,  2020 ) is a British mathematician, and Professor Emeritus in the Department of Mathematics at the University of Calgary.
He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory, but he has also published over 100 papers and books covering combinatorial game theory, number theory and graph theory.
He is said to have developed the partially tongue-in-cheek "Strong Law of Small Numbers," which says there are not enough small integers available for the many tasks assigned to them — thus explaining many coincidences and patterns found among numerous cultures.
Additionally, around 1959, Guy discovered a unistable polyhedron having only 19 faces; no such construct with fewer faces has yet been found. Guy also discovered the glider in Conway's Game of Life.
Guy is also a notable figure in the field of chess endgame studies. He composed around 200 studies, and was co-inventor of the Guy-Blandford-Roycroft code for classifying studies. He also served as the endgame study editor for the British Chess Magazine from 1948 to 1951.
Guy wrote four papers with Paul Erdős, giving him an Erdős number of 1. He also solved one of Erdős problems.
His son, Michael Guy, is also a computer scientist and mathematician. *Wik

1918 Leslie Fox (30 September 1918 – 1 August 1992) was a British mathematician noted for his contribution to numerical analysis. *Wik

DEATHS

1953 Lewis Fry Richardson, FRS (11 October 1881 - 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration.
*Big whirls have little whirls,
That feed on their velocity;
And little whirls have lesser whirls,
And so on to viscosity.
~Lewis Richardson

1985 Dr. Charles Francis Richter (26 Apr 1900, 30 Sep 1985) was an American seismologist and inventor of the Richter Scale that measures earthquake intensity which he developed with his colleague, Beno Gutenberg, in the early 1930's. The scale assigns numerical ratings to the energy released by earthquakes. Richter used a seismograph (an instrument generally consisting of a constantly unwinding roll of paper, anchored to a fixed place, and a pendulum or magnet suspended with a marking device above the roll) to record actual earth motion during an earthquake. The scale takes into account the instrument's distance from the epicenter. Gutenberg suggested that the scale be logarithmic so, for example, a quake of magnitude 7 would be ten times stronger than a 6.*TIS  The quote "logarithmic plots are a device of the devil" is attributed to Richter.

2014 Martin Lewis Perl (June 24, 1927 – September 30, 2014) was an American physicist who won the Nobel Prize in Physics in 1995 for his discovery of the tau lepton.
He received his Ph.D. from Columbia University in 1955, where his thesis advisor was I.I. Rabi. Perl's thesis described measurements of the nuclear quadrupole moment of sodium, using the atomic beam resonance method that Rabi had won the Nobel Prize in Phyics for in 1944.
Following his Ph.D., Perl spent 8 years at the University of Michigan, where he worked on the physics of strong interactions, using bubble chambers and spark chambers to study the scattering of pions and later neutrons on protons.[1] While at Michigan, Perl and Lawrence W. Jones served as co-advisors to Samuel C. C. Ting, who earned the Nobel Prize in Physics in 1976.
Seeking a simpler interaction mechanism to study, Perl started to consider electron and muon interactions. He had the opportunity to start planning experimental work in this area when he moved in 1963 to the Stanford Linear Accelerator Center (SLAC), then being built in California. He was particularly interested in understanding the muon: why it should interact almost exactly like the electron but be 206.8 times heavier, and why it should decay through the route that it does. Perl chose to look for answers to these questions in experiments on high-energy charged leptons. In addition, he considered the possibility of finding a third generation of lepton through electron-positron collisions. He died after a heart attack at Stanford University Hospital on September 30, 2014 at the age of 87. *Wik

2017 Vladimir Voevodsky (Jun 4, 1966 - Sep 30, 2017) formerly a gifted but restless student who flunked out of college out of boredom before emerging as one of the most brilliant and revolutionary mathematicians of his generation, died on Sept. 30 at his home in Princeton, N.J. He was 51.

Dr. Voevodsky was renowned for founding entirely new fields of mathematics and creating groundbreaking new tools for computers to confirm the accuracy of proofs. In 2002, he was awarded the Fields Medal, which recognizes brilliance and promise in mathematicians under 40.
He was “one of the giants of our time,” Thomas Hales, a mathematician at the University of Pittsburgh, said in an interview. Dr. Voevodsky, he said, transformed every field he touched. In his work using computers, for example, he upended mathematical thinking to such a degree that he changed the meaning of the equals sign.

He added: “His ideas gave a new way for all mathematicians to do what they do, a new foundation. The foundations of math are like a constitutional document that spells out the governing rules all mathematicians agree to play by. He has given us a new constitution.”

Vladimir Voevodsky was born in Moscow. His father, Alexander, directed a laboratory in experimental physics at the Russian Academy of Sciences; his mother, Tatyana Voevodskaya, was a chemistry professor at Moscow University. *obit NYTimes

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