## Tuesday 30 January 2024

### On This Day in Math - January 30

God may not play dice with the universe,
but something strange is going on with the prime numbers.
~Paul Erdos **

(Not realy, Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes.")

The 30th day of the year; 30 is the difference between 2 ,and $2^5$, so

But since 30 is also the difference between 6 and $6^2$,   then

Both the dodecahedron and the icosahedron have 30 edges. They may be positioned at a common center so that in the center of each of the 12 faces of the dodecahedron is one of the 12 vertices of the icosahedron, in the center of each of the 20 faces of the icosahedron is one of the 20 vertices of the dodecahedron, and the 30 edges of the dodecahedron and the 30 edges of the icosahedron cross each other at right angles at their midpoints. (I find this incredibly wonderful)

astounding to me, but 11+22+33...+3030 = 208492413443704093346554910065262730566475781 is prime Republic of Math ‏@republicofmath If there is another prime of this type, it will have over 20025 digits.

7! hours is 30 weeks

and from *@MathYearRound
30 = 2*3*5 (first 3 primes).
30 =${1}^{2}+{2}^{2}+{3}^{2}+{4}^{2}$(first 4 perfect squares).
30 = 1*1*2*3*5 (first 5 Fibonacci #).

EVENTS

10 BCE Solar eclipse in Iran, as reported on a cuneiform tablet from the British Museum *History of Astronomy ‏@hist_astro  (I have to admit that every time I look at this image it reminds me of the map of Michigan's lower peninsula, and that little chip up by the little finger is Grand Traverse Bay, which I see from my dining room)

1610 Galileo writes to Belisario Vinta, with notes on his long observation of the moon with a new twenty-power scope. A letter containing much of what was to appear about the Moon in Sidereus Nuncius, two months later. *Drake, Galileo at Work; 1978
Belisario Vinta was born in Volterra and became a Florentine citizen in 1579. He began a brilliant political career and held numerous offices, attaining the highest rank of First Secretary of State of the Grand Duchy. In this capacity he met Galileo during his teaching years at Padua and personally managed the negotiations which brought Galileo back to Tuscany after his astronomical discoveries. To Belisario Vinta goes the credit for choosing to call the moons of Jupiter the Medicean Planets and not, as Galileo had proposed, the Cosmic Planets after the name of Grand Duke Cosimo II (1590-1621). In a letter of February 10, 1610 Vinta wrote to Galileo: "[...] Your idea of naming the new planets you have discovered after His Highness is generous and heroic and in keeping with the your unique and wonderful genius. And since you have done me the honor of asking my opinion about what name to give to these planets, whether the Cosmic or the Medicean Stars, I openly state my feeling that the latter will be more appealing, in so far as the Greek word Cosmic can be taken in various ways and would perhaps not be wholly attributed by all to the glory of the royal name of the Medici Dynasty and their city-state of Florence, as would necessarily be the case of the name Medicean Stars. And so I firmly hold to the latter".

1830 In a letter to Laplace, Gauss writes about a "curious problem" that he had been working on for twelve years.  He gives the limiting value of  the frequency of distribution of positive integers in the continued fraction of a random number (now called the Gauss-Kuzmin Distribution) as $lo{g}_{2}\left(1+x\right)$ . He then asks if Laplace can offer help in finding the error term. *Math World
In mathematics, the Gauss–Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929.*Wik

1897 Mary Frances Winston elected to membership in the American Mathematical Society. The previous year she received her PhD at G¨ottingen, being the ﬁrst American woman to receive a PhD in mathematics at a German university. *G. B. Price, History of the Department of Mathematics of the University of Kansas, 1866–1970, p. 70
 *Wik

1884 Sonja Kovelevskiaya gives her ﬁrst university lecturer. This was the ﬁrst regular lecture by a woman at a research institution in any ﬁeld in modern times. [The Mathematical Intelligencer, 6(1984), no. 1, p. 29] *VFR

1925 The U.S. History of Science Society was incorporated under the laws of the District of Columbia. The ﬁrst president was Lawrence Joseph Henderson (1878–1924). The movement to form the society was begun by David Eugene Smith and today is the most important historical society in the world. *VFR

1952 Two New Primes Found with SWAC. Using the Standards Western Automatic Computer (SWAC), researchers found two new prime numbers the first time they attempted a prime-searching program on the computer. Within the year, three other primes had been found. The National Bureau of Standards funded construction of the SWAC in Los Angeles in 1950 and it ran, in one form or another, until 1967.
*CHM {The first two primes found with SWAC were M521, M607. In 1951 Ferrier used a mechanical desk calculator to find the 44 digit prime (2148+1)/17 = 20988936657440586486151264256610222593863921.
The first primes found with an electronic computer were by Miller and Wheeler (Nature, 168  in 1951  they found several new primes, including the 79 digit 180 (2127-1)2+1 }

1958 The first two-way, moving sidewalk, 1,425 feet long, was put in service at Love Field Air Terminal in Dallas, TX. It consisted of three loops. In each loop a continuous rubber carpet was attached to a continuous train of wheeled pallets, flexibly interconnected so they could follow vertical or horizontal curves as required. It was known not only as a moving sidewalk, but also as a passenger conveyor.  The first commercial moving walkway in the United States was installed in 1954 in Jersey City, New Jersey, inside the Hudson & Manhattan Railroad Erie station at the Pavonia Terminal. Named the "Speedwalk" and built by Goodyear, it was 84.5 meters (277 feet) long and moved up a 10 percent grade at a speed of 2.4 km/h (1.5 mph). The walkway was removed a few years later when traffic patterns at the station changed.
The first moving walkway debuted at the World's Columbian Exposition of 1893, in Chicago, Illinois, in the United States as The Great Wharf Moving Sidewalk and was designed by architect Joseph Lyman Silsbee. It had two different divisions: one where passengers were seated, and one where riders could stand or walk. It ran in a loop down the length of a lakefront pier to a casino.
The Great Wharf, Moving Sidewalk, 1893

1982 First computer virus, the Elk Cloner, written by 15-year old Rich Skrenta, is found in the wild. It infects Apple II computers via floppy disk. *Wik

1988 Science News reports that Noam D. Elkies, age 21, of Harvard found four fourth-powers whose sum is another fourth-power, thereby providing a counterexample to a conjecture of Euler in 1769. (Euler's conjecture was that the sum of the first n integers each raised to the nth power can not be an nth power.) The smallest number in his counterexample had eight digits. Later Roger Frye of Thinking Machines Corporation, Cambridge, MA, found the smallest counterexample:
95,8004 + 217,5194 + 414,5604 + 414 5604 = 422,4184 .
This took some 100 hours on a Connection Machine. Can you ﬁgure out how to verify this example using your calculator (which only displays 8 or 10 digits)? [Mathematics Magazine 61 (1988), p 130; Science 239 (1988), p 464]. *VFR
(Euler's general conjecture had been proven false by L. J. Lander and T. R. Parkin in 1966 when they found a counterexample for fifth powers. Elkies had suggested the computer approach that provided the minimal solution. It is still unknown if there are counterexamples above n=5)

1990 Ruth Lawrence sends a paper on homological representations of the Hecke algebra, introducing, among other things, certain novel linear representations of the braid group, the Lawrence–Krammer representation to the journal, Communications in Mathematical Physics
*Wik

1996 Yuji Hyakutake in Japan discovered a new comet using 25x150 binoculars. The comet was designated Comet C/1996 B2 (Hyakutake). As subsequent observations of the new comet were obtained, Brian Marsden from the IAU Central Bureau was able to compute the comet's orbital elements, and these computations indicated that the comet will pass as close as 0.10 AU (9.3 million miles) from the Earth on March 25, 1996! The comet has become a bright naked-eye object and remained so in March, April and May in 1996. The comet had exceeded expectations, becoming the brightest comet since Comet West in 1976. A long tail of up to 100 degrees was reported, and small fragments have been observed to break off the main nucleus. Comet Hyakutake is indeed the Great Comet of 1996. *jpl.nasa
Hyakutake discovered C/1996 B2 while looking for C/1995 Y1, a comet he had discovered a few weeks before. He died in Kokubu, Kagoshima, in 2002 at age 51 of an aneurysm which had led to internal bleeding. *Wik
Hyakutake is a long-period comet. Before its most recent passage through the Solar System, its orbital period was about 17,000 years, but the gravitational perturbation of the giant planets has increased this period to 70,000 years

BIRTHS

1619 Michelangelo Ricci  (30 Jan 1619 in Rome, Italy - : 12 May 1682 in Rome) In 1666, he found the tangent lines to the parabolas of Fermat. *VFR Michelangelo Ricci was a friend of Torricelli; in fact both were taught by Benedetti Castelli. He studied theology and law in Rome and at this time he became friends with René de Sluze. It is clear that Sluze, Torricelli and Ricci had a considerable influence on each other in the mathematics which they studied.
Ricci made his career in the Church. His income came from the Church, certainly from 1650 he received such funds, but perhaps surprisingly he was never ordained. Ricci served the Pope in several different roles before being made a cardinal by Pope Innocent XI in 1681.
Ricci's main work was Exercitatio geometrica, De maximis et minimis (1666) which was later reprinted as an appendix to Nicolaus Mercator's Logarithmo-technia (1668). It only consisted of 19 pages and it is remarkable that his high reputation rests solely on such a short publication.
In this work Ricci finds the maximum of xm(a - x)n and the tangents to ym = kxn. The methods are early examples of induction. He also studied spirals (1644), generalized cycloids (1674) and states explicitly that finding tangents and finding areas are inverse operations (1668). *SAU

1755 Nikolai Fuss (30 Jan 1755 in Basel, Switzerland - 4 Jan 1826 in St Petersburg, Russia) was a Swiss mathematician whose most important contribution was as amanuensis to Euler after he lost his sight. Most of Fuss's papers are solutions to problems posed by Euler on spherical geometry, trigonometry, series, differential geometry and differential equations. His best papers are in spherical trigonometry, a topic he worked on with A J Lexell and F T Schubert. Fuss also worked on geometrical problems of Apollonius and Pappus. He made contributions to differential geometry and won a prize from the French Academy in 1778 for a paper on the motion of comets near some planet Recherche sur le dérangement d'une comète qui passe près d'une planète. Fuss won other prizes from Sweden and Denmark. He contributed much in the field of education, writing many fine textbooks. *SAU
Nicholas Fuss was an amanuensis to Euler for 10 years and and married one of Euler's granddaughters after his death: Johann Albrecht Euler's daughter Albertine. He gave the Eulogy for Euler's funeral

1805 Edward Sang,(30 Jan 1805 in Kirkcaldy, Fife, Scotland - 23 Dec 1890) A native of Fife, Sang wrote extensively on mathematical, mechanical, optical and actuarial topics. *SAU

1865 Georg Landsberg (30 Jan 1865 , 14 Sept 1912) studied the theory of functions of two variables and also the theory of higher dimensional curves. In particular he studied the role of these curves in the calculus of variations and in mechanics.
He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums. His most important work, however was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen (Leipzig, 1902) which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years. *SAU

1911 Marie Paris Pişmiş de Recillas (30 January 1911 – 1 August 1999) was an Armenian-Mexican astronomer.

Pişmiş was born Mari Sukiasian (Armenian: Մարի Սուքիասեան) in 1911, in Ortaköy, Istanbul. She completed her high school studies at Üsküdar American Academy. In 1937, she became the first woman to get a Ph.D. from the Science Faculty of Istanbul University. Her advisor was Erwin Finlay Freundlich. Later, she went to Harvard University where she met her future husband Félix Recillas, a Mexican mathematician. They settled in Mexico, and she became the first professional astronomer in Mexico. According to Dorrit Hoffleit, "she is the one person most influential in establishing Mexico’s importance in astronomical education and research".

For more than 50 years she worked at UNAM which awarded her a number of prizes including the "Science Teaching Prize". She was a member of the Mexican Academy of Sciences.

Pişmiş studied among others the kinematics of galaxies, H II nebulae, the structure of open star clusters and planetary nebulae. She compiled the catalogue Pismis of 24 open clusters and 2 globular clusters in the southern hemisphere.

In 1998, she published an autobiography entitled "Reminiscences in the Life of Paris Pişmiş: a Woman Astronomer". She died in 1999. According to her wish, she was cremated. Her daughter Elsa Recillas Pishmish, son-in-law Carlos Cruz-González, and grand-daughter Irene Cruz-González also became astronomers. *Wik

1918 Heinz Rutishauser (30 January 1918 in Weinfelden, Switzerland; 10 November 1970 in Zürich) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science. *Wik

1925 Douglas Engelbart (January 30, 1925 – July 2, 2013), best known for inventing the computer mouse. Engelbart publicly demonstrated the mouse at a computer conference in 1968, where he also showed off work his group had done in hypermedia and on-screen video teleconferencing. The founder of the Bootstrap Institute, Engelbart has 20 patents to his name.*CHM

DEATHS

1910  Granville Tailer Woods (April 23, 1856 – January 30, 1910) was an American inventor who held more than 50 patents in the United States. He was the first African American mechanical and electrical engineer after the Civil War. Self-taught, he concentrated most of his work on trains and streetcars. One of his inventions is the Synchronous Multiplex Railway Telegraph, a variation of the induction telegraph that relied on ambient static electricity from existing telegraph lines to send messages between train stations and moving trains.
Granville T. Woods invented and patented Tunnel Construction for the electric railroad system and was referred to by some as the "Black Edison". Over the course of his lifetime, Granville Woods obtained more than 50 patents for inventions including an automatic brake and an egg incubator and for improvements to other technologies such as the safety circuit, telegraph, telephone, and phonograph.*Wik

1948 Orville Wright (August 19, 1871 – January 30, 1948) American inventor and aviator, who with his brother, Wilbur, invented the first powered airplane, Flyer, capable of sustained, controlled flight (17 Dec 1903). At Kitty Hawk, North Carolina, Orville made the first ever manned powered flight, airborn for 12 sec. By 1905, they had improved the design, built and and made several long flights in Flyer III, which was the first fully practical airplane (1905), able to fly up to 38-min and travel 24 miles (39-km). Their Model A was produced in 1908, capable of flight for over two hours of flight. They sold considerable numbers, but European designers became strong competitors. After Wilbur died of typhoid in 1912, Orville sold his interest in the Wright Company in 1915. *TIS
 *Wik

1954 Gino Benedetto Loria
(19 May 1862 in Mantua, Italy - 30 Jan 1954 in Genoa, Italy) In his day, Loria was arguably the pre-eminent historian of mathematics in Italy. A full professor of higher geometry at the University of Genoa beginning in 1891, Loria wrote the history of mathematics as a mathematician writing for other mathematicians. He emphasised this approach repeatedly in his works. For instance, in the introduction to his 'Storia delle matematiche dall'alba della civilità al tramonto del secolo XIX' (History of Mathematics from the Dawn of Civilisation to the End of the 19th Century), he stated that general history of mathematics was written "by a mathematician for mathematicians". *SAU
 *Wik

1977 Harry Clyde Carver (December 4, 1890 – January 30, 1977) was an American mathematician and academic, primarily associated with the University of Michigan. He was a major influence in the development of mathematical statistics as an academic discipline.
Born in Waterbury, Connecticut, Carver was educated at the University of Michigan, earning his B.S. degree in 1915, and the next year becoming an instructor in mathematics; he taught statistics in actuarial applications. At the time, the University of Michigan was only the second such institution in the United States to offer this type of course, after the pioneering Iowa State University. Carver was appointed assistant professor at Michigan in 1918, then associate professor (1921) and full professor (1936); during this period the University's program in mathematical statistics and probability underwent significant expansion.
In 1930 Carver founded the journal Annals of Mathematical Statistics, which over time became an important periodical in the field. Financial support, however, was lacking in the midst of the Great Depression; in January 1934 Carver undertook financial responsibility for the Annals and maintained the existence of the journal at his own expense. In 1935 he helped to start the Institute of Mathematical Statistics, which in 1938 assumed control over the journal; Samuel S. Wilks succeeded Carver as editor in the same year. The Institute has named its Harry C. Carver Medal after him.
With the coming of World War II, Carver devoted his energies to solving problems in aerial navigation, an interest he maintained for the remainder of his life. *Wik

1991 John Bardeen (23 May 1908, 30 Jan 1991) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS
##### Bell Labs scientists John Bardeen, William Shockley, and Walter Brattain.

1992 Dom George Frederick James Temple​ FRS(born 2 December 1901, London; died 30 January 1992, Isle of Wight) was an English mathematician, recipient of the Sylvester Medal in 1969. He was President of the London Mathematical Society in the years 1951-1953.[2]
Temple took his first degree as an evening student at Birkbeck College, London, between 1918 and 1922, and also worked there as a research assistant. In 1924 he moved to Imperial College as a demonstrator, where he worked with Professor Sydney Chapman. After a period spent with Eddington at Cambridge, he returned to Imperial as reader in mathematics. He was appointed professor of mathematics at King's College London in 1932, where he returned after war service with the Royal Aircraft Establishment at Farnborough. In 1953 he was appointed Sedleian Professor of Natural Philosophy at the University of Oxford, a chair which he held until 1968, and in which he succeeded Chapman. He was also an honorary Fellow of Queen's College, Oxford.
After the death of his wife in 1980, Temple, a devout Christian, took monastic vows in the Benedictine order and entered Quarr Abbey on the Isle of Wight, where he remained until his death. *Wik

1998 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

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