## Monday 17 June 2024

### On This Day in Math - June 17

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I have made, I ended up in the domain of mathematics, Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

M. C. Escher, Quoted in To Infinity and Beyond, E Maor (Princeton 1991)

The 168th day of the year; there are 168 prime numbers less than 1000. *Prime Curios

168 is the product of the first two perfect numbers. *jim wilder ‏@wilderlab

The smallest number that is the product of reversible number  in two different ways is 2520 = 120 x 021 = 210 x 012.
The smallest with no zeros is   144648 = 861 x 168 = 492 x 294.  The two smaller numbers in each pair (168 & 294) are called Reversible product twins.
The number 144646 is called a double reversible number.  Sometimes one of the two numbers is a palindrome, such as, 63504 = 252^2 = 441 x 144.  This one is interesting because it involves so many square numbers.   *HT *Number Recreations by Shyam Sunder Gupta ("http://www.shyamsundergupta.com/")

$2^{168} = 374144419156711147060143317175368453031918731001856$ lacks the digit 2; no larger 2n exists for $n \lt 10^{399}$ that is not pandigital.

There are 168 hours in a week.

168 is also the number of moves that it takes a dozen frogs to swap places with a dozen toads on a strip of 2(12) + 1=25 squares (or positions, or lily pads) where a move is a single slide or jump. This activity dates back to the 19th century, and the incredible recreational mathematician, Edouard Lucas *OEIS.
Prof. Singmasters Chronology of Recreational Mathematics suggests that this was first introduced in the American Agriculturalist in 1867, and I have an image of the puzzle below. The fact that they call it, "Spanish Game" suggests it has an older antecedent. (anyone know more?)

EVENTS

1713  Leibniz replies from Vienna to Johan (I) Bernoulli's letter of June 7th informing him of the book from London accusing Leibniz of "plagiary".  "I have not yet seen the little English book directed against me. .... it appears that he (Newton) no more knew our calculus than Apollonius knew the algebraic calculus of Viete and Descartes." In this letter he will deny being the author of a critical review of Newton's tracts in the Arcta Eruditorum. (A lie.) *The Correspondence of Isaac Newton

image: Statues of Isaac Newton and Gottfried Wilhelm Leibniz in the courtyard of the Oxford University Museum of Natural History, collage

1867 Nobel invented dynamite. It is from this invention that he earned the fortune that he used to endow the Nobel Prizes.*VFR
There is a well known story about the origin of the Nobel Prize, although historians have been unable to verify it and some dismiss the story as a myth. In 1888, the death of his brother Ludvig supposedly caused several newspapers to publish obituaries of Alfred in error. One French newspaper condemned him for his invention of military explosives—in many versions of the story, dynamite is quoted, although this was mainly used for civilian applications—and this is said to have brought about his decision to leave a better legacy after his death. The obituary stated, Le marchand de la mort est mort ("The merchant of death is dead"), and went on to say, "Dr. Alfred Nobel, who became rich by finding ways to kill more people faster than ever before, died yesterday." Nobel read the obituary and was appalled at the idea that he would be remembered in this way. His decision to posthumously donate the majority of his wealth to found the Nobel Prize has been credited to him wanting to leave behind a better legacy. However, it has been questioned whether or not the obituary in question actually existed.

On 27 November 1895, at the Swedish-Norwegian Club in Paris, Nobel signed his last will and testament and set aside the bulk of his estate to establish the Nobel Prizes, to be awarded annually without distinction of nationality

A well known incorrect reason for why there is no Nobel prize in that some mathematician seduced Nobel's wife.  One such story is frequently attributed to Niels Bohr, who used to say that there is no Nobel Prize in mathematics because the Swedish mathematician Gösta Mittag-Leffler had seduced Nobel’s wife. When Bohr was reminded that this was impossible, because Nobel had never married, Bohr answered, “Never let facts interfere with a good story.”

1870  Benjamin Peirce, Superintendent U. S. Coast Survey, sends letter of introduction for his son to August De Morgan, "I presume upon the unseen brotherhood of science to introduce to you my son Charles S. Peirce Esq. who is a devoted student of Logic and I think that he has original thoughts which you may regard as deserving your consideration. He carries with him a memoir which he has written upon one of the subjects of your own learned investigations... " *Universidad de Navarra

 C. S. Pierce, *Wik

1928,  Amelia Earhart  embarked on a trans-Atlantic flight from Newfoundland to Wales; she was  the first woman to fly across the Atlantic Ocean, though as a passenger  in a plane piloted by Wilmer Stultz. In 1932, she became the first  woman to fly solo across that ocean.  Wilmer Stutz flew the plane, with Louis Gordon as co-pilot, as the trio made their challenging--and successful--journey from Newfoundland to Wales.
After becoming the first woman to fly across the Atlantic Ocean in 1928, Amelia Earhart was immediately -- inevitably -- compared to the similarly lanky Charles Lindbergh, whose 1927 solo transatlantic flight made him the world's most famous pilot. For his part, Lindbergh appreciated all that "Lady Lindy" did to bring press attention to aviation -- and to take it off him.

BIRTHS

1714  César-François Cassini de Thury (17 June 1714 – 4 September 1784), French astronomer and geodesist (Cassini III), who continued surveying work he began while assisting his father, Jacques Cassini (Cassini II), resulting in the first topographical map of France produced by modern principles. His grandfather, Giovanni Domenico Cassini  (Cassini I) discovered four satellites of Saturn, a band on planet's  surface, and that its ring was subdivided. Cassini I was the first to  assume effective direction (1671) of the new observatory established by  the Académie Royale des Sciences in Paris, which his descendants in turn  continued. Cassini III was the first official director of the  observatory when the post was created by the king in 1771. His son was  Jean-Dominique Cassini (Cassini IV) *TIS

Image: The Paris meridian from Paris to Dunkirk, with triangulations, engraving, César-François Cassini de Thury, La meridienne de l'observatoire Royal de Paris, 1744 (Linda Hall Library)

 Victorian picture "Leviathan of Parsonstown" *Wik

1800  William Parsons (17 June 1800 – 31 October 1867), 3rd Earl of Rosse was an Irish astronomer  who built the largest reflecting telescope of the 19th century. He  learned to polish metal mirrors (1827) and spent the next few years  building a 36-inch telescope. He later completed a giant 72-inch  telescope (1845) which he named "Leviathan," It remained the largest  ever built until decades after his death. He was the first to resolve  the spiral shape of objects - previously seen as only clouds - which  were much later identified as galaxies independent of our own Milky Way  galaxy and millions of light-years away. His first such sighting was  made in 1845, and by 1850 he had discovered 13 more. In 1848, he found  and named the Crab Nebula (because he thought it resembled a crab), by which name it is still known.*TIS

1832 Sir William Crookes, OM, FRS (17 June 1832 – 4 April 1919) was a British chemist and physicist who attended the Royal College of Chemistry, London, and worked on spectroscopy. He was a pioneer of vacuum tubes, inventing the Crookes tube.*Wik

 Crooke's tube, two views

1898 Maurits Cornelius Escher (17 June 1898 – 27 March 1972)   an artist whose works have included a considerable mathematical content.  He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *Wik

1903 Sir. William Valance Douglas Hodge (1903 -Jun 17, 2011 ).*VFR  Hodge also wrote, with Daniel Pedoe, a three-volume work Methods of Algebraic Geometry, on classical algebraic geometry, with much concrete content — illustrating though what Élie Cartan  called 'the debauch of indices', in its component notation. According  to Atiyah, this was intended to update and replace H. F. Baker's Principles of Geometry. *Wik

1906 Samuel Stanley Wilks (June 17, 1906 – March 7, 1964) was an American mathematician and academic who played an important role in the development of mathematical statistics, especially in regard to practical applications.
Born in Little Elm, Texas (Little Elm was once a quiet farm town, and today is one of the fastest growing municipalities in Texas) and raised on a farm, Wilks was educated at the University of Iowa, where he acquired his Ph.D. under Everett F. Linquist; his thesis dealt with a problem of statistical measurement in education, and was published in the Journal of Educational Psychology. Wilks became an instructor in mathematics at Princeton University in 1933; in 1938 he assumed the editorship of the journal Annals of Mathematical Statistics in place of Harry C. Carver. Wilks assembled an advisory board for the journal that included major figures in statistics and probability, among them Ronald Fisher, Jerzy Neyman, and Egon Pearson.
Wilks was named professor of mathematics and director of the Section of Mathematical Statistics at Princeton in 1944, and became chairman of the Division of Mathematics at the University in 1958. He was noted for his work on multivariate statistics and unit-weighted regression.
From the start of his career, Wilks favored a strong focus on practical applications for the increasingly abstract field of mathematical statistics; he also influenced other researchers, notably John Tukey, in a similar direction. Drawing upon the background of his thesis, Wilks worked with the Educational Testing Service in developing the standardized tests like the SAT that have had a profound effect on American education. He also worked with Walter Shewhart on statistical applications in quality control in manufacturing.
During World War II he was a consultant with the Office of Naval Research. Both during and after the War he had a profound impact on the application of statistical methods to all aspects of military planning.
The American Statistical Association named its Wilks Memorial Award in his honor.
Wilks' lambda distribution is a probability distribution related to two independent Wishart distributed variables. It is important in multivariate statistics and likelihood-ratio tests. *Wik

1908 Gunnar Af Hallstrom born. He determined the congruence axioms which Hilbert used in his famous axiomatization of geometry. *VFR

1919  William Kaye Estas  (June 17, 1919 – August 17, 2011) American psychologist, a leader in bringing mathematical methods into  psychological research, who was awarded the National Medal of Science in  1997 for "his fundamental theories of cognition and learning that  transformed the field of experimental psychology. His pioneering methods  of quantitative modeling and an insistence on rigor and precision  established the standard for modern psychological science." In his early  professional research he partnered with another pioneering psychologist  B. F. Skinner in studying animal learning and behavior. The  quantitative method they devised to measure emotional reactions is still  widely used today. From 1979, Estes focused on investigating human  memory and classification learning.

1939 Carlo Cercignani (17 June 1939 in Teulada – 7 January 2010 in Milan) was an Italian mathematician known for his work on the kinetic theory of gases. His contributions to the study of Boltzmann's equation include the proof of the H-theorem for polyatomic gases. The Cercignani conjecture is named after him.

Cercignani's conjecture is "sometimes true and always almost true", as proved by the Fields medalist mathematician Cedric Villani.

He is the author of several monographs and more than 300 papers in kinetic theory, as well as of a biography of Boltzmann. Cercignani was member of the French Academy of Sciences and of the Accademia dei Lincei. He received the Humboldt Prize in 1994.

DEATHS

1994 Frank Yates FRS (May 12, 1902 – June 17, 1994) was one of the pioneers of 20th century statistics.   He was born in Manchester. He spent two years teaching mathematics to secondary school pupils before heading to Africa where he was mathematical advisor on the Gold Coast Survey. He returned to England due to ill health and met and married a chemist, Margaret Forsythe Marsden, the daughter of a civil servant.  This marriage was dissolved in 1933 and he later married Pauline Penn,  previously the partner of the well-known architect. After her death in  1976 he married Ruth Hunt, his long-time secretary.
In 1931 Yates was appointed assistant statistician at Rothamsted Experimental Station by R.A. Fisher. In 1933 he became head of statistics when Fisher went to University College London. At Rothamsted he worked on the design of experiments, including contributions to the theory of analysis of variance and originating Yates' algorithm and the balanced incomplete block design.
During World War II he worked on what would later be called operational research.
After the war he worked on sample survey design and analysis. He became an enthusiast of electronic computers, in 1954 obtaining an Elliott 401 for Rothamsted and contributing to the initial development of statistical computing. In he was awarded the Guy Medal in Gold of the Royal Statistical Society, and in 1966 he was awarded the Royal Medal of the Royal Society. He retired from Rothamsted to become a Senior Research Fellow at Imperial College London. He died in 1994, aged 92, in Harpenden.*Wik

1996 Thomas S(amuel) Kuhn (July 18, 1922 – June 17, 1996) was an American historian of science, MIT professor, noted for The Structure of Scientific Revolutions (1962), one of the most influential works of history and philosophy written in the 20th century. His thesis was that science was not a steady, cumulative acquisition of knowledge, but it is "a series of peaceful interludes punctuated by intellectually violent revolutions." Then appears a Lavoisier or an Einstein, often a young scientist not indoctrinated in the accepted theories, to sweep the old paradigm away. Such revolutions, he said, came only after long periods of tradition-bound normal science. "Frameworks must be lived with and explored before they can be broken," *TIS This was the first modern use of the term "paradigm" in this way.

2012 Nathan Joseph Harry Divinsky (October 29, 1925 – June 17, 2012) was a Canadian mathematician, university professor, chess master, chess writer, and chess official. Divinsky was also known for being the former husband of the 19th prime minister of Canada, Kim Campbell. Divinsky and Campbell were married from 1972 to 1983.*Wik

During the 1950s and 1960s Divinsky published papers on ring theory. For example, he published On commuting automorphisms of rings (1955), Commutative subdirectly irreducible rings (1957), On simple, semi-radical and radical algebras (1959) and General radicals that coincide with the classical radical on rings with D.C.C. (1961). In 1965 he published the book Rings and radicals. I [EFR] began my research career in 1965 and found Divinsky's book very inspiring. In fact, although my topic of research was group theory, I did produce one or two papers on ring theory as a result of Divinsky's book.

Although Divinsky continued to publish the occasional mathematics paper during the 1970s and 1980s, he began to apply mathematical techniques to a study of the strength of various chess champions. In collaboration with the English grandmaster Raymond Keene, he published Warriors of the Mind: A Quest for the Supreme Genius of the Chess Board in 1989.  *SAU

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