## Thursday 20 June 2024

### On This Day in Math - June 20

the enormous success of mathematics in the natural
sciences is something bordering on the mysterious and ...
there is no natural explanation for it.

—Eugene Wigner

The 171st day of the year; 171 has the same number of digits in Roman numerals as its cube.
CLXXI^3 =$\overline{V}CCXI$  5000211

$10^{171 } - 171$ is a prime number with 168 9's followed by 829

Google calculator gives 171! = infinity. (close enough in many cases)

171 is the 18th triangular number and is the last year-day that is both a triangular number and a palindrome. *Ben Vitale

EVENTS

1667 Louis XIV, The Sun King of France, attends the ceremony of inauguration of the Observatoire de Paris, the oldest working observatory in the world. *Amir D. Aczel, Pendulum, pg 66

1686 Halley Writes to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton will respond On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

1688 Newton, in a letter to Edmund Halley, again expresses his exasperation with carping critics. [Thanks to Howard Eves]*VFR

1788; Washington Writes to Nicholas Pike to Thank him for a copy of his "A New and Complete System of Arithmetic" , published in 1786 by Nicholas Pike, a Newburyport schoolmaster. In his letter, sent June 20, 1788, from Mount Vernon, Washington writes: "The handsome manner in which that Work is printed and the elegant manner in which it is bound, are pleasing proofs of the progress which the Arts are making in this Country. Washington's letter to Pike also commended him on his accomplishments and the importance of his work.
Pike had written to  Washington on March 25,1786 requesting permission to dedicate the book to Washington. On June 20 of 1786, Washington had replied that, "I must therefore beg leave to decline the honour which you would do me, as I have before done in two or three cases of a similar kind."

1808 Poisson submitted his ﬁrst paper on the stability of the planetary system, one day before his twenty-seventh birthday. *VFR

His memoirs on celestial mechanics," in which he proved himself a worthy successor to Pierre-Simon Laplace. The most important of these are his memoirs Sur les inégalités séculaires des moyens mouvements des planètes."  In this memoir, Poisson discusses the famous question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces. Poisson showed that the result could be extended to a second approximation, and thus made an important advance in planetary theory. The memoir is remarkable inasmuch as it roused Lagrange, after an interval of inactivity, to compose in his old age one of the greatest of his memoirs, entitled Sur la théorie des variations des éléments des planètes, et en particulier des variations des grands axes de leurs orbites. So highly did he think of Poisson's memoir that he made a copy of it with his own hand, which was found among his papers after his death. Poisson made important contributions to the theory of attraction. *Wik

1831 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

1877 Georg Cantor, in a letter to Dedekind, announced a proof that the points inside a square are in one-to-one correspondence with those on a line segment. Three years earlier, Cantor had intimated that this was clearly impossible. *VFR

1908 Count Zeppelin made his first flight in his fourth new airship at Friedrichshafen, Germany. The Luftschiff LZ4 had its first flight 20 Jun 1908. Its first extended flight (12 hours) was taken to Switzerland 1 Jul 1908. At the beginning of August, it embarked on an extended flight which had taken it among other places to Basel, Straussberg, and many of the major cities of southern Germany. While moored at Echterdingen on 5 Aug 1908, it was torn from the mast by high winds and destroyed. As interest in the Zeppelins ran high in German, the incident was felt as a national disaster. Spontaneous donations resulted in approximately 5.5 million Marks and made it possible for Zeppelin to continue his work. *TIS

 *Wik

In 1979, 32 solar panels on the White House roof, installed by the Carter administration, were dedicated. President Carter wished to demonstrate a committment to renewable energy use, as a model for the nation. About 3m x 1m x 10cm deep, the dark surfaces of the panels absorbed energy from sunlight, heating water passing through pipes snaking below them. Carter stated, “In the year 2000 this solar water heater behind me, which is being dedicated today, will still be here supplying cheap, efficient energy.” That was not to be. The subsequent Republican President, Ronald Reagan, with one of the worst environmental records of any president, while the roof was being resurfaced in 1986, had them removed and sent to warehouse storage. In the same year he slashed the research and development budget for renewable energy, and eliminated tax breaks for wind turbines and solar projects. *TiS

BIRTHS

1775 Jacques Frédéric Français (20 June 1775 in Saverne, Bas-Rhin, France - 9 March 1833 in Metz, France) In September 1813 Français published a work in which he gave a geometric representation of complex numbers with interesting applications. This was based on Argand's paper which had been sent, without disclosing the name of the author, by Legendre to François Français. Although Wessel had published an account of the geometric representation of complex numbers in 1799, and then Argand had done so again in 1806, the idea was still little known among mathematicians. This changed after Français' paper since a vigorous discussion between Français, Argand and Servois took place in Gergonne's Journal. In this argument Français and Argand believed in the validity of the geometric representation, while Servois argued that complex numbers must be handled using pure algebra. *SAU

1838 Theodor Reye (20 June 1838 in Ritzebüttel, Germany and died 2 July 1919 in Würzburg, Germany) worked in Geometry and Projective Geometry.*SAU

He is best known for his introduction of configurations in the second edition of his book, Geometrie der Lage (Geometry of Position, 1876). The Reye configuration of 12 points, 12 planes, and 16 lines is named after him.

Reye also developed a novel solution to the following three-dimensional extension of the problem of Apollonius: Construct all possible spheres that are simultaneously tangent to four given spheres.

1873 Alfred Loewy born.(20 June 1873 in Rawitsch, Germany (now Rawicz, Poznań, Poland) - 25 Jan 1935 in Freiburg im Breisgau, Germany) He worked in group theory and differential equations. *VFR

Loewy was appointed as an extraordinary professor at Freiburg in 1902. This made him secure enough financially to marry and in that year he married Therese Neuburger. Loewy became an honorary ordinary professor at Freiburg in 1916 before his appointment as ordinary professor in 1919. He was thesis advisor to a number of famous students, in particular Wolfgang Krull, who was awarded his doctorate in 1922, and Friedrich Karl Schmidt, who was awarded his doctorate in 1925. Other algebraists who spent some time in Freiburg working under Loewy are E Witt, Bernhard Neumann, R Brauer, R Baer, and A Scholz.

Anti-Semitism increased in Germany following the end of World War I. Anti-Semites joined forces with nationalists in attempting to blame the Jews for Germany's defeat. Increasing discrimination was not the only source of difficulty in Loewy's life. Already by 1916 he had lost the sight of one eye. His eyesight began to fail completely from about 1920 and he became totally blind before his death after a failed operation in 1928 left his other eye completely blind also. Despite these severe health problems Loewy continued to carry out his teaching duties. He could battle against blindness and against the hurt of anti-Semitism directed at him, but the final blow came in 1933 when anti-Semitism became part of the law of the land. On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law was passed that provided the means of removing Jewish teachers from the universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. Loewy was forced to retire in 1933 under the Civil Service Law.

Among Loewy's most famous books are Lehrbuch der Algebra Ⓣ (1915) and Mathematik des Geld- und Zahlungsverkehrs Ⓣ (1920). The first of these was one of the first works to introduce into Germany the methodology, the terminology and the achievements of postulational analysis as it was being developed in the United States.

Loewy was Abraham Fraenkel's uncle by marriage and he exerted a large influence on Fraenkel's career in its early stages. It was Loewy who persuaded Fraenkel to travel to Marburg to study under Hensel and it was Loewy who had helped Fraenkel publish his early work in Crelle's journal with a paper about the date of Easter. But the mathematical topics Fraenkel studied were also influenced by Loewy whose interest in the study of axiomatic systems encouraged a similar interest by Fraenkel. The relationship worked both ways round, however, and Loewy's Grundlagen der Arithmetik Ⓣ, published in 1915, was prepared with Fraenkel's assistance. Loewy mentioned in this work that in the system of integers, the product of any two integers is zero, if and only if one of them is zero. Such ideas clearly influenced Fraenkel to introduce the notion of a ring, and in particular zero-divisors in rings. *SAU

1917 Helena Rasiowa (20 June 1917 – 9 August 1994) was a Polish mathematician. She worked in the foundations of mathematics and algebraic logic.

There was an impressive collection of mathematicians at the University of Warsaw at this time including Borsuk, Łukasiewicz, Mazurkiewicz, Sierpiński, Mostowski and others. They had organised an underground version of the university which was strongly opposed by the Nazi authorities. Borsuk, for example, was imprisoned after the authorities found that he was helping to run the underground university.

In this dangerous situation Rasiowa learnt mathematics, knowing that the penalties for being discovered were extreme. Yet in this environment Rasiowa studied for her Master's Degree under Łukasiewicz's supervision.

In 1946, having obtained her Master's degree, she was appointed as an assistant at the University of Warsaw and continued to work for her doctorate under Mostowski's supervision. Her thesis, presented in 1950, was on algebra and logic Algebraic treatment of the functional calculus of Lewis and Heyting and these topics would be the main areas of her research throughout her life.

Rasiowa was promoted steadily, reaching the rank of Professor in 1957 and Full Professor in 1967. She led the Foundations of Mathematics Section from 1964 and the Mathematical Logic Section after its creation in 1970.

Her main research was in algebraic logic and the mathematical foundations of computer science. In algebraic logic she continued work by Post, Stone, Tarski and Łukasiewicz [1]:-

... aimed at finding a precise description for the mathematical structure of formalised logical systems.

Of course Rasiowa's work on algebraic logic was in precisely the right area to make her a natural contributor to theoretical computer science. However it is one thing to be in the right area and yet another to have the ability to see the importance of a new subject such as computer science. Her contributions are described in :-

Her contribution to theoretical computer science stems from her conviction that there are deep relations between methods of algebra and logic on the one side and essential problems of foundations of computer science on the other. Among these problems she clearly distinguished inference methods characteristic of computer science and its applications. This conviction of hers had been supported by her results on many-valued and non-classical logics, especially on applications of various generalisations of Post algebras to logics of programs and approximation logics.

In fact in 1984 Rasiowa introduced an important concept of inference where the basic information was incomplete. This led to approximate reasoning and approximate logics which are now central to the study of artificial intelligence. *SAU

1940 Leonard Susskind ( June(20ish 1940)(The professor's real birthday seems difficult to determine; perhaps only known to him and his parents, perhaps only to his parents) is the Felix Bloch Professor of Theoretical Physics at Stanford University, and Director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.
Susskind is widely regarded as one of the fathers of string theory, having, with Yoichiro Nambu and Holger Bech Nielsen, independently introduced the idea that particles could in fact be states of excitation of a relativistic string. He was the first to introduce the idea of the string theory landscape in 2003. *Wik

1942  Neil Sidney Trudinger (born 20 June 1942) is an Australian mathematician, known particularly for his work in the field of nonlinear elliptic partial differential equations.

At the ANU Trudinger served as Head of the Department of Pure Mathematics, as Director of the Centre for Mathematical Analysis and as Director of the Centre for Mathematics and its Applications, before becoming Dean of the School of Mathematical Sciences in 1992. He currently coordinates ANU's Applied and Nonlinear Analysis program. He is co-author, together with his thesis advisor, David Gilbarg, of the book Elliptic Partial Differential Equations of Second Order.

His long list of awads includes :

2008, awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society.

2012, elected as a fellow of the American Mathematical Society.

2014, gave the Łojasiewicz Lecture (on the "Optimal Transportation in the 21st Century") at the Jagiellonian University in Kraków. *Wik

1946 Nigel John Kalton (June 20, 1946 – August 31, 2010) was a British-American mathematician, known for his contributions to functional analysis.

After studying mathematics at Trinity College, Cambridge, he received his PhD, which was awarded the Rayleigh Prize for research excellence, from Cambridge University in 1970. He then held positions at Lehigh University in Pennsylvania, Warwick, Swansea, University of Illinois, and Michigan State University, before becoming full professor at the University of Missouri, Columbia, in 1979.

He received the Stefan Banach Medal from the Polish Academy of Sciences in 2005] A conference in honour of his 60th birthday was held in Miami University of Ohio in 2006. He died in Columbia, Missouri, aged 64.

David Kazhdan (Hebrew: דוד קשדן), born Dmitry Aleksandrovich Kazhdan 20 June 1946), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 MacArthur Fellow.

In 2002, he immigrated to Israel and is now a professor at the Hebrew University of Jerusalem as well as a professor emeritus at Harvard. Perhaps the most famous of the students that Kazhdan advised for a Ph.D. at Harvard was Vladimir Voevodsky who was awarded a Ph.D. in 1992 for his thesis Homology of Schemes and Covariant Motives. The ideas in this thesis eventually led to work which saw Voevodsky awarded a Fields Medal in 2002.

On October 6, 2013, Kazhdan was critically injured in a car accident while riding a bicycle in Jerusalem.

DEATHS

1800 Abraham Kästner (27 September 1719 – 20 June 1800) was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. *SAU

He was known in his professional life for writing textbooks and compiling encyclopedias rather than for original research. Georg Christoph Lichtenberg was one of his doctoral students, and admired the man greatly. He became most well-known for his epigrammatic poems. The crater Kästner on the Moon is named after him.

An epigram is a brief, interesting, memorable, sometimes surprising or satirical statement.  This literary device has been practiced for over two millennia. The presence of wit or sarcasm tends to distinguish non-poetic epigrams from aphorisms and adages, which typically do not show those qualities.

What is an Epigram? a dwarfish whole,

Its body brevity, and wit its soul.

— Samuel Taylor Coleridge ("Epigram", 1809)

Here lies my wife: here let her lie!

Now she's at rest – and so am I.

— John Dryden

*Wik

1807 Ferdinand Berthoud (19 March 1727 – 20 June 1807) Outstanding Swiss horologist and author of extensive treatises on timekeeping who became involved in the attempt to solve the problem of determining longitude at sea. His major achievement was his further development of an accurate and practical marine clock, or chronometer. (Such an instrument had previously been constructed in expensive and delicate prototypes by Pierre Leroy of France and John Harrison of England.) He made his first chronometer in 1754, which was sent for trial in 1761. Berthoud's improvements to the chronometer have been largely retained in present-day designs. *TIS

1861 Sir Frederick Gowland (Hoppy) Hopkins OM PRS (20 June 1861 – 16 May 1947) was an English biochemist who was awarded the Nobel Prize in Physiology or Medicine in 1929, with Christiaan Eijkman, for the discovery of vitamins. He also discovered the amino acid tryptophan, in 1901. He was President of the Royal Society from 1930 to 1935. His Cambridge students included neurochemistry pioneer Judah Hirsch Quastel and pioneer embryologist Joseph Needham.
During his life, in addition to the Nobel Prize, Hopkins was awarded the Royal Medal of the Royal Society in 1918 and the Copley Medal of the Royal Society in 1926. Other significant honours were his election in 1905 to fellowship in the Royal Society, Great Britain's most prestigious scientific organisation; his knighthood by King George V in 1925; and the award in 1935 of the Order of Merit, Great Britain's most exclusive civilian honour. From 1930 -1935 he served as president of the Royal Society and in 1933 served as President of the British Association for the Advancement of Science. *Wik

1865 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

=

1963 Raphaël Salem (November 7, 1898 in Salonika, Ottoman Empire (now Thessaloniki, Greece) – June 20, 1963 in Paris, France) was a Greek mathematician after whom are named the Salem numbers and Salem–Spencer sets, and whose widow founded the Salem Prize.

Salem left England in the autumn of 1940 and emigrated to the United States where he settled in Cambridge, Massachusetts. In 1941, he was appointed as a lecturer in mathematics at MIT, where he was rapidly promoted and became an assistant and associate professor. In 1958, he was appointed as Professor at the Sorbonne and lived in Paris until his death in 1963. In 1967, Éditions Hermann published Salem's Oeuvres mathématiques, edited by his collaborators Antoni Zygmund and Jean-Pierre Kahane. After Salem's death, his widow established the Salem Prize, an international prize given to young researchers for outstanding contributions to Fourier series.

In mathematics, a Salem number is a real algebraic integer 𝛼>1 whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in Diophantine approximation and harmonic analysis. They are named after Raphaël Salem. Because it has a root of absolute value 1, the minimal polynomial for a Salem number must be a reciprocal polynomial. This implies that 1/𝛼 is also a root, and that all other roots have absolute value exactly one. As a consequence α must be a unit in the ring of algebraic integers, being of norm 1.

1966 Georges (Henri) Lemaître (17 July 1894 – 20 June 1966) was a Belgian astronomer and cosmologist, born in Charleroi, Belgium. He was also a civil engineer, army officer, and ordained priest. He did research on cosmic rays and the three-body problem. Lemaître formulated (1927) the modern big-bang theory. He reasoned that if the universe was expanding now, then the further you go in the past, the universe’s contents must have been closer together. He envisioned that at some point in the distant past, all the matter in the universe was in an exceedingly dense state, crushed into a single object he called the "primeval super-atom" which exploded, with all its constituent parts rushing away. This theory was later developed by Gamow and others.*TIS  The term "big bang" was created shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders

He was the first to theorize that the recession of nearby galaxies can be explained by an expanding universe, which was observationally confirmed soon afterwards by Edwin Hubble.He first derived "Hubble's law", now called the Hubble–Lemaître law by the IAU, and published the first estimation of the Hubble constant in 1927, two years before Hubble's article. Lemaître also proposed the "Big Bang theory" of the origin of the universe, calling it the "hypothesis of the primeval atom", and later calling it "the beginning of the world".*Wik

Cosmic Anniversary: 'Big Bang Echo' Discovered 50 Years Ago ...

On May 20, 1964, American radio astronomers Robert Wilson and Arno Penzias discovered the cosmic microwave background radiation (CMB), the ancient light that began saturating the universe 380,000 years after its creation.

2003 I. Bernard Cohen (1 March 1914 – 20 June 2003) was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton.
Cohen was the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton who was the founder of Isis and the History of Science Society. Cohen taught at Harvard from 1942 until his death, and his tenure was marked by the development of Harvard's program in the history of science. *Wik

2005 Jack St. Clair Kilby (8 November 1923 - 20 June 2005) was an American electrical engineer who took part, along with Robert Noyce of Fairchild Semiconductor, in the realization of the first integrated circuit while working at Texas Instruments (TI) in 1958. He was awarded the Nobel Prize in Physics on 10 December 2000.

Kilby was also the co-inventor of the handheld calculator and the thermal printer, for which he had the patents. He also had patents for seven other inventions. *Wik

Jack Kilby's original integrated circuit

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