## Friday 28 June 2024

### On This Day in Math - June 28

In my opinion, a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy -- an opinion, moreover, which has been expressed by many philosophers.

Henri Lebesgue

The 179th day of the year

179 is a "Knockout Prime" of the form K(3,2) since 17, 19, and 79 are all prime.

179 is an emirp, a prime whose reversal, 971 is also prime, and the combination sum and product 179 * 971 + 179 + 971=174959 is also an emirp.

1793 has all odd digits, 5735339. *Derek Orr

179 is a prime whose square, 32041, has one each of the digits from 0 to 4.

179 is an emirp, a prime whose reversal, 971 is also prime, and the combination sum and product 179 * 971 + 179 + 971=174959 is also an emirp.

179 = (17 * 9) + (17 + 9)

A winning solution to the 15-hole triangular peg solitaire game is: (4,1), (6,4), (15,6), (3,10), (13,6), (11,13), (14,12), (12,5), (10,3), (7,2), (1,4), (4,6), (6,1). The term (x,y) means move the peg in hole x to y. Not only does this solution leave the final peg in the original empty hole, but the sum of the peg holes in the solution is prime. But not just any prime, it is 179.

Between the beginning and the 179th digit of π, an equal number of five different decimal digits occur (there are 18 each of the digits 0, 3, 4, 5, and 9). Mike Keith conjectures this to be the last digit of π for which this happens (there are no others up to 10^9 digits). *Prime Curios

1/179 has a repeating patter of 178 digits, called a full repetend prime.

179 is a strictly non-palindromic number. It is not a palindromic number in any base.*Wikipedia

EVENTS

1451 Sort of the American version of the Medes and Lydians. The Seneca and Mohawk tribes were preparing for war when a total solar eclipse swept over both their camps late in the afternoon of this early summer day. Both immediately sued for peace. (ref. DB 6/97: "A star Called the Sun" by George Gamow). *NSEC

This Total, or near total eclipse is thought by many to have marked the beginning of the Haudenosaunee (Iroquois) Confederacy, the oldest living democracy in North America and possibly on Earth. American democracy is said to have been modeled upon the democratic ideals of the Iroquois Confederacy, which originally consisted of five nations (Mohawk, Oneida, Onondaga, Cayuga and Seneca). *Earth Sky

Iroquois, one of the historical figures of the Maisonneuve Monument, by Louis-Philippe Hébert, 1895, Place d’Armes, Montreal. Photo via Wikimedia Commons.

1489 Last total solar eclipse on Easter Island before the one on 11 July 2012. The next will be on 25 February 2324. Ref. More Mathematical Astronomical Morsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

1751 The ﬁrst volume of Diderot’s and d’Alembert’s Encyclopedie appeared. See Hawkins, Jean d’Alembert p. 69.*VFR

Between 1751 and 1780 French philosopher, art critic, and writer Denis Diderot and French mathematician, mechanician, physicist and philosopher Jean le Rond d'Alembert edited and wrote portions of the Encyclopédie ou dictionnaire des sciencesOffsite Link, des arts et des métiers, par une société‚ de gens de lettres in 17 folio volumes of text plus 11 folio volumes (i.e., 10 volumes in 11) of plates. This is usually described as the first encyclopedia ever printed.

1774 A Bill passed by Parliament included a clause to pay John Harrison for inventing a Timekeeper for finding Longitude at Sea. H5 was put on trial by the King himself in 1772, and performed superbly. The Board of Longitude, however, had refused to recognize the results of this trial, so John and William petitioned Parliament. They were finally awarded £8750 by this Act of Parliament. Perhaps more importantly, John Harrison was finally recognized as having solved the longitude problem. *Nat. Maritime Museum ‏@NMMGreenwich, *ticktocktony.com

1832 the first American case of a cholera epidemic was reported in New York City. Previously, Europe and the Americas were unaffected by the First Cholera pandemic of 1817 when cholera, long endemic to the Indian subcontinent, spread to Arabia, Syria, and southern Russia. This abated in the early 1820's, but a new cholera cycle began in 1826. It invaded the British Isles in Oct 1831. Canada was struck shortly before cholera reached New York. Cholera was a horrible disease, spread through fouled water. Its victims died after hours of cramps, diarrhea, and vomiting. Crowded into unsanitary slums, the poor suffered most. Many of the city's elite fled to the countryside. In America, the disease's hold broke by Dec 1832.*TIS

1884 Sonya Kovalevskaya officially appointed extraordinary professor at Stockholm University, thus becoming Sweden's first female professor, and the world's first female professor of mathematics.  [The Mathematical Intelligencer, vol. 6, no. 1, p. 29; *VFR ]

Following his first meeting with Sofia in 1876, Gösta Mittag-Leffler said of Sofia that, I understand perfectly why Weierstrass regards her as the most talented of his students. It was the fact that he held her in such high regard which made him determined to find a suitable position for her. During his time at the University of Hilsingfors he had tried to find a place for her on the faculty yet was unsuccessful not due to the fact that she was a woman, but due to the fact that she was Russian with what those in charge of the institution regarded as radical beliefs. On taking up his place as the head of mathematics at the recently founded Stockholm University however, he was to find himself in a position where he could actually offer her a job. From the very beginning Stockholm University offered great academic freedoms to those students in attendance. Classes were open to both sexes, and there were no examinations until a student decided that they wished to sit for a degree. Mittag-Leffler was to use his considerable diplomatic and organisational skills to offer Sofia a temporary position before those who opposed such a move had the chance to gather their forces. She readily accepted this position as a sub-professor without pay or official affiliation to the university, and hoped that by doing so she would open up the profession to women throughout Europe.

Sophia wrote to Mittag-Leffler at around this time that, Weierstrass is much more anxious than I for my appointment. It is certainly true that he wanted to see her flourish in her role as a mathematician and that this was what they both felt should be the next step on her path. He did however urge her to take the time to prepare properly for her new role knowing that her work would be subject to far more rigorous scrutiny than that of her male counterparts. Her arrival in Stockholm was thus delayed until November 1883, when her appointment made the front page of the newspapers. *SAU

1949 Wolfgang Pauli writes to Carl Jung to with theories of the "Pauli effect", which Jung described as synchronicity. Pauli was famous among his colleagues for the numerous instances in which demonstrations involving equipment suffered technical problems only when he was present. He was actually banned from the laboratory of Otto Sturn a frequent dinner companion. Pauli and Jung both believed there was an effect, and tried to explain it. In this letter Pauli uses an example from the I-ching, the Chinese book of changes, to describe his thoughts on the effect. *Charles P. Enz, No Time to be Brief: A Scientific Biography of Wolfgang Pauli,

In 1958, the Mackinac Bridge, the world longest suspension bridge, was dedicated. Ceremonies began on 24 Jun with the first "Governor's Walk" across the bridge. (It had opened to traffic on 1 Nov 1957.) This bridge joins the upper and lower peninsulas of the state of Michigan, reducing the crossing time, from a couple of hours, to just 10 minutes. Ceremonial groundbreaking took place at the St. Ignace end of the bridge on 7 May 1954, and on the opposite shore at Mackinaw City the next day. Meanwhile caissons and superstructures were assembled as far away as Indiana, Pennsylvania and Ohio. Including approaches, the total length is 26,444-ft, needing 34 bridge support foundations. The main span is 3,800-ft long. *TIS

1979 New Scientist publishes "The Man Who Invented Black Holes,"  about a description of black holes from 1783 by English natural philosopher John Michell presented to the Royal Society in November, :

"Let us now suppose the particles of light to be attracted in the same manner as all other bodies with which we are acquainted; that is, by forces bearing the same proportion to their vis inertiae (or mass), of which there can be no reasonable doubt, gravitation being, as far as we know, or having any reason to believe, an universal law of nature. ... [I]f the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it, would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity."  Futility closet

 Michell's torsion balance, used inthe Cavendish experiment, *Wik

2009 Stephen Hawking gave a party for time travelers at 12:00 UT on this day. He did not announce the event until after it was over, and it appears that no one else cared to attend. Below is the invitation, so if you missed it up until now, it's not to late to choose not to attend. (So much for free will)

*daily Mail online

2011 "6.28" has become popular as Tau day with many people who think 2 pi (or 6.28...) is more appropriate, or just a nice addition to Pi-day, on March 14 (or 3.14... )

Births

1858 Alice Lee (1858–1939) was a British statistician and mathematician, one of the first women to graduate from London University. She was awarded a PhD in 1901. She worked with Karl Pearson from 1892. She was notable for demonstrating that the correlation between cranial capacity and gender was not a sign of greater intelligence in men compared to women.

From about 1895 Lee attended Karl Pearson's statistics lectures at University College London and became interested in his application of statistical methods to evolutionary biology. Under his direction she studied for an advanced degree. Her research topic was an investigation of variation in cranial capacity in humans and its correlation with intellectual ability. Lee courted controversy with her first published paper on the subject in 1901 A study of the correlation of the human skull. She examined three groups - women students from Bedford College, male faculty at University College, and a collection of distinguished male anatomists. The study demonstrated that there was no correlation between skull size and intelligence. Through a formula Lee calculated the cranial capacity from the anatomical measurements. The individuals in the groups were ranked in order of decreasing skull size, and identified by name. The dissertation was completed in 1899 and the findings caused considerable controversy. It was then an accepted theory in craniology that brain power increased with size, hence skull capacity was a measure of mental ability. As a consequence it was believed that men, who generally had larger heads than women, were mentally superior. Lee's findings shed doubt on that belief. Furthermore, one of the examiners of her dissertation was an anatomist with a low ranking in the skull capacity table of her study. Lee's study drew considerable criticism from her thesis examiners and from eugenicist Francis Galton, who questioned the originality and the scientific quality of her work. It was through Pearson's intervention that Lee was finally awarded a PhD in 1901. The following year Pearson published two papers which answered to the criticism that had been levelled at the findings of Lee's study. As there were no effective challenges this work was soon accepted. *Wik

1875 Henri Lebesgue (June 28, 1875 – July 26, 1941) He introduced the concept of Lebesgue Measure, a device for measuring the ‘length’ of complicated sets of points on the line, and so is known as the father of modern integration theory. *VFR French mathematician whose generalization of the Riemann integral revolutionized the field of integration. He was maître de conférences (lecture master) at the University of Rennes until 1906, when he went to Poitiers, first as chargé de cours (assistant lecturer) of the faculty of sciences and later as...*TIS

1894 Einar Hille (28 June 1894 – 12 February 1980) born. In the preface of his Analytic Function Theory (1959) he wrote “It is my hope that students of this book may come to respect the historical continuity of the subject.” More authors should include historical footnotes as good as those in this book.*VFR Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. His name persists among others in the Hille–Yosida theorem. *Wik

1906  Maria Goeppert Mayer (June 28, 1906 – February 20, 1972) was a German-born American theoretical physicist, and Nobel laureate in Physics for proposing the nuclear shell model of the atomic nucleus. She was the second woman to win a Nobel Prize in physics, the first being Marie Curie. In 1986, the Maria Goeppert-Mayer Award for early-career women physicists was established in her honor.

 *Wik

1920 Nicolaas Hendrik "Nico" Kuiper (28 June 1920, Rotterdam - 12 December 1994, Utrecht) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.
Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.
He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985.*Wik

1934 Michael Artin (German: [ˈaʁtiːn]; born 28 June 1934) is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.

Artin was born in Hamburg, Germany, and brought up in Indiana. His parents were Natalia Naumovna Jasny (Natascha) and Emil Artin, preeminent algebraist of the 20th century of Armenian descent. Artin's parents left Germany in 1937, because his mother's father was Jewish. His elder sister is Karin Tate, who was married to mathematician John Tate until the late 1980s.

In the early 1960s, Artin spent time at the IHÉS in France, contributing to the SGA4 volumes of the Séminaire de géométrie algébrique, on topos theory and étale cohomology, jointly with Alexander Grothendieck. He also collaborated with Barry Mazur to define étale homotopy theory which has become an important tool in algebraic geometry, and applied ideas from algebraic geometry (such as the Nash approximation) to the study of diffeomorphisms of compact manifolds.

His work on the problem of characterising the representable functors in the category of schemes has led to the Artin approximation theorem in local algebra as well as the "Existence theorem". This work also gave rise to the ideas of an algebraic space and algebraic stack, and has proved very influential in moduli theory.

He also has made important contributions to the deformation theory of algebraic varieties, serving as the basis for all future work in this area of algebraic geometry. With Peter Swinnerton-Dyer, he provided a resolution of the Shafarevich-Tate conjecture for elliptic K3 surfaces and the pencil of elliptic curves over finite fields.

In 2002, Artin won the American Mathematical Society's annual Steele Prize for Lifetime Achievement.

In 2005, he was awarded the Harvard Centennial Medal.

In 2013, he won the Wolf Prize in Mathematics, and in 2015 was awarded the National Medal of Science from the President Barack Obama. *Wik

1943 Klaus von Klitzing (born 28 June 1943, Schroda) is a German physicist, known for discovery of the integer quantum Hall effect, for which he was awarded the 1985 Nobel Prize in Physics.

German physicist who was awarded the Nobel Prize for Physics in 1985 for his discovery, made in 1980, of the quantized Hall effect. Under appropriate conditions the resistance offered by an electrical conductor is quantized; that is, it varies by discrete steps rather than smoothly and continuously. His experiments enabled other scientists to study the conducting properties of electronic components with extraordinary precision. His work also aided in determining the precise value of the fine-structure constant and in establishing convenient standards for the measurement of electrical resistance.*TiS

1948 Kenneth Alan "Ken" Ribet (June 28, 1948 -) is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include algebraic number theory and algebraic geometry.
He earned his bachelor's degree and master's degree from Brown University in 1969, and his Ph.D. from Harvard University in 1973.
Ribet is credited with paving the way towards Andrew Wiles's proof of Fermat's last theorem. Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre was indeed true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama–Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curves, sufficed. An earlier theorem of Ribet's, the Herbrand–Ribet theorem, the converse to Herbrand's theorem on the divisibility properties of Bernoulli numbers, is also related to Fermat's Last Theorem. *Wik

1972 Ngô Bảo Châu (June 28, 1972 - ) is a Vietnamese and French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands and Diana Shelstad. In 2004, Chau and Laumon were awarded the Clay Research Award for their achievement in solving the fundamental lemma proposed by Robert Langlands for the case of unitary groups. Chau also became the youngest professor in Vietnam in 2005. His proof of the general case was selected by Time as one of the Top Ten Scientific Discoveries of 2009. In 2010, he received the Fields Medal and in 2012, the Legion of Honour He is the first Vietnamese to receive the Fields Medal *Wik

DEATHS

1527  Abraham Ortelius, (?4 or 14 Apr 1527,  28 June 1598) a Flemish cartographer. In 1570, Ortelius published Theatrum Orbis Terrarum, or Theater of the World. This was the first modern world atlas. It contained 53 maps, and its novelty lay in the fact that the maps were uniform in style, size, and lettering; had been engraved especially for this work; had descriptive text on the back of each map; and covered the entire world, region by region. Most of the maps were not original with Ortelius—he borrowed freely from previous cartographers and he fully credited all his sources—but many of the maps, such as the world map, are brand new.
The Theatrum was an immediate publishing success, and it went through 23 editions and translations in Ortelius’ own lifetime (he died in 1598).  *Linda Hall Library
 *Ortelius by Peter Paul Rubens

1768 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church.

1889 Maria Mitchell (August 1, 1818 – June 28, 1889) First American professional woman astronomer, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report.  She died at age 70 in Lynn, Mass.

In 1847, she discovered a comet named 1847 VI (modern designation C/1847 T1) that was later known as "Miss Mitchell's Comet" in her honor. She won a gold medal prize for her discovery, which was presented to her by King Christian VIII of Denmark in 1848. Mitchell was the first internationally known woman to work as both a professional astronomer and a professor of astronomy after accepting a position at Vassar College in 1865.[ She was also the first woman elected Fellow of the American Academy of Arts and Sciences and the American Association for the Advancement of Science

 Maria Mitchell, painting by Herminia Borchard Dassel, 1852, *Wik

1930 William J Greenstreet graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette.

1956 Friedrich Riesz (Jan. 22, 1880, in Győr; Feb. 28, 1956, in Budapest)
One of the most significant personalities among Hungarian mathematicians.
At the beginning he studied engineering at the Technical University of Zurich, but he soon realized that he was much more interested in mathematics than in technical subjects. So he continued to study at the Royal Hungarian University of Sciences in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he studied for a year in Göttingen and attended the lectures of David Hilbert and Hermann Minkowski. He obtained his PhD degree and diploma of secondary school teacher of mathematics and physics in Budapest.

1952 William Watson (15 June 1884, Musselburgh, East Lothian, Scotland
- 28 June 1952 , Edinburgh, Scotland) graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh.*SAU

1972 Prasanta Chandra Mahalanobis FRS (29 June 1893 – 28 June 1972) was an Indian scientist and applied statistician. He is best remembered for the Mahalanobis distance, (a statistical measure of the distance between a point P and a distribution D, - a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. ) and for being one of the members of the first Planning commission of free india. He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute, and contributed to the design of large-scale sample surveys *Wik

1893 Eduard Cech, (June 29, 1893 – March 15, 1960) Czech topologist born in Stračov, Bohemia (then Austria-Hungary, now Czech Republic). His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin.

He received his doctoral degree in 1920 at Charles University; his thesis, titled On Curves and Plane Elements of the Third Order, was written under the direction of Karel Petr. He died in Prague.*Wik

1984 Claude Chevalley (11 February 1909, Johannesburg – 28 June 1984, Paris) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group.

In his PhD thesis, Chevalley made an important contribution to the technical development of class field theory, removing a use of L-functions and replacing it by an algebraic method. At that time use of group cohomology was implicit, cloaked by the language of central simple algebras. In the introduction to André Weil's Basic Number Theory, Weil attributed the book's adoption of that path to an unpublished manuscript by Chevalley.

Around 1950, Chevalley wrote a three-volume treatment of Lie groups. A few years later, he published the work for which he is best remembered, his investigation into what are now called Chevalley groups. Chevalley groups make up 9 of the 18 families of finite simple groups. *Wik

Y. Akizuki, C. Chevalley and A. Kobori

1974  Vannever Bush (March 11, 1890 – June 28, 1974) American electrical engineer and administrator who and oversaw government mobilization of scientific research during World War II. At the age of 35, in 1925, he developed the differential analyzer, the world's first analog computer. It was capable of solving differential equations. He put into concrete form that which began 50 years earlier with the incomplete efforts of Babbage, and the theoretical details developed by Kelvin. This machine filled a 20 x 30 foot room. He innovated one of the largest growing media in our time, namely hypermedia as fulfilled in the Internet with hypertext links *TIS

1989 Charles Wilderman Trigg,(Feb 7, 1898 Baltimore, Md; June 28, 1989 San Diego, Ca.) American engineer, mathematician and educator. Educated in engineering, mathematics and education at University of Pittsburgh, University of Southern California and University of California at Los Angeles. Worked as an industrial chemist and engineer, 1917-1943, and as an educator and administrator, 1946-1963. Served in the United States Navy during World War II. Book review editor of the Journal of Recreational Mathematics. Considered one of the foremost recreational mathematicians of the twentieth century. *U of Calgary Archives

2015 Louis Norberg Howard, (12 March, 1929; Chicago, Il - June 28,2015) emeritus professor of mathematics at MIT, and McKenzie emeritus professor at Florida State University, died on Sunday, at the age of 86.
Howard joined the MIT mathematics faculty in 1955 as an assistant professor, and was promoted to full professor in 1964. He retired from MIT in 1984.
Howard was an applied mathematician who worked primarily in the field of fluid dynamics. He made fundamental contributions to a broad range of subjects, including hydrodynamic stability and geophysical flows. He made a number of key advances in our understanding of turbulent convection, flows in Hele-Shaw cells, salt-finger zones, rotating flows, and reaction-diffusion equations. The power of his mathematical modeling was evident when he transformed qualitative ideas about the bounds on turbulent transport into rigorous mathematical arguments that initiated the field of upper-bound theory.
He received his BA in physics from Swarthmore College in 1950, and his MA and PhD in mathematical physics from Princeton, in 1952 and 1953, respectively, under the supervision of Donald Spencer. He took an appointment as a Higgins lecturer in mathematics at Princeton in 1953, after which he became a research associate in mathematics and aeronautics at Caltech in 1955.
Howard was named a fellow of the American Academy of Arts and Sciences in 1965 and the American Physical Society in 1984, and was elected to the National Academy of Sciences in 1977. In 1997, he was honored with the prestigious Fluid Dynamics Prize of the American Physical Society. *MIT News

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