## Friday 26 July 2024

### On This Day in Math - July 26

Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional
~Steinmetz, Charles P.

This is the 207th day of the year; 207 is the smallest possible sum of primes which are formed using each of the digits 1 through 9 (i.e., 89 + 61 + 43 + 7 + 5 + 2 = 207) *Prime Curios (So how many such sums can there be? And which of such sums are prime?)

There are exactly 207 different matchstick graphs with eight edges ( a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line segments with length one that do not cross each other) Here are a few of them:

EVENTS

1609 Thomas Harriot was the first person to make a drawing of the Moon through a telescope, on July 26, 1609, over four months before Galileo. Factoring to solve equations was once frequently called “Harriot’s Method.” *Wik

Thony Christie points out that, "Harriot’s drawings are very primitive, mere sketches, and cannot be compared with the justifiably famous moon drawings published by Galileo Galilei in his Sidereus Nuncius from 1610. Galileo unlike Harriot was a trained artist and realised that what he was seeing through his telescope were three dimensional landscape features, mountains, valleys, etc." Thony has a great blog about the naming of the features on the moon with more great images.

1712 Brooke Taylor describes what we now call a “Taylor series” in a letter to John Machin on July 26, 1712. He would not publish about them until three years later. It would be another fifty years before the power of the method is realized by Lagrange, and another fifty before Cauchy gives a formal proof.

1732 George Berkeley gave his farm near Newport, Rhode Island to the College of New Haven [now Yale University] to endow two graduate Fellows in Greek and Latin. This was the ﬁrst provision for graduate study in America. Berkeley is known in mathematics for his Analyst (1734), which criticized the foundations of the calculus. See G. P. Conroy, “Berkeley and Education in America,” Journal for the History Ideas, 21(1960), pp. 211-221.

1766 “To your care and recommendation am I indebted for having replaced a half-blind mathematician by a mathematician with both eyes, which will especially please the anatomical members of the academy.” So wrote Frederick the Great to d’Alembert, thanking him for his suggestion of hiring Lagrange to succeed Euler at the Berlin Academy. [AMM 34(1927), p 128]

1775 Benjamin Franklin became Postmaster-General of the United States *TIS

1800 Caroline Herschel gets annual salary from George III. "William Herschel was paid £200 in annual salary as King’s Astronomer. His sister Caroline was paid £50 to act as his assistant, making her the first professional female astronomer.
A note from Herschel’s wife Mary says that the handwriting is that of King George III himself. " *sciencemuseum.org.uk

1895 Marie Sklodovska became Marie(CURIE) (1867-1934) entered the Sorbonne in 1891 and came in first in physics in 1893 and second in mathematics in 1894. She first lived with her sister and brother-in-law at 92 Avenue Jean-Jaurès, La Villette, 19e. Married Pierre Curie (1859-1906), a teacher at the École de Physique et Chimie, 42 Rue Lhomond, on 26 Jul 1895
In 1896, Marie Curie decided to investigate Henri Becquerel's discovery of the radioactivity of uranium, as a research topic for her doctoral thesis. Pierre subsequently followed her into research into radioactivity (1898), for which they were later awarded a Nobel Prize. In 1897 she gave birth to a daughter, Irène who later married Frédéric Joliot and became Irène Joliot-Curie (1926). With her husband, she continued the family's work into radioactivity. They, too, received a Nobel Prize *TIS

1976 Kenneth Appel and Wolfgang Haken of the University of Illinois communicated their solution to the Four Color Problem to the Bulletin of the American Mathematical Society. The solution used over 1000 hours of computer calculation. *VFR

1989 A federal grand jury indicts Cornell University student Robert Tappan Morris, Jr. for releasing a computer virus, making him the first person to be prosecuted under the 1986 Computer Fraud and Abuse Act in the United States. *Wik

2009 An event was held at Syon House, West London, to celebrate the 400th anniversary of Thomas Harriot's first observations of the moon. This event, Telescope400, included the unveiling of a plaque to commemorate Harriot by Lord Egremont. The plaque can now be seen by visitors to Syon House, the location of Harriot's historic observations. His drawing made 400 years earlier is believed to be based on the first ever observations of the moon through a telescope. The event (sponsored by the Royal Astronomical Society) was run as part of the International Year of Astronomy (IYA).
The original documents showing Harriot's moon map of c. 1611, observations of Jupiter's satellites, and first observations of sunspots were on display at the Science Museum, London, from 23 July 2009 until the end of IYA. *Wik

The Thomas Harriot plaque in the grounds of Syon House (W. London)

 *Wik

BIRTHS

1271 Zhao Youqin's name is sometimes written as Chao Yu-Chhin or Chao Yu-Ch'in. (July 26, 1271, Poyang, China— c. 1335, Longyou Mountains, Zhejiang province) He was born at a time of conflict when the Mongol leader Kublai Khan began attacking the Song Dynasty of China. The Song imperial family surrendered in 1276 and the last of the resistance was crushed in 1296. One source suggests that Zhao was injured in the fighting surrounding these dramatic events. When he was a young man he learnt astronomy and obtained a secret book on alchemy from a Daoist master. He joined the northern branch of the Quanzhen sect of Daoism and became a Daoist hermit, spending ten years writing a commentary on the Book of Changes . No trace of this commentary has survived. He later became the patriarch of the Quanzhen (Complete Perfection) School of Song-Yuan Daoism, ordained by the preceding patriarch, Zhang Mo.
Zhao Youqin was skilled in a large range of topics. He was an expert in astronomy, mathematics and physics, with particular skills in optics. He was also, however, a religious philosopher and a specialist in alchemy. Before he died he gave a copy of the manuscript of his book Ge xiang xin shu, to his disciple Zhu Hui. The manuscript was passed from Zhu Hui to Zhang Jun who published the work. *SAU

1852 Francis Robbins Upton (1852 in Peabody, Massachusetts – March 10, 1921 in Orange, New Jersey) was an American physicist and mathematician.
Upton graduated from Phillips Academy, Andover in 1870. He studied at Bowdoin College in Brunswick, Maine, at Princeton University where he received his M.S., and in Berlin, where he worked together with Hermann von Helmholtz.
In 1878, he joined the laboratory of Thomas Alva Edison in Menlo Park, New Jersey. There he dealt with technical problems in a mathematical way, including electric light, the watt-hour meter, and large dynamos. In October 1879, the first electric light was presented to the public. He was partner and general manager of the Edison Lamp Works, which he founded together with Edison in 1880. Upton published articles in Scribner's Monthly and Scientific American. Since 1958, the Princeton University has had the Francis Upton Graduate Fellowships.
In 1890, Upton patented the first electric fire alarm and detector along with a Mr. Fernando J. Dibble, an accomplishment of his which is often overlooked, stemming most probably from a typographical error that labels the device a "Portable Electric Tire-Alarm." (Google Books; U.S. Congressional Serial Set).*Wik

1863 Paul Walden (26 July 1863 – 22 January 1957) was a Latvian chemist who, while teaching at Riga, discovered the Walden inversion, a reversal of stereochemical configuration that occurs in many reactions of covalent compounds (1896). Due to this discovery, Walden's name is mentioned almost in all textbooks on organic chemistry published throughout the world. Walden revealed autoracemization and put the foundations to electrochemistry of nonaqueous solutions. Walden is also known for Walden's rule, which relates the conductivity and viscosity of nonaqueous solutions.*TIS

1902 Stanisław Gołąb (July 26, 1902 – April 30, 1980) was a Polish mathematician from Kraków, working in particular on the field of affine geometry.
In 1932, he proved that the perimeter of the unit disc can take any value in between 6 and 8, and that these extremal values are obtained if and only if the unit disc is an affine regular hexagon resp. a parallelogram.

In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle.*Wik

1903 Kurt Mahler (26 July 1903, Krefeld, Germany – 25 February 1988, Canberra, Australia) was a mathematician and Fellow of the Royal Society. Mahler proved that the Prouhet–Thue–Morse constant and the Champernowne constant 0.1234567891011121314151617181920... are transcendental numbers.
He was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D. from Johann Wolfgang Goethe University of Frankfurt am Main in 1927. He left Germany with the rise of Hitler and accepted an invitation by Louis Mordell to go to Manchester. He became a British citizen in 1946.
He was elected a member of the Royal Society in 1948 and a member of the Australian Academy of Science in 1965. He was awarded the London Mathematical Society's Senior Berwick Prize in 1950, the De Morgan Medal, 1971, and the Thomas Ranken Lyle Medal, 1977. *Wik

1907 Nachman Aronszajn (26 July 1907, Warsaw, Poland – 5 February 1980 Corvallis, Oregon, U.S) was a Polish American mathematician of Ashkenazi Jewish descent. Aronszajn's main field of study and expertise was mathematical analysis. He also contributed to mathematical logic.
He received his Ph.D. from the University of Warsaw, in 1930, in Poland. Stefan Mazurkiewicz was his thesis advisor. He also received a Ph.D. from Paris University, in 1935; this time Maurice Fréchet was his thesis advisor. He joined the Oklahoma A&M faculty, but moved to the University of Kansas in 1951 with his colleague Ainsley Diamond after Diamond, a quaker, was fired for refusing to sign a newly-instituted loyalty oath. Aronszajn retired in 1977. He was a Summerfield Distinguished Scholar from 1964 to his death.
He introduced, together with Prom Panitchpakdi, the injective metric spaces under the name of "hyperconvex metric spaces". Together with Kennan T. Smith, Aronszajn offered proof of the Aronszajn–Smith theorem. Also, the existence of Aronszajn trees was proven by Aronszajn; Aronszajn lines, also named after him, are the lexicographic orderings of Aronszajn trees.
He also has a fundamental contribution to the theory of reproducing kernel Hilbert space, the Moore–Aronszajn theorem is named after him. *Wik

1926 Joseph F. Engelberger (New York City, July 26, 1925 - ) American engineer who, with George Devol, developed the first industrial robot in the United States, the Unimate, in the 1950's. Engelberger is often referred to as the "Father of Robotics." When he and his partner founded Unimation in 1956, the company was the first major manufacturer of industrial robotic arms in the U.S. By 1962, they had installed their first industrial robots at the auto manufacturer, General Motors. *TIS

1945 Karl Sigmund (born July 26, 1945) is a Professor of Mathematics at the University of Vienna and one of the pioneers of evolutionary game theory.

Sigmund was head of the Institute of Mathematics at the University of Vienna from 1983 to 1985, managing editor of the scientific journal Monatshefte für Mathematik from 1991 to 2001, vice-president (1995 to 1997) and president (1997 to 2001) of the Austrian Mathematical Society, corresponding member (1996) and full member (1999) of the Austrian Academy of Sciences, and member of the Leopoldina (2003). He has also given many plenary lectures, for instance at the International Congress of Mathematicians in 1998. He was awarded the Gauss Lectureship in 2003.

In 2010 he received an honorary doctorate (Doctor Philosophiae Honoris Causa) from the University of Helsinki. In 2012 he received the Isaacs Award.

During the last decade, Sigmund became increasingly interested in the history of mathematics and in particular, the Vienna Circle. He co-edited the mathematical works of Hans Hahn and Karl Menger and organised in 2001 an exhibition on the exodus of Austrian mathematicians fleeing the Nazis and in 2006 an exhibition on Kurt Gödel. From 2003 to 2005 he was vice-president of the Austrian Science Fund (FWF).

Because of his intimate knowledge of the Vienna Circle, Sigmund was invited to the Illinois Institute of Technology to speak at the inaugural Remembering Menger event on April 9, 2007.

1969 Andrei Yuryevich Okounkov (born July 26, 1969 - ) is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions. He is currently a professor at the Columbia University and the academic supervisor of HSE International Laboratory of Representation Theory and Mathematical Physics.

He has worked on the representation theory of infinite symmetric groups, the statistics of plane partitions, and the quantum cohomology of the Hilbert scheme of points in the complex plane. Much of his work on Hilbert schemes was joint with Rahul Pandharipande.

Okounkov, along with Pandharipande, Nikita Nekrasov, and Davesh Maulik, has formulated well-known conjectures relating the Gromov–Witten invariants and Donaldson–Thomas invariants of threefolds.

In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry." In 2016, he became a fellow of the American Academy of Arts and Sciences.

DEATHS

1925 Gottlob Frege (8 November 1848 – 26 July 1925) died. He was the greatest logician since Aristotle. *VFR (Friedrich Ludwig) Gottlob Frege was a German mathematician and logician, founder of modern symbolic logic and first to put forward the view that mathematics is reducible to logic. He extended Boole's work by inventing logical symbols (symbols for "or"," if-then", etc.) that improved on the syllogistic logic it replaced. He also worked on general questions of philosophical logic and semantics. His theory of meaning, based on makig a distinction between what a linguistic term refers to and what it expresses, is still influential. Frege tried to provide a rigorous foundation for mathematics on the basis of purely logical principles, but abandoned the attempt when Bertrand Russell, on whose work he had a profound influence, pointed out a paradox that made the system inconsistent. *TIS

1941 Henri L´eon Lebesgue (June 28, 1875 – July 26, 1941) French mathematician who developed a theory of integration, now known by his name. By extending the work of Camille Jordan and Émile Borel on the Riemann integral, Lebesgue provided a generalization that solved many of the difficulties in using Riemann's theory of integration. Lebesque provided a foundation for subsequent development of integration theory and its further application in calculus, curve rectification and theory of trigonometric theory. He also contributed in several fields of mathematics, including set theory, caluclus of variation and function theory*TIS

1942 Georg Alexander Pick (August 10, 1859 – July 26, 1942) was an Austrian mathematician. He died in the Theresienstadt concentration camp. Today he is best known for Pick's formula for determining the area of lattice polygons. He published it in an article in 1899; it was popularized when Hugo Dyonizy Steinhaus included it in the 1969 edition of Mathematical Snapshots. Pick headed the committee at the (then) German university of Prague which appointed Albert Einstein to a chair of mathematical physics in 1911. Pick introduced Einstein to the work of Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita in the field of absolute differential calculus, which later in 1915 helped Einstein to successfully formulate General relativity.*Wik  My article Pick's Theorem, Some History is here.

1955 Raymond C Archibald (Colchester County, Nova Scotia, October 7, 1875 - July 26, 1955, in Sackville, New Brunswick) studied in Canada, at Harvard and at Strasbourg. He spent most of his career at Brown University in Rhode Island. His main interests were in the History of Mathematics. *SAU

1977 Oskar Morgenstern (January 24, 1902 – July 26, 1977) German-American economist and mathematician who popularized "game theory" which mathematically analyzes behaviour of man or animals in terms of strategies to maximize gains and minimize losses. He coauthored Theory of Games and Economic Behavior (1944), with John von Neumann, which extended Neumann's 1928 theory of games of strategy to competitive business situations. They suggested that often in a business situation ("game'), the outcome depends on several parties ("players"), each estimating what all of the others will do before determining their own strategy. Morgenstern was a professor at Vienna University, Austria, from 1931 until the Nazi occupation in 1938), when he fled to America and joined the faculty at Princeton University. His later publications included works on economic prediction and aspects of U.S. defence.*TIS

1984 George Horace Gallup (November 18, 1901 – July 26, 1984) was an American pioneer of survey sampling techniques and inventor of the Gallup poll, a successful statistical method of survey sampling for measuring public opinion.
Gallup was born in Jefferson, Iowa, the son of George Henry Gallup, a dairy farmer. His higher education took place at the University of Iowa. He served as a journalism professor at Drake and Northwestern for brief periods. In 1932 he moved to New York City to join the advertising agency of Young and Rubicam as director of research (later as vice president from 1937 to 1947). He was also professor of journalism at Columbia University, but he had to give up this position shortly after he formed his own polling company, the American Institute of Public Opinion (Gallup Poll), in 1935.
In 1936, his new organization achieved national recognition by correctly predicting, from the replies of only 50,000 respondents, that Franklin Roosevelt would defeat Alf Landon in the U.S. Presidential election. This was in direct contradiction to the widely respected Literary Digest magazine whose poll based on over two million returned questionnaires predicted that Landon would be the winner. Not only did Gallup get the election right, he correctly predicted the results of the Literary Digest poll as well using a random sample smaller than theirs but chosen to match it.
Twelve years later, his organization had its moment of greatest ignominy, when it predicted that Thomas Dewey would defeat Harry S. Truman in the 1948 election, by five to fifteen percentage points. Gallup believed the error was mostly due to ending his polling three weeks before Election Day.
Gallup died in 1984 of a heart attack at his summer home in Tschingel, a village in the Bernese Oberland of Switzerland. He was buried in Princeton Cemetery. *Wik

1997 Kunihiko Kodaira (16 March 1915 – 26 July 1997) Japanese mathematician who was awarded the Fields Medal in 1954 for his work in algebraic geometry and complex analysis. Kodaira's work includes applications of Hilbert space methods to differential equations which was an important topic in his early work and was largely the result of influence by Weyl. Through the influence of Hodge, he also worked on harmonic integrals and later he applied this work to problem in algebraic geometry. Another important area of Kodaira's work was to apply sheaves to algebraic geometry. In around 1960 he became involved in the classification of compact, complex analytic spaces. One of the themes running through much of his work is the Riemann-Roch theorem. He won the 1985 Wolf Prize. *TIS

2000 John Wilder Tukey (June 16, 1915 – July 26, 2000) was an American statistician. He was awarded the IEEE Medal of Honor in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform (FFT) algorithm."
Tukey retired in 1985. He died in New Brunswick, New Jersey Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science.
While working with John von Neumann on early computer designs, Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948.
The term "software", which Paul Niquette claims he coined in 1953, was first used in print by Tukey in a 1958 article in American Mathematical Monthly, and thus some attribute the term to him.
In the fall of 2003 a post to the APStats electronic discussion list from Ron Dirkse pointed out that the Japanese word for statistics, toukei, sounds very much like the name of the famous American statistician John Tukey. Ron Dirkse, who taught at the American School in Japan, added that "according to a native speaker the tou means something like 'put together' and the kei is 'measure, calculate or total'. She thought it was interesting that there was a Tukey famous in statistics, but this word pre-dates him by a lot."

Other terms credited to Tukey below are from http://www.stat.berkeley.edu/~brill/Papers/life.pdf That site Also includes a list of his honors, and Ph.D. students
alias (in time series)
ANOVA
bagplot
batch
bispectrum
bit
biweight
bland distribution
borrowing strength
boxplot
cepstrum
coco
complex demodulation
confirmatory data analysis (CDA).

2004 - William A. Mitchell died (October 21, 1911 – July 26, 2004). Mitchell was an American food chemist who was the inventor of Pop Rocks, instant Jell-O, Cool Whip and the orange drink, Tang. While working for the General Foods Corporation, he received over 70 patents.
Pop Rocks were the center of an urban legend where the kid from the Life cereal commercials died when he ate the candy and washed it down with a cola making his stomach explode. General Foods countered the claims with an ad campaign in 45 major publications and 50,000 letters to school principals. Mitchell toured the country to show people that Pop Rocks weren't dangerous. *Science History

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