Push on and faith will catch up with you.
~Jean d'Alembert [advice to those who questioned the calculus](probably also great for students struggling with mathematics at any level)
The 302nd day of the year; There are 302 ways to play the first three moves in checkers.
302 is the sum of three consecutive squares 92+102+112
302 is a semiprime, 2 x 151. Its reversal 203 = 7 x 29, is also a semiprime
1669 Newton, aged twenty-six, appointed Lucasian Professor at Cambridge. This post required Newton to lecture once each week on “some part of Geometry, Astronomy, Geography, Optics, Statics, or some other Mathematical discipline,” and to deposit ten of those lectures in the library each year. The students were required to attend, but like all other requirements they ignored this one too. We know of only three people who attended a lecture at Cambridge by Newton. [Westfall 208–210; Works, 3, xv] *VFR
The post was founded in 1663 by Henry Lucas, who was Cambridge University's Member of Parliament in 1639–1640, and it was officially established by King Charles II on 18 January 1664. It was described by The Daily Telegraph as one of the most prestigious academic posts in the world. Since its establishment, the professorship has been held by, among others, Isaac Newton, Charles Babbage, George Stokes, Joseph Larmor, Paul Dirac, and Stephen Hawking.
Michael Elmhirst Cates FRS FRSE HonFInstP is the 19th Lucasian Professor of Mathematics at the University of Cambridge and has held this position since 1 July 2015. He was previously Professor of Natural Philosophy at the University of Edinburgh, and has held a Royal Society Research Professorship since 2007. His work focuses on the theory of soft matter, such as polymers, colloids, gels, liquid crystals, and granular material.
The First Lucasian Professor at Cambridge was Isaac Barrow
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| Statue of Isaac Barrow in the chapel of Trinity College, Cambridge*Wik |
1675 Leibniz first used the integral sign. Also first used “d”. He also constructed what he calls the “triangulum characteristicum,” which had been used before him by Pascal and Barrow. [Cajori, History of Mathematical Notations, vol. 2, p. 2; Struik’s Source Book mistakenly has 26 October]
VFR Historical notes for the calculus classroom ,
In these same pages he will write examples of the integrals of x2 and x3,and then illustrate that a constant multiple may be taken outside the integral as shown in the image below.
On the left is Liebniz integral sign with a vincula in place of todays parentheses to show that he is integrating the quantity (a/b) l Then the open bottomed box is Liebniz symbol for equality,then he shows the constant (a/b) multiplied by the integral of l .
At this point, Leibniz does not include the dx, as in \( \int x^2 = \frac{x^3}{3} \) even though it seems his definition of an integral as a summation would seem to require it. By 1686 he will adopt it, as he wrote \( \int \rho dx \)
1745/46 The first Polish encyclopedia, titled Nowe Ateny, or “New Athens,” was published. It differed greatly in style from the encyclopedias of today. It included entries for dragons, headless humans, and an ant that could eat a pound of meat. The author had little time for mundane entries like “horse,” whose description was simply “What a horse is like, anyone can see.” *Britannica
1856 William Rowan Hamilton submits a paper on "New Roots of Unity" which will be the foundation of his Icosian Calculus, and the Icosagon game he used as a simplification of the operations of the group. The symbols of the icosian calculus can be equated to moves between vertices on a dodecahedron. Hamilton’s work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory. *Wik
The game set shown below included numbered pegs that could track your path around the twenty vertices of the dodecahedron
1878 Patent issued for Odhner calculating machine. *VFR Willigot T. Odhner was granted a patent for a calculating machine that performed multiplications by repeated additions. The patent, a modified and compact version of Gottfried von Leibniz stepped wheel, was acquired and embodied in Brunsviga calculators that sold into 1950s.*CHM
1929 "Black Tuesday", the great USA stock market crash. About 16 million shares were traded, and the Dow lost an additional 30 points, or 12%.. "Anyone who bought stocks in mid-1929 and held onto them saw most of his or her adult life pass by before getting back to even." Richard M. Salsman *Wik
In fact it wasn't until October of 1954 before it regained its 1929 High, The Dow Jones Industrial Average dropped significantly from a high of around 381 in September 1929 to a low of 41.22 in July 1932, losing nearly 90% of its value during the 1929 crash and subsequent Great Depression. After reaching this low point, it gradually began to recover, peaking again in 1937 before experiencing another sharp decline in 1937-1938. By 1940, the index had not yet returned to its 1929 peak but was on an upward trend, finishing the year around 150.
1964 Asteroid "Lucifer" is discovered by astronomer Elizabeth Roemer. amhistorymuseum @amhistorymuseum Roemer was the winner of the 1946 National Westinghouse Science Talent Search, and became Professor Emerita, Lunar and Planetary Laboratory, University of Arizona. *Smithsonian Institution Archives (Ok, it's pure trivia, but is she somehow related to Ole, who first measured the speed of light???)
Elizabeth Roemer was an active member of the astronomy community until her death in 2016. She became a member of the Friends of Lowell Observatory in 2006, as well as a member of the Percival Lowell Society.
1930 Lucifer, provisional designation 1964 UA, is a carbonaceous asteroid from the outer regions of the asteroid belt, approximately 34 kilometers in diameter. It was discovered on 29 October 1964, by American astronomer Elizabeth Roemer at the Flagstaff station (NOFS) of the United States Naval Observatory (USNO). It is named after Lucifer, the "shining one" or "light-bearer" from the Hebrew Bible.
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1985 On October 29th, 1985, the 329th birthday of Edmond Halley, the British threw a big party in honor of the return of Halley's Comet. The Halley's Comet Royal Gala was held at Wembley Conference Centre, London. It was a combination Variety Show and "Who's Who" in British Society, hosted by Princess Anne of the British Royal Family. *Joseph M. Laufer, Halley's Comet Society, USA
Halley's Comet was approaching Earth in 1985, making the 1985-86 apparition the most significant for centuries and the subject of major scientific and public interest. During this time, ground-based telescopes and several spacecraft, including the European Space Agency's Giotto probe, were deployed for close-up studies, though the comet's closest approach to Earth was in April 1986. Halley's Comet was last visible from Earth in 1986 and is not expected to return until 2061. *PB
TIME Magazine Cover: Halley's Comet - Dec. 16, 1985
In 1991, space probe Galileo become the first human object to fly past an asteroid, Gaspra, making its closest approach at a distance of 1,604 km, passing at a speed of 8 km/sec (5 mi/sec). The encounter provided much data, including 150 images, which showed Gaspra has numerous craters indicating it has suffered numerous collisions since its formation. Gaspra is about 20-km long and orbits the Sun in the main asteroid belt between Mars and Jupiter. Gaspra, asteroid 951, was discovered by Ukrainian astronomer Grigoriy N. Neujamin (1916) who named it after a Black Sea retreat. In the photograph, subtle color variations have been exaggerated by NASA to highlight changes in reflectivity, surface structure and composition. *TIS
1998, Nearly four decades after he became the first American to orbit Earth, John Glenn is relaunched into space. *@HISTORYmag
Nearly four decades after his famous orbital flight, the 77-year-old Glenn became the oldest human ever to travel in space. During the nine-day mission, he served as part of a NASA study on health problems associated with aging.
On Oct. 29, 1998, the gavel came down at the auction of an ugly-looking medieval manuscript (first image above). Splotched with mildew, displaying a Greek prayer book of no special interest, the codex appeared to have little going for it except its age, which was 13th century. But one important feature had brought bidders from around the globe and on the phone to Christie’s in New York: the manuscript was a palimpsest, which means the parchment had been scraped and reused, and there was another text, several centuries older and only faintly visible, lying under the prayer text. That "other text" proved to be a collection of seven of the works of Archimedes, in Greek, including a treatise, "The Method," for which no other copy exists.
The Archimedes palimpsest first came to light in 1906, when Johan Heiberg, a scholar of ancient Greek mathematics, had examined it in Constantinople and recognized the underlying script as Archimedean. The manuscript subsequently turned up in the library of a French collector, then disappeared for 75 years, and then emerged again in 1998, when Christie’s offered it up at auction (second image). When the gavel dropped, the winning bid was an even $2 million (with another $200,000 in premiums added on top). *Linda Hall Org
1897 Edwin James George Pitman (29 October 1897 – 21 July 1993) was born in Melbourne on 29 October 1897 and died at Kingston near Hobart on 21 July 1993. In 1920 he completed the degree course and graduated B.A. (1921), B.Sc. (1922) and M.A. (1923). In the meantime he was appointed Acting Professor of Mathematics at Canterbury College, University of New Zealand (1922-23). He returned to Australia when appointed Tutor in Mathematics and Physics at Trinity and Ormond Colleges and Part-time Lecturer in Physics at the University of Melbourne (1924-25). In 1926 Pitman was appointed Professor of Mathematics at the University of Tasmania, a position he held until his retirement in 1962.
Pitman described himself as 'a mathematician who strayed into Statistics'; nevertheless, his contributions to statistical and probability theory were substantial.
Pitman was active in the formation of the Australian Mathematical Society in 1956. He also took an active part in the Summer Research Institutes organized by the Mathematical Society, and used them as a sounding board for his research on statistical inference.
He was a renowned member of the Statistical Society of Australia, attending its biennial conferences. In 1978 the Statistical society established the Pitman Medal.
Pitman presented the first systematic account of non-parametric inference and lectured extensively on the subject, both in Australia and in the United States. The kernel of the subject, as described by him, is 'Suppose that the sum of two samples A, B is the sample C. Then A, B are discordant if A is an unlikely sample from C.' Again, he writes, 'The approach to the subject, starting from the sample and working towards the population instead of the reverse, may be a bit of a novelty'; and later, 'the essential point of the method is that we do not have to worry about the populations which we do not know, but only about the sample values which we do know'.
The notes of the 'Lectures on Non-parametric Inference' given in the United States, though never published, have been widely circulated and have had a major impact on the development of the subject. Among the new concepts introduced in these Lectures are asymptotic power, efficacy, and asymptotic relative efficiency.
A major contribution to probability theory is his elegant treatment of the behavior of the characteristic function in the neighborhood of the origin, in three papers. This governs such properties as the existence of moments. There are also interesting properties of the Cauchy distribution, and of subexponential distributions.
On his death, on 21 July 1993, Edwin was buried at the Hobart Regional Cemetery in Kingston. He lives on in the memory of many of us who are grateful for his life and legacy.
*Evan J. Williams, Australian Academy of Science
1925 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.
Divinsky received a Bachelor of Science from the University of Manitoba in 1946. He received a Master of Science in 1947, and a PhD in Mathematics under A. A. Albert in 1950 from the University of Chicago after which he returned to Winnipeg and was on the staff of the Mathematics Department of the University of Manitoba for most of the '50s. Divinsky then moved to Vancouver where he served as a mathematics professor, and also as an assistant dean of science, at the University of British Columbia in Vancouver, where he spent the remainde] of his professional career.
He was featured in many segments relating to mathematics and chess on the Discovery Channel Canada program @discovery.ca, now called Daily Planet. During the first two seasons of the show, he presented a weekly contest segment emphasizing math puzzles.
Divinsky served on the Vancouver School Board, from 1974 to 1980, and was the Chair from 1978 to 1980. He served as an alderman on Vancouver's city council from 1981 to 1982.
Divinsky learned his early chess as a teenager at the Winnipeg Jewish Chess Club, along with Yanofsky. He tied for 3rd–4th places in the Closed Canadian Chess Championship, held at Saskatoon 1945, with 9.5/12, along with John Belson; the joint winners were Yanofsky and Frank Yerhoff at 10.5/12. In the 1951 Closed Canadian Chess Championship, held at Vancouver, Divinsky scored 6/12 to tie for 5th–7th places. He won the Manitoba Championship in both 1946 and 1952, and finished runner-up in 1945. He tied for first place in the 1959 Manitoba Open. Divinsky scored 7.5/11 at Bognor Regis 1966, finishing in a tie for 7–13th places.
He represented Canada twice at the Chess Olympiads, in 1954 at Amsterdam (second reserve board, 0.5/1), and in 1966 at Havana (second reserve board, 4.5/8). Divinsky served as playing captain for both teams, and was the non-playing captain for the 1988 Canadian Olympiad team. Divinsky attained the playing level of National Master in Canada, and received through the Commonwealth Chess Association (founded by English Grandmaster Raymond Keene) the honorary title of International Master (although he did not receive this title officially from FIDE, the World Chess Federation).
Divinsky was also a Life Master at Bridge from 1972.
1925 Klaus Friedrich Roth (29 October 1925 – 10 November 2015) German-born British mathematician who was awarded the Fields Medal in 1958. His major work has been in number theory, particularly the analytic theory of numbers. He solved in the famous Thue-Siegel problem (1955) concerning the approximation to algebraic numbers by rational numbers (for which he won the medal). Roth also proved in 1952 that a sequence with no three numbers in arithmetic progression has zero density (a conjecture of Erdös and Turán of 1935).*TIS
1783 Jean le Rond D'Alembert (16 Nov 1717, 29 Oct 1783) was abandoned by his parents on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame, qv in Section 7-A-1. Foster parents were found and he was christened with the name of the saint. [Eves, vol. II, pp. 32 33. Okey, p. 297.] When he became famous, his mother attempted to reclaim him, but he rejected her. *VFR Known for his work in various fields of applied mathematics, in particular dynamics. In 1743 he published his Traité de dynamique (Treatise on Dynamics). The d'Alembert principle extends Newton's third law of motion, that Newton's law holds not only for fixed bodies but also for free moving bodies. D'Alembert also wrote on fluid dynamics, the theory of winds, the properties of vibrating strings and conducted experiments on the properties of sound . His most significant purely mathematical innovation was his invention and development of the theory of partial differential equations. He published eight volumes of mathematical studies (1761-80). He was editor of the mathematical and scientific articles for Denis Diderot's Encyclopédie.*TIS
1917 Giovanni Battista Guccia (21 Oct 1855 in Palermo, Italy - 29 Oct 1914 in Palermo, Italy) Guccia's work was on geometry, in particular Cremona transformations, classification of curves and projective properties of curves. His results published in volume one of the Rendiconti del Circolo Matematico di Palermo were extended by Corrado Segre in 1888 and Castelnuovo in 1897. *SAU
1921 Konstantin Alekseevich Andreev (26 March 1848 in Moscow, Russia - 29 Oct 1921 Near Sevastopol, Crimea) Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions. *SAU
1931 Gabriel Xavier Paul Koenigs (17 January 1858 Toulouse, France – 29 October 1931 Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.
He was awarded the Poncelet Prize for 1913.*Wik
1933 Paul Painlevé ( 5 December 1863 – 29 October 1933) worked on differential equations. He served twice as prime-minister of France. *SAU
Some differential equations can be solved using elementary algebraic operations that involve the trigonometric and exponential functions (sometimes called elementary functions). Many interesting special functions arise as solutions of linear second order ordinary differential equations. Around the turn of the century, Painlevé, É. Picard, and B. Gambier showed that of the class of nonlinear second order ordinary differential equations with polynomial coefficients, those that possess a certain desirable technical property, shared by the linear equations (nowadays commonly referred to as the 'Painlevé property') can always be transformed into one of fifty canonical forms. Of these fifty equations, just six require 'new' transcendental functions for their solution. These new transcendental functions, solving the remaining six equations, are called the Painlevé transcendents, and interest in them has revived recently due to their appearance in modern geometry, integrable systems and statistical mechanics *Wik
1951 Robert Aitken (31 Dec 1864, 29 Oct 1951) American astronomer who specialized in the study of double stars, of which he discovered more than 3,000. He worked at the Lick Observatory from 1895 to 1935, becoming director from 1930. Aitken made systematic surveys of binary stars, measuring their positions visually. His massive New General Catalogue of Double Stars within 120 degrees of the North Pole allowed orbit determinations which increased astronomers' knowledge of stellar masses. He also measured positions of comets and planetary satellites and computed orbits. He wrote an important book on binary stars, and he lectured and wrote widely for the public. *TI
1959 Edith Clarke (February 10, 1883 – October 29, 1959) was an American electrical engineer. She was the first woman to be professionally employed as an electrical engineer in the United States, and the first female professor of electrical engineering in the country. She was the first woman to deliver a paper at the American Institute of Electrical Engineers; the first female engineer whose professional standing was recognized by Tau Beta Pi, the oldest engineering honor society and the second oldest collegiate honor society in the United States; and the first woman named as a Fellow of the American Institute of Electrical Engineers. She specialized in electrical power system analysis and wrote Circuit Analysis of A-C Power Systems.
After being orphaned at age 12, she was raised by an older sister. She used her inheritance to study mathematics and astronomy at Vassar College, where she graduated in 1908.
Unable to find work as an engineer, Clarke went to work for General Electric as a supervisor of computers in the Turbine Engineering Department. During this time, she invented the Clarke calculator, an early graphing calculator, a simple graphical device that solved equations involving electric current, voltage and impedance in power transmission lines. The device could solve line equations involving hyperbolic functions ten times faster than previous methods. She filed a patent for the calculator in 1921 and it was granted in 1925.
She was offered a job by GE as a salaried electrical engineer in the Central Station Engineering Department – the first professional female electrical engineer in the United States. She retired from General Electric in 1945.
Her background in mathematics helped her achieve fame in her field. On February 8, 1926, as the first woman to deliver a paper at the American Institute of Electrical Engineers' (AIEE) annual meeting, she showed the use of hyperbolic functions for calculating the maximum power that a line could carry without instability. The paper was of importance because transmission lines were getting longer, leading to greater loads and more chances for system instability, and Clarke's paper provided a model that applied to large systems.
In 1943, Clarke wrote an influential textbook in the field of power engineering, Circuit Analysis of A-C Power Systems, based on her notes for lectures to GE engineers. This two-volume textbook teaches about her adaption of the symmetrical components system, in which she became interested while working for the second time at GE.
In 1947, she joined the faculty of the Electrical Engineering Department at the University of Texas at Austin, making her the first female professor of electrical engineering in the country.
Ms. Clarke died in 1959 at the age of seventy-six.
Her calculator was a dynamic nomogram
1993 Lipman Bers (May 22, 1914 – October 29, 1993) was an American mathematician born in Riga who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.
Bers' doctoral work was on the subject of potential theory. While in Paris, he worked on Green's function and on integral representations. After first moving to the US, while working for YIVO, he researched Yiddish mathematics textbooks rather than pure mathematics.
At Brown, he began working on problems of fluid dynamics, and in particular on the two-dimensional subsonic flows associated with cross-sections of airfoils. At this time, he began his work with Abe Gelbart on what would eventually develop into the theory of pseudoanalytic functions. Through the 1940s and 1950s he continued to develop this theory, and to use it to study the planar elliptic partial differential equations associated with subsonic flows. Another of his major results in this time concerned the singularities of the partial differential equations defining minimal surfaces. Bers proved an extension of Riemann's theorem on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result at the 1950 International Congress of Mathematicians and published it in Annals of Mathematics.
Later, beginning with his visit to the Institute for Advanced Study, Bers "began a ten-year odyssey that took him from pseudoanalytic functions and elliptic equations to quasiconformal mappings, Teichmüller theory, and Kleinian groups". With Lars Ahlfors, he solved the "moduli problem", of finding a holomorphic parameterization of the Teichmüller space, each point of which represents a compact Riemann surface of a given genus. During this period he also coined the popular phrasing of a question on eigenvalues of planar domains, "Can one hear the shape of a drum?", used as an article title by Mark Kac in 1966 and finally answered negatively in 1992 by an academic descendant of Bers. In the late 1950s, by way of adding a coda to his earlier work, Bers wrote several major retrospectives of flows, pseudoanalytic functions, fixed point methods, Riemann surface theory prior to his work on moduli, and the theory of several complex variables. In 1958, he presented his work on Riemann surfaces in a second talk at the International Congress of Mathematicians
In 1961, Bers was elected a Fellow of the American Academy of Arts and Sciences, and in 1965 he became a Fellow of the American Association for the Advancement of Science. He joined the National Academy of Sciences in 1964. He was a member of the Finnish Academy of Sciences, and the American Philosophical Society. He received the AMS Leroy P. Steele Prize for mathematical exposition in 1975 for his paper "Uniformization, moduli, and Kleinian groups". In 1986, the New York Academy of Sciences gave him their Human Rights Award. In the early 1980s, the Association for Women in Mathematics held a symposium to honor Bers' accomplishments in mentoring women mathematicians.*Wik
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| Photo by Paul Halmos *SAU |
1993 Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician. His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right". He is best known for Dilworth's theorem (Dilworth 1950) relating chains and antichains in partial orders; he was also the first to study antimatroids (Dilworth 1940). Dilworth advised 17 Ph.D. students and as of 2010 has 373 academic descendants listed at the Mathematics Genealogy Project, many through his student Juris Hartmanis, a noted complexity theorist.*Wik
2013 Douglas Samuel Jones (10 January 1922 – 29 November 2013) was a mathematician and electrical engineer known for his works in the field of electromagnetism.
In 1940, Jones began studying electrical engineering at Clarendon Laboratory of the Corpus Christi College, Oxford University.
Jones joined the RAF in 1942 and graduated MA in applied mathematics from Oxford in 1947. He then went to Massachusetts Institute of Technology to study electrical engineering, but switched to physics, studying under Victor Weisskopf, Herman Feshbach, and Robley Evans. In the same years he led a research team looking at equipment for night fighter operations. Awarded MBE in 1945 for his work with the RAF.
Jones then worked as a lecturer at Manchester University. In 1957 he was appointed chair of Mathematics at the University of Keele.
During his time at Keele, Jones wrote the book The Theory of Electromagnetism in 1964 which established him as a leader in this field.
In 1965, Jones was appointed to the Ivory Chair of Applied Mathematics at Queen's College, Dundee, then part of the University of St Andrews, but which became the University of Dundee in 1967.
Jones retired from the University of Dundee in 1992, gaining the title Emeritus Professor.
He was described by The Scotsman as "one of the most outstanding British mathematicians of his generation". *Wik
Jones received many honours for his outstanding contributions. He was elected a fellow of the Royal Society of Edinburgh (1967), a fellow of the Royal Society of London (1968), awarded the Keith Prize by the Royal Society of Edinburgh (1971-73), given an Honorary DSc from the University of Strathclyde (1975), awarded the Marconi Prize by the Institute of Electrical Engineers (1975), made an Honorary Fellow of Corpus Christi College Oxford (1980), awarded the Balthasar van der Pol Gold Medal by the International Union of Radio Science (1981), awarded the Naylor Prize and Lectureship of the London Mathematical Society (1986), elected a fellow of the Institution of Electrical Engineers (1989), made a life member of the Institute of Electrical and Electronics Engineers (2013).*SAU
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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
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