Friday 3 November 2023

On This Day in Math - November 3


The teaching of Algebra in the early stages ought to consist of a gradual generalisation of Arithmetic; in other words, Algebra ought, in the first instance to be taught as Arithmetica Universalis in the strictest sense.
~George Chrystal in the Preface to Algebra (1886)

The 307th day of the year; 307 is the last day of the year whose square is a palindrome, 307^2=94249
The next number whose square Is a palindrome is 836. it is the only number less than 100,000 with a palindromic square with an even number of digits; 8362=698896 Another Ambigram Palindrome, 180 degree rotation becomes 968869

The smallest number that is the sum of any set of primes containing all digits 0-9  : 2 + 5 + 41 + 67 + 83 + 109 = 307.

The largest number that you can type in Excel is 9.999 * 10307. If you type in a larger number, Excel will treat it as a character string.  *Prime Curios  (Is this still true? Afraid I don't use Excel much anymore.)


In 1664, Robert Hooke showed an advanced copy of his classic book Micrographia, or some Physiological Descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon to the Royal Society in London. This large volume contained sketches of practically everything Hooke could view with the latest invention of the day, the microscope. It was also history's first treatise on microbiology, and coined the word "cell" in the biological context. Also included in this volume are many snow crystal drawings, which for the first time revealed the complexity and intricate symmetry of snow crystal structure. The book was published in 1665 and became promptly a best-seller.*TIS
My favorite, a louse looks like he's carrying a stick

1832 Janos Bolyai in a letter to his father Farkas when he told of his work on non-Euclidean geometry. The young Janos Bolyai perhaps expressed the revelation afforded by the new mathematics most eloquently in 1823, when he wrote breathlessly to his father about his work in non‐Euclidean geometry: “I have made such wonderful discoveries that I have been almost overwhelmed by them. … I can only say this: I have created a new universe from nothing.” * Amir R. Alexander , Tragic Mathematics, Isis, Vol. 97, No. 4, December 2006
Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father.
Carl Friedrich Gauss, on reading the Appendix, wrote to a friend saying "I regard this young geometer Bolyai as a genius of the first order."
In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers. Although he never published more than the 24 pages of the Appendix, he left more than 20,000 pages of mathematical manuscripts when he died.
Portrait of J. Bolyai by Ferenc Márkos *Wik

1863 Arthur Cayley gave his Inaugural lecture at Cambridge. The topic was a survey of his course in analytic geometry. *A. J. Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age

1937 Howard. H. Aiken (Harvard University) writes a letter to J. W. Bryce (IBM) starting a discussion on automatic calculating machinery for use in computing physical problems. This would lead to the creation of The Harvard Mark I, the fifty-one feet long, eight feet high, and weighing nearly five tons Giant Brain. With high-speed electromechanical units for multiplication and division, electromechanical tables of functions, three paper-tape interpolator units, 72 accumulating storage registers and 60 dial-switch constant register, all called into play by commands read from the punched-tape sequence control, The Harvard Mark I was the most powerful calculating machine of its day.*CHM
Aiken with Mark I

In 1957, Sputnik 2 was launched, with the first live animal sent into space - a Siberian husky dog, Laika ("barker" in Russian). By design, the craft was not planned for recovery, and Laika died in orbit. Biological data, the first data of its kind, was transmitted back to Earth while she lived. The data showed scientists how Laika was adapting to space - information important to the imminent planned manned missions. The 508-kg satellite remained in orbit 162 days. Laika was considered a hero in the Soviet Union. The first human to pilot a spacecraft, Yuri Gagarin, followed on 12 Apr 1961, aboard Vostok 1.*TIS
Laika died within hours from overheating, possibly caused by a failure of the central R‑7 sustainer to separate from the payload. The true cause and time of her death were not made public until 2002; instead, it was widely reported that she died when her oxygen ran out on day six or, as the Soviet government initially claimed, she was euthanized prior to oxygen depletion.


1867 Martin Wilhelm Kutta (3 Nov 1867 in Pitschen, Upper Silesia - 25 Dec 1944 in Fürstenfeldbruck, Germany) was a German engineer who is best known for his work on the numerical solution of differential equations (the Runge-Kutta method). Kutta also worked on research on glaciers and also research in the history of mathematics. He wrote a paper on Wallis's 1659 work on integration and the length of an ellipse.*SAU

1878 Arthur Byron Coble (November 3, 1878 – December 8, 1966) was an American mathematician. He did research on finite geometries and the group theory related to them, Cremona transformations associated with the Galois theory of equations, and the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface. He was President of the American Mathematical Society from 1933 to 1934.*Wik

1896 Raymond Louis Wilder (3 November 1896, Palmer, Massachusetts – 7 July 1982, Santa Barbara, California) was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests.*Wik

1906 Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was a historian of sciences, and especially mathematics. David Foster Wallace called him the "Gibbon of math history". He wrote the books History of Analytic Geometry, The History of the Calculus and Its Conceptual Development, A History of Mathematics, and The Rainbow: From Myth to Mathematics. He served as book-review editor of Scripta Mathematica *Wik


1643 Paul Guldin died (original name Habakkuk Guldin) (June 12, 1577 – November 3, 1643) was a Swiss Jesuit mathematician and astronomer. He discovered the Guldinus theorem to determine the surface and the volume of a solid of revolution. This theorem is also known as Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria. He was noted for his association with the German mathematician and astronomer Johannes Kepler
He was born in Mels, Switzerland and was a professor of mathematics in Graz and Vienna.
In Paolo Casati's astronomical work Terra machinis mota (1658), Casati imagines a dialogue between Guldin, Galileo, and Marin Mersenne on various intellectual problems of cosmology, geography, astronomy and geodesy. *Wik

1832 John Leslie (17 April 1766 in Largo, Fife, Scotland - 3 Nov 1832 in Coates (near Largo), Fife, Scotland) Leslie was a successful professor of mathematics, attracting large classes of students and publishing his lectures in popular textbooks such as the three part work Elements of Geometry​, Geometrical Analysis, and Plane Trigonometry (1809). He mixed classical mathematical teaching with some new continental approaches to analysis and algebra particularly in his advanced classes. Leslie became professor in Natural Philosophy in 1819 after the chair fell vacant on (John) Playfair's death. This was not without a battle, for again the Church put up a candidate but, having won a victory in the earlier encounter, this time proved much more straightforward. He gave courses which were filled with experiments on specially made apparatus, for which Leslie himself had paid over half the cost from his own pocket. He soon discovered that one of the main problems of teaching university level physics was the lack of mathematical background of most of his students. He wanted to rectify this by teaching mathematics courses specially tailored for his physics students, but the University of Edinburgh senate prevented him from giving such courses since these topics were deemed the responsibility of the professor of mathematics. *SAU

1911 George Chrystal (8 March 1851 in Old Meldrum (near Aberdeen), Scotland
- 3 Nov 1911 in Edinburgh, Scotland)is best remembered today for Algebra: a two volume work which was completed by 1889. He was also involved in educational reform throughout his career and was a major figure in setting up an educational system in Scotland. He became one of the first honorary members of the EMS in 1883. *SAU Chrystal was (one of?) the first to use the inverted exclamation mark for the subfactorial notation.
The first volume of the book, entitled Algebra : An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges was published in 1886. He continued his project producing the second volume in November 1889. A review which appeared in the Athenaeum comments:-
It is the completest work on Algebra that has yet come before us, and in lucidity of exposition it is second to none. The author views his subject from the high ground of the educationist, without reference to the exigencies of established examinations; yet neither the candidates who are training for such nor the teachers who prepare them will act wisely if they neglect his lessons.
Another review in the Academy states:-
The explanations are admirably clear, and the arrangement appears to be a very good one. No teacher of the high classes in our schools or of students preparing for the university examinations should be without this book. There is nothing like it in English, and it forms an excellent introduction to the various applications of Algebra to the higher analysis.


1918 Aleksandr Mikhailovich Lyapunov (June 6 [O.S. May 25] 1857 – November 3, 1918) was a Russian mathematician, mechanician and physicist. His surname is sometimes romanized as Ljapunov, Liapunov or Ljapunow. He is known for his development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory. In the theory of probability, he generalised the works of Chebyshev and Markov, and proved the Central Limit Theorem under more general conditions than his predecessors. The method he used for the proof found later widespread use in probability theory. *Wik
Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values A and B.
A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour (measured using the Lyapunov exponent \(\lambda\)

1960 Sir Harold Spencer Jones (29 Mar 1890, 3 Nov 1960) English astronomer who was 10th astronomer royal of England (1933–55). His work was devoted to fundamental positional astronomy. While HM Astronomer at the Cape of Good Hope, he worked on proper motions and parallaxes. Later he showed that small residuals in the apparent motions of the planets are due to the irregular rotation of the earth. He led in the worldwide effort to determine the distance to the sun by triangulating the distance of the asteroid Eros when it passed near the earth in 1930-31. Spencer Jones also improved timekeeping and knowledge of the Earth’s rotation. After WW II he supervised the move of the Royal Observatory to Herstmonceux, where it was renamed the Royal Greenwich Observatory.*TIS

1967 Alexander Craig Aitken (Born: 1 April 1895 in Dunedin, New Zealand
- 3 Nov 1967 in Edinburgh, Scotland) served at Gallipoli and in France with the New Zealand army. His experiences here affected him for the rest of his life. He studied at Edinburgh University after World War I and was then given a post there. He had a prodigious memory and calculating ability. He worked in Statistics, Numerical Analysis and Algebra and made important contributions in all these areas. He became President of the EMS in 1931 and 1951 and an honorary member in 1967. *SAU  Someone once asked Aitken to divide 4 by 47; He paused for four seconds, then; began to read off a digit every second or so.  After 26 digits, he paused to talk about the problem for a second, then continued with successive digits until he reached the end of the cycle and added, "... it starts again with 085.  So if that's forty-six places I'm right."  *Walter Gratzer, Eurekas and Euphorias, pg 21
Aitken was one of New Zealand's most eminent mathematicians.In a 1935 paper he introduced the concept of generalized least squares, along with now standard vector/matrix notation for the linear regression model. Another influential paper co-authored with his student Harold Silverstone established the lower bound on the variance of an estimator, now known as Cramér–Rao bound.


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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