## Friday 20 January 2023

### On This Day in Math - January 20

If you are afraid of something, measure it, and you will realize it is a mere trifle.
~Renato Caccioppoli

The 20th day of the year; 20 is the smallest number that cannot be either prefixed or followed by one digit to form a prime. (What is next smallest?)

The 20th palindromic prime (929) has a digit sum of 20. *jim wilder ‏@wilderlab ... There is no larger nth prime palindrome for which digit sum = n less than $10^7$  *Derek Orr & *David ‏@InfinitelyManic

$e^{\pi}-\pi$ = 20, well, almost,  It's about19.99909997..... (e^pi is often called Gelford's number after Aleksandr  Gelford, who proved it was transcendental.) John H Conway noticed this approximation in 1988.

20 is involved in a challenge by Fermat in 1647 to "find a cube, that when increased by the sum of its aliquot parts, is a square, "

And in Paul Halcke observed that 20 was one of three (all rather modestly sized) numbers for which the product of their aliquot divisors equaled their square.  Can you find others?

EVENTS

In 1633, Galileo, at age 68, left his home in Florence, Italy, to face the Inquisition in Rome. By 22 Jun 1633, he buckled under the threats and interrogation by the Inquisition, and renounced his belief that the Earth revolved around the Sun. *TIS

1748 In a surprising letter of January 20, 1748, D'Alembert wrote to Euler [Euler 1980] to suggest a new theory: perhaps the moon (or at least its distribution of mass) was not spherical. If, after all, we only see one side from the Earth, we can't know how far back it truly extends. And perhaps if it extends far enough back, the apsidal motion would indeed be 3 degrees, as observed. In an even more surprising response written less than four weeks later [Euler 1980], Euler says that he too had considered this idea, and had worked out the details! He found that moon would have to extend back about 2 1/2 Earth diameters in the direction away from us, which seemed untenable. *VFR

1896, X-rays were reported by Henri Poincaré reading a letter from Wilhelm Roentgen to the weekly meeting of the Academie des Sciences in Paris, and members viewed some of his X-ray photographs. Henri Becquerel was present, and took note that X-rays seemed to come from the phosphorescent patch on the glass tube where the cathode rays struck it. This inspired him to study if the phosphorescence of minerals was related to X-rays. (Instead, a few weeks later, he discovered the radioactivity of a uranium mineral.) *TIS

1969, the New York Times made public the news of the discovery a few days earlier of the first optical pulsar by astronomers at the University of Arizona on 16 Jan 1969. It was the result of a year's search using a stroboscopic technique. Flashes of light in the optical range were found coming from the same location in the Crab Nebula as a previously known pulsar emitting radio bursts. The rate of pulsation of the two signals was found to be the same, and thus presumed to be from a single star. Other observatories were immediately notified and the flashing was confirmed by the McDonald Observatory and by the powerful 84-inch reflector telescope at the Kitt Peak National Observatory in Arizona. The star was flashing at a rate of about 30 times per second, with intermediate flashes of lesser intensity. *TIS
This image is of the Crab Nebula in visible light photographed by the Hale Observatory optical telescope in 1959. The faint object at the centre had been identified as a pulsar and is thought to be the remains of the original star. It has been observed as a pulsar in visible light, radio wave, x-rays, and gamma-rays.*The Hindu Digital

1983 The Department of Commerce officially withdrew the commercial standard for the sizing of women's apparel on January 20, 1983. In the mid-1940's, the Mail-Order Association of America, a trade group representing catalog businesses such as Sears Roebuck and Spiegel, asked the Commodity Standards Division of the National Bureau of Standards (NBS, now NIST )to conduct research to provide a reliable basis for industry sizing standards for women's clothing. Men's clothing had become somewhat standardized as early as the American Civil War due to demands for quick manufacture of uniforms. The resulting commercial standard was distributed by NBS to the industry for comment in 1953, formally accepted by the industry in 1957, and published as Commercial Standard (CS)215-58 in 1958.
However, with the passage of time, the standard became outdated. Both American men and women were becoming heavier. Whereas the average woman's figure once came a little closer to approaching the hourglass shape of the fashion magazines, she was now becoming more pear-shaped, with a thicker waist and fuller hips. At the same time that the average woman's body was changing shape, manufacturers discovered the advantage of appealing to women's vanity. They began selling bigger clothes labeled with smaller size numbers. Today only pattern makers consistently use the old commercial standard.*NIST

1989 Statistician and political scientist Edward R Tufte sent a letter to the New York Times with a copy of his book on statistical graphics. On a visit later to New York, the Times called it as "founding document of New York Times Graphics" *
Edward Tufte@EdwardTufte

BIRTHS

1573 Simon Marius (20 Jan 1573, 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611 *TIS Galileo initially named his discovery the Cosmica Sidera ("Cosimo's stars"), but names that eventually prevailed were chosen by Simon Marius and were suggested by Johannes Kepler, in his Mundus Jovialis​, published in 1614. *Wik You can find a nice blog about the conflict with Galileo by the Renaissance Mathematicus.

1775 André-Marie Ampère (20 January 1775 – 10 June 1836) was a French physicist and mathematician who is generally regarded as one of the main discoverers of electromagnetism. The SI unit of measurement of electric current, the ampere, is named after him.*Wik

1820 Alexandre-Emile Beguyer de Chancourtois (20 Jan 1820; 14 Nov 1886) French geologist who was the first to arrange the chemical elements in order of atomic weights (1862). De Chancourtois plotted the atomic weights on the surface of a cylinder with a circumference of 16 units, the approximate atomic weight of oxygen. The resulting helical curve which he called the telluric helix brought closely related elements onto corresponding points above or below one another on the cylinder. Thus, he suggested that "the properties of the elements are the properties of numbers." Although his publication was significant, it was ignored by chemists as it was written in the language of geology, and the editors omitted a crucial explanatory table. It was Dmitry Mendeleyev's table published in 1869 that became most recognized.*TIS

1831 Edward John Routh FRS (20 January 1831–7 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematize the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.*Wik

1834 William Watson born in Nantucket, MA. In 1862 he earned his Ph.D. at the University of Jena, being the ﬁrst American to receive a Ph.D. in mathematics at a foreign university. Later he taught at Harvard and MIT. In the same year Yale was the ﬁrst American school to grant a Ph.D. in mathematics (to J. H. Worall).*VFR

1895 Gabor Szego, Professor Emeritus at Stanford. He co-authored with George (originally Gy¨orogy) P´olya the renown book Problems and Theorems in Analysis. *VFR worked in the area of extremal problems and Toeplitz matrices.*SAU

1904 Renato Caccioppoli ( 20 January 1904 – 8 May 1959) was an Italian mathematician. His most important works, out of a total of around eighty publications, relate to functional analysis and the calculus of variations. Beginning in 1930 he dedicated himself to the study of differential equations, the first to use a topological-functional approach. Proceeding in this way, in 1931 he extended the Brouwer fixed point theorem, applying the results obtained both from ordinary differential equations and partial differential equations. *Wik

1931 David M. Lee (20 Jan 1931, ) American physicist who, with Robert C. Richardson and Douglas D. Osheroff, was awarded the Nobel Prize for Physics in 1996 for their joint discovery of superfluidity in the isotope helium-3.*TIS

DEATHS

1590 Giovanni Battista Benedetti died. In one of his books he forecast his death for 1592. Hence, on his deathbed, he recomputed his horoscope and declared that an error of four minutes must have been made in the original data, thus evincing his lifelong faith in the doctrines of judicial astrology.*VFR "The essence of Galileo’s laws of fall can be found in the work of Giambattista Bendetti: *RMAT

1760 John Colson (1680–20 January, 1760) was an English clergyman and mathematician, Lucasian Professor of Mathematics at Cambridge University.
Colson was educated at Lichfield School before becoming an undergraduate at Christ Church, Oxford, though he did not take a degree there. He became a schoolmaster at Sir Joseph Williamson's Mathematical School in Rochester, and was elected Fellow of the Royal Society in 1713. He was Vicar of Chalk, Kent from 1724 to 1740. He relocated to Cambridge and lectured at Sidney Sussex College, Cambridge. From 1739 to 1760 he was Lucasian Professor of Mathematics. He was also Rector of Lockington, Yorkshire.
In 1726 he published his Negativo-Affirmativo Arithmetik advocating a modified decimal system of numeration. It involved "reduction [to] small figures" by "throwing all the large figures 9, 8, 7, 6 out of a given number, and introducing in their room the equivalent small figures $1\overline{1},1\overline{2},1\overline{3},1\overline{4}$ respectively".
He translated several of Isaac Newton's works into English, including De Methodis Serierum et Fluxionum in 1736. It was Colsen who mistranslated the name of the curve that Maria Gaetana Agnesi called 'versiera' to become the Witch of Agnesi.*Wik

1864 Giovanni Antonio Amedeo Plana (6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician.
His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age.
The crater Plana on the Moon is named in his honor.*Wik

1907 Agnes Mary Clerke (10 Feb 1842, 20 Jan 1907) Irish astronomical writer who was a diligent compiler of facts rather than a practicing scientist. Nevertheless, by 1885, her exhaustive treatise, A Popular History of Astronomy in the Nineteenth Century gained international recognition as an authoritative work. In 1903, with Lady Huggins, she was elected an honorary member of the Royal Astronomical Society, a rank previously held only by two other women, Caroline Herschel and Mary Somerville. Her publications included several books and 55 pieces in the Edinburgh Review. She contributed some astronomer biographies to the Dictionary of National Biography and some astronomical entries in the Encyclopaedia Britannica. *TIS

1921 Mary Watson Whitney (11 Sep 1847, 20 Jan 1921) American astronomer who trained with Maria Mitchell and succeeded her as professor and director of the Vassar College Observatory. As Mitchell had before her, Whitney championed science education the advancement of professional opportunities for women. She developed the astronomy department. Four years before her 1910 retirement, there were 160 students and eight different astronomy courses, including some of the first courses anywhere on astrophysics and on variable stars. During her tenure as director, the Observatory staff published 102 papers in major astronomical journals reporting their work on comets, asteroids, and variable stars. From 1896, photographic plates were used to study and measure star clusters.*TIS
 *Wik

1922 Camille Jordan (5 Jan 1838, 20 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik)

1944 James McKeen Cattell (25 May 1860, 20 Jan 1944) American psychologist who had a talent in mathematics from a young age, and accordingly applied objective, quantitative methods with his career in experimental psychology. As a university professor, he was the first in America to teach a course in statistical analysis. From 1890, he termed his investigations “mental testing,” with such goals as measuring the amount of pressure required to produce pain, or reaction time to sounds. He developed the order of merit ranking method. Fields in which he applied psychology were broad, including education, business, industry, and advertising. The ideas in Galton's eugenics theory also interested him, and he did support such concepts as sterilization of persons of lower intelligence. He originated professional directories, published scientific periodicals and founded the Science Press (1923) *TIS

1971 Jan Arnoldus Schouten (28 Aug 1883 in Nieuwer Amstel (now part of Amsterdam), Netherlands - 20 Jan 1971 in Epe, The Netherlands) worked on tensor analysis and its applications. He produced 180 papers and 6 books on tensor analysis, applying tensor analysis to Lie groups, general relativity, unified field theory, and differential equations. Influenced by Weyl and Eddington, Schouten investigated affine, projective and conformal mappings. Klein's Erlanger Programm of 1872 looked at geometry as properties invariant under the action of a group. This approach had a large influence on Schouten's approach to his topic. *SAU

2001 Crispin St. John Alvah Nash-Williams (December 19, 1932 – January 20, 2001) was a British and Canadian mathematician. His research interest was in the field of discrete mathematics, especially graph theory. *Wik

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