Wednesday 20 September 2023

On This Day in Math - September 20


Here I am: My brain is open.

[As an itinerant scholar, this was greeting he often gave, ready to collaborate, upon arrival at the home of any mathematician colleague.]
~ Paul Erdös

The 263rd day of the year;

263 is an irregular prime. (a regular prime is an  odd prime which divides the numerator of a Bernoulli Number) They became of great interest after 1850 when Kummer proved that Fermat's Last Theorem was true for any exponent that was a regular prime.

\( 263^2 = 69169 \) A strobogrammatic number (appears the same rotated by 180o. *Prime Curos adds that it is the largest known number for which this is true.

Jim Wilder@wilderlab pointed out also that the length of 263!! (Hate that notation, it is the product of all the odds from 263 down to 1) is 263 digits. Once more pushing for a different and clearer notation. Even Prime Curios \(263!_2\) is better, but doesn't allow for partial descent, so \(n!_{a,b}\) with a as step size, and b as number of steps would allow \(43!_{5, 3} = 43 * 38 * 33 \) And if you changed the lowered text to upper, the 5 could mean count UP.

263 is the sum of five consecutive primes, 263 = 43 + 47 + 53 + 59 + 61 , and the average of the primes on each side of it, \( 263 = \frac{257 + 269}{2} \)

263 is the sum of three primes that are all palindromes, 151 + 101 + 11, ending in the sum of the digits of 263.

In 1919 Ramunjan wrote a new proof of Bertrand's Postulate, which he points out was first stated by Chebyshev, and I always give it in the poetic form I learned it first.

Chebyshev said it
So I'll say it again
There is always a Prime Between n and 2n
Of course Chebyshev actually said between n and 2n-2, but.....
He created a sequence of integers that incremented no more than one as the primes grew. That sequence of Primes, 2, 11, 17, 29, 41.. are called Ramanujan primes, and 263 is one of them. It turns out that there are 24 primes between 263 and 263/2. 131 is the 32nd Prime, 263 is the 56th. Guess Ramanujan got that one right. the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n,


1623 Schickard writes to Kepler about Schickard's new calculating machine:

What you have done by calculation I have just tried to do by way of mechanics. I have conceived a machine consisting of eleven complete and six incomplete sprocket wheels; it calculates instantaneously and automatically from given numbers, as it adds, subtracts, multiplies and divides. You would enjoy seeing how the machine accumulates and transports spontaneously a ten or a hundred to the left and, vice-versa, how it does the opposite if it is subtracting ..."

Long before Pascal and Leibniz, Schickard invented a calculating machine, the 'Rechenuhr', in 1623 *SAU

 1717  Colin Maclaurin was appointed to the Mathematics Chair at Marischal College, Aberdeen at the age of 19. This is the youngest at which anyone has been appointed a full professor at a university.

 Maclaurin was a Scottish mathematician who published the first systematic exposition of Newton's methods, written as a reply to Berkeley's attack on the calculus for its lack of rigorous foundations.

1756 David Rittenhouse at age 24, wrote to Thomas Barton about his interest in optics during the French Indian War. “I have no health for a soldier,…I am so taken with optics that I do not know whether, if the enemy should invade this part of the country, as Archimedes was slain while making geometrical figures on the sand, so I should die making a telescope.” Barton was a minister and a graduate of Trinity College Dublin. They had met when Barton came to teach at Norriton, Pa. in 1751. They developed a friendship and Barton loaned Rittenhouse books with which he learned Latin and Greek. Later, Barton would marry Rittenhouse’s Sister, Esther. *Harpers Monthly Magazine, vol LXIV 1882,

A clockmaker by trade, Rittenhouse built mathematical instruments and, it is believed, the first telescope in the United States. He also introduced the use of natural spider webbing to form the reticle (system of cross hairs) in telescope transits and other position-measuring instruments.

In his book Notes on the State of Virginia, Thomas Jefferson listed Rittenhouse alongside Benjamin Franklin and George Washington as examples of New World genius when disputing French naturalist Georges-Louis Leclerc, Comte de Buffon's claim that the environment and climate of North America had stunted the intellect of peoples living there both native and European.

The magnificent Rittenhouse Orrery at the University of Pennsylvania. 

1786 Galvani made the crucial experiment on "animal electricity" when he proved that a dead and “prepared” frog jumped without an external electric source, just by touching muscles and nerves with a metallic arc. The frog functioned as a Leyden jar; it was an electric engine. Galvani made a breakthrough that was judged revolutionary by all the scientists of his time. *Walter Bernardi, The Controversy on Animal Electricity (paper on web)

1848 The American Association for the Advancement of Science met for the first time, in Philadelphia. *VFR It was a reformation of the Association of American Geologists and Naturalists. The society chose William Charles Redfield as their first president because he had proposed the most comprehensive plans for the organization.*Wik

1916 The National Research Council met for the first time, in New York. President Woodrow Wilson founded it for “encouraging the investigation of natural phenomena” for American business and national security. *VFR

1948 John von Neumann gave his first lecture on the theory of automata. In this lecture, which was later published, he drew attention to the fundamental importance of the Universal Turing Machine. *A. Hodges, Alan Turing. The Enigma, p. 388

1954 Harlan Herrick of IBM runs the first successful FORTRAN program. *VFR (Anyone know what it did?) FORTRAN, which is an acronym for "FORmula TRANslator," was invented at IBM by a group led by John Backus. FORTRAN's purpose was to simplify the programming process by allowing the programmer ("coder") to use simple algebra-like expressions when writing software. It also took over the task of keeping track of where instructions were kept in memory--a very laborious and error-prone procedure when undertaken by humans. FORTRAN is still in use today in scientific and engineering applications, making it one of the oldest programming languages still in use (COBOL is another). *CHM
The image shows members of the original FORTRAN team at a reunion at the National Computer Conference in 1982 *IBM Icons of Progress

1973 Skylab III Crew Encounters Strange Object In Orbit.  On the 59th day of flight Skylab III, the three-man crew saw and photographed a strange red object (see photos). Not more than 30-50 nautical miles from them, Alan Bean, Owen Garriott and Jack Lousman reported the object was brighter than any of the planets. First UFO in space?


1842 Sir James Dewar (20 Sep 1842; 27 Mar 1923) British chemist and physicist. Blurring the line between physics and chemistry, he advanced the research frontier in several fields at the turn of the century, and gave dazzling lectures. His study of low-temperature phenomena entailed making an insulating double-walled flask of his own design by creating a vacuum between the two silvered layers of steel or glass (1892). This Dewar flask that has been named for him led to the domestic Thermos bottle. In June 1897, The Scientific American reported that "Dewar has just succeeded in liquefying fluorine gas at a temperature of -185 degrees C." He obtained liquid hydrogen in 1898. Dewar also invented cordite, the first smokeless powder.*TIS  In his book, Napoleon's Hemorrhoids, Phil Mason points out that Dewar never patented his vacuum flask.  His student, Reinhold Burger saw the commercial potential and began making the devices in Germany in 1904 under the patented name, thermos, Greek for heat.  Dewar was knighted, and Reinhold made millions.

James Dewar lecturing at the Royal Institution, painting by Henry J. Brooks, 1904

*Linda Hall org

1842 Alexander Wilhelm von Brill (20 Sept 1842, 8 June 1935) It is clear that Brill was much influenced by being a colleague of Klein's for five years and the influence would show up in many different ways throughout Brill's career. Brill taught a remarkably talented collection of students while at the Technische Hochschule in Munich including, for example Hurwitz, von Dyck, Rohn, Runge, Planck, Bianchi and Ricci-Curbastro. Although Klein left Munich in 1880, Brill was to remain there for a few more years, taking up the chair of mathematics in the University of Tübingen in 1884. Brill held this chair until he retired in 1918 at the age of 76, but continued to live and do mathematics in Tübingen after his retirement until his death at age 92.
He contributed to the study of algebraic geometry, trying to bring the rigour of algebra into the study of curves. In 1874 he published a joint work with Max Noether on properties of algebraic functions which are invariant under birational transformations. His work allowed the notion of genus of a curve, introduced by Clebsch, to be extended to singular and non-singular curves. In 1894 he wrote, again in collaboration with Max Noether, an extremely important survey of the development of the theory of algebraic functions.Brill also wrote on determinants, elliptic functions, special curves and surfaces. He wrote articles on the methodology of mathematics and on theoretical mechanics. At age 87 he wrote a book on Kepler's astronomy. *SAU

1887 Erich Hecke  (20 September 1887 – 13 February 1947) was a German mathematician. He obtained his doctorate in Göttingen under the supervision of David Hilbert. Kurt Reidemeister and Heinrich Behnke were among his students.
Hecke was born in Buk, Posen, Germany (now Poznań, Poland), and died in Copenhagen, Denmark. His early work included establishing the functional equation for the Dedekind zeta function, with a proof based on theta functions. The method extended to the L-functions associated to a class of characters now known as Hecke characters or idele class characters: such L-functions are now known as Hecke L-functions. He devoted most of his research to the theory of modular forms, creating the general theory of cusp forms (holomorphic, for GL(2)), as it is now understood in the classical setting.*Wik

1915 Joseph Waksberg, (20 September 1915, 10 January 2006) born in Kielce, Poland, came to the United States with his family in 1921. He joined the Census Bureau in 1940, remaining there for 33 years. He then joined the stat-research firm Westat, becoming Chairman of the Board in 1990, taking over for Morris Hansen. Also, from 1967 to 1997, he served as a consultant to CBS and other TV networks for Election Night analysis.
Mr. Waksberg's 1978 paper in JASA, "Sampling Methods for Random Digit Dialing", resulted in the Mitofsky-Waksberg Method of RDD. [For a description of the Method, see the Sept 17th posting for Warren Mitofsky.] Generally, Warren Mitofsky developed the Method intuitively and Waksberg, on Mitofsky's request, developed it mathematically, resulting in his 1978 paper. *David Bee


1804 Pierre (-François-André) Méchain (16 Aug 1744, 20 Sep 1804) was a French astronomer and hydrographer at the naval map archives in Paris recruited by Jean Delambre. He was a mathematical prodigy. In 1790, they were chosen by the National Assembly to establish a decimal system of measurement based on the meter. Since this was defined to be one ten-millionth of the distance between the Earth's pole and the equator, Mechain led a survey of the meridian arc from Dunkirk, France, to Barcelona, Spain. Through his astronomical observations, Mechain discovered 11 comets and provided 26 additions to Messier's catalog. He calculated the orbits of the two comets he found in 1781. Mechain died of yellow fever while making further surveys for the meridian measurement. *TIS

1873 Giovanni Battista Donati (16 Dec 1826, 20 Sep 1873) Italian astronomer who, on 5 Aug 1864, was first to observe the spectrum of a comet (Tempel 1864 II), showing not merely reflected sunlight but also spectral lines from luminous gas forming the comet tail when near the Sun. Earlier, he discovered the comet known as Donati's Comet at Florence, on 2 Jun 1858. When the comet was nearest the earth, its triple tail had an apparent length of 50°, more than half the distance from the horizon to the zenith and corresponding to the enormous linear figure of more than 72 million km (about 45 million mi). With an orbital period estimated at more than 2000 years, it will not return until about the year 4000.*TIS This comet is often called the 2nd most brilliant of the 19th Century. 

1878 George Parker Bidder (13 June 1806 – 20 September 1878) was an English engineer and calculating prodigy. Born in the town of Moretonhampstead, Devon, England, he displayed a natural skill at calculation from an early age. In childhood, his father, William Bidder, a stonemason, exhibited him as a "calculating boy", first in local fairs up to the age of six, and later around the country. In this way his talent was turned to profitable account, but his general education was in danger of being completely neglected.
Still many of those who saw him developed an interest in his education, a notable example being Sir John Herschel. His interest led him to arrange it so George could be sent to school in Camberwell. There he did not remain long, being removed by his father, who wished to exhibit him again, but he was saved from this misfortune and enabled to attend classes at the University of Edinburgh, largely through the kindness of Sir Henry Jardine,
On leaving college in 1824 he received a post in the ordnance survey, but gradually drifted into engineering work.
Bidder died at Dartmouth, Devon and was buried at Stoke Fleming.
His son, George Parker Bidder, Jr. (1836–1896), who inherited much of his father's calculating power, was a successful parliamentary counsel and an authority on cryptography. His grandson, also named George Parker Bidder, became a marine biologist and president of the Marine Biological Association of the United Kingdom from 1939 to 1945. *Wik

1882 Charles Auguste Briot (19 July 1817,  20 Sept 1882) undertook research on analysis, heat, light and electricity. His first major work on analysis was Recherches sur la théorie des fonctions which he published in the Journal of the École Polytechnique in 1859, and he also published this work as a treatise in the same year. His researches on heat, light and electricity was all based on his theories of the aether. He was strongly influenced in developing these theories by Louis Pasteur, the famous chemist. Of course Pasteur was a great scientist, but Briot had an additional reason to hold him in high esteem for, like himself and his friend Bouquet, Pasteur was brought up in the Doubs region of France.
In 1859 Briot and Bouquet published their important two volume treatise on doubly periodic functions. They published another joint effort in 1875 when their treatise on elliptic functions appeared. In this same year they published a second edition to their two volume work of 1859. In 1879 Briot, this time in a single author work, produced his treatise on abelian functions. The physical motivation for the mathematical theories which gave rise to this work in analysis was published by Briot in 1864 when he published his work on light, Essai sur la théorie mathématique de la lumière and five years later when he published his work on heat, Théorie mécanique de la chaleur.
We noted above that Briot was a dedicated teacher and as such he wrote a great number of textbooks for his students. This was certainly a tradition in France at this time and it was natural for a teacher of Briot's quality to write up his courses as textbooks. He wrote textbooks which covered most of the topics from a mathematics course: arithmetic, algebra, calculus, geometry, analytic geometry, and mechanics. For his outstanding contributions to mathematics the Académie des Sciences in Paris awarded Briot their Poncelet Prize in 1882 shortly before he died. *SAU

1930 Moritz Pasch (8 Nov 1843, 20 Sept 1930) was a German mathematician who worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before. "Pasch's analysis relating to the order of points on a line and in the plane is both striking and pertinent to its understanding. Every student can draw diagrams and see that if a point B is between A and a point C, then C is not between A and B, or that every line divides a plane into two parts. But no one before Pasch had laid a basis for dealing logically with such observations. These matters may have been considered too obvious; but the result of such neglect is the need to refer constantly to intuition, so that the logical status of what is being done cannot become clear." *SAU

1939 Karl Hermann Brunn (August 1, 1862 – September 20, 1939) was a German mathematician, known for his work in convex geometry and in knot theory. He is recognized with the Brunn–Minkowski inequality and in Brunnian links in knot theory. A Brunnian link is a nontrivial link that becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that no two loops can be directly linked).
1982 Frederick Bath graduated from Bristol and Cambridge and held posts at King's College London, University College Dundee, St Andrews and Edinburgh. He worked in Geometry. He was president of the EMS in 1938 and 1939. *SAU

1996 Paul Erdös ( 26 Mar 1913, 20 Sep 1996) Hungarian mathematician, who was one of the century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. At age 20, he discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and moved to the USA by the late 1930s when his Jewish origins made a return to Hungary impossible. Affected by McCarthyism in the 1950s, he spent much of the next ten years in Israel. Writing his many hundreds of papers made him one of history's most prolific mathematicians. *TIS I received a post from Raymond Johnson relating an interest in Erdos by the FBI, "I guess I shouldn't be surprised that our FBI kept files on Paul Erdős, given the communist paranoia in the United States of the 1950s and 1960s. My favorite line in his files has to be this: 'Subject visited and traveled in Netherlands for a period in 1951, and was described as lazy, preoccupied and seemingly scholarly." ( I learned of his death after some students in my Pre-calc class told me on the 21st. He was one of my favorites and I had been talking about him just days before. They had seen it on the morning news)

Erdos was known to just show up at the home of Ron Graham  and his wife, Fan Chung, both brilliant mathematicians, and just stay and "do math".  At times these visits to other mathematicians were unannounced.

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 M = Women of Mathematics, Grinstein & Campbell

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