## Monday 11 March 2024

### On This Day in Math - March 11

*Wik

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
~Vannevar Bush

The 70th day of the year; 70 is the smallest "Weird" number. In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.

270 = 1180591620717411303424. The sum of the digits is 70, and if you reverse the order, 424303114717026195081,  it is a prime #.

All the primes in the 70's, are emirps, primes that are still prime when you reverse the order of the digits, 71----17 etc.

$1^2 + 2^2 + 3^2 + \cdots + 24^2 = 70^2$

Several languages, especially ones with vigesimal(base 20) number systems, do not have a specific word for 70: for example, French soixante-dix "sixty-ten"; Danish halvfjerds, short for halvfjerdsindstyve "three and a half score". (For French, this is true only in France; other French-speaking regions such as Belgium, Switzerland, Aosta Valley and Jersey use septante.) *Wik

70 is the second smallest number where the sum of its divisors is a perfect square.  $1 + 2 + 5 + 7 + 10 + 14 + 35 + 70= 12^2 = 144$  There are only three year dates (to my knowledge)  for which the sum of the divisors is a square.

EVENTS

1574 By means of an equinoctial armillary which he constructed on the facade of the church of Santa Maria Novella, Egnatio Danti observed that the vernal equinox occurred eleven days earlier than it should have according to the Julian Calendar. This is one of the many events which led to the Gregorian calendar reform of 1584. *VFR

 *Renaissance Mathematicus

1582 At noon the sun shone in through the mouth of the South Wind, a mural on one wall, and crossed the meridional sundial line in the Meridian Room in the Tower of Winds in Rome. This should have happened on March 21, so Pope Gregory VIII was (supposedly) convinced of the need for calendar reform. *Sky and Telescope, 64(1982), 530–533

1672 Robert Hooke FRS started writing his ‘Memoranda’, as he called his daily entries, on 10 March 1672. There’s no clear statement about why he started this project, just the terse entry ‘Memoranda begun’, followed by some characteristically abrupt notes about the weather and so on. It’s worth reproducing the whole of his first entry here:
Sun. 10 [mercury] fell from 170 to 185. most part of ye Day cleer but cold & somewhat windy at the South. [I was this morning better with my cold then I had been 3 months before] [moon] apogeum. It grew cloudy about 4. [mercury] falling still.
I told Cox how to make Reflex glasses by Silver and hinted to him making them by printing. Hewet brought me £10 from Brother John Hooke. News of 3 empty Dutch ships taken by ye montacu frigat
*Robert Hooke's London
1680 Portrait of a Mathematician by Mary Beale, conjectured to be of Hooke but also conjectured to be of Isaac Barrow

1702  The UK’s first daily newspaper hit the streets on this day. Called The Daily Courant, it owed its appearance to the fact that control of the Press by the Government had been abandoned some five years earlier. The Courant also owed its existence to a remarkable and determined woman – Elizabeth Mallet, the newspaper’s first proprietor and editor.

1711 Robert Simson, who had no formal training in mathematics, was elected to the chair of mathematics at the University of Glasgow on the condition that “he give satisfactory proof of his skill in mathematics previous to his admission.” *VFR He must have proved his skill as he held the position until 1761. The pedal line is often called the Simson line.

1782 Euler writes to accept membership in the American Academy of Arts and Sciences. He was the first foreign member.

1794 At the instigation of Monge the Ecole Polytechnique was founded. *VFR The Polytechnique was established during the French Revolution, it became a military school under Napoleon in 1804. It is still under the control of French Ministry of Defense today.

In 1811, the Luddite riots began in Nottingham, England. There was poverty and misery, made worse by the new inventions - machinery which could do jobs better and faster than people. In those days of low wages and the ever-present threat of actual starvation should those wages stop for any reason, these innovations must have made the prospect even more gloomy. There were food shortages resulting from the Napoleonic Wars, and high unemployment. A group of laborers attacked a factory, breaking up 63 stocking and lace manufacturing frames, the machines which they feared would replace them. During the next three weeks gangs of upwards of fifty men, armed with pistols, guns and heavy hammers broke two hundred more frames. *TIS
Nottingham’s textile workers claimed to be following the orders of a mysterious “General Ludd.” Merchants received threatening letters addressed from “Ned Ludd’s office, Sherwood Forest.” Newspapers reported that Ludd had been a framework knitting apprentice who had been whipped at the behest of his master and took his revenge by demolishing his master’s machine with a hammer.

Ned Ludd, however, was likely no more real than another legendary denizen of Sherwood Forest who fought against injustice, Robin Hood. Mythic though he may have been, Ned Ludd became a folk hero in parts of Nottingham and inspired verses such as:

Chant no more your old rhymes about bold Robin Hood

His feats I but little admire

I will sing the Achievements of General Ludd

Now the Hero of Nottinghamshire  *History

1878 Shortly after Edison developed his phonograph, the French Academy of Sciences had it demonstrated by the Count du Moncel.  Edison's French licensee was represented by a man named Puskas who set in front of the committee and spoke into the phonograph, then fitted a large horn to the device for amplification and to the astonishment of all they heard the phonograph express its pleasure at being presented to the Academy in Puskas' nasal American-French.
Some were more astonished than others.  Physician Jean Bouillard, 82, confronted Puskas for his Parlor trick as no machine could produce accents.  To calm, and convince the doctor, Moncel himself set down and spoke into the machine, "We thank Mr Edison for having sent us his phonograph." When du Moncel's words were reproduced in his Parisian French accent, the Doctor was convinced.

BIRTHS

1780 August Leopold Crelle (11 Mar 1780; died 6 Oct 1855 at age 75). Although always interested in mathematics he lacked the money to enroll at a university and so became an engineer instead. In 1826, when he had the money, he founded the Journal f¨ur die rein und angewandte Mathematik and edited ﬁfty two volumes. Although not a great mathematician he had a gift for recognizing the abilities of such men as Abel, Jacobi, Steiner, Dirichlet, Pl¨ucker, M¨obius, Eisenstein, Kummer, and Weierstrass and oﬀered to publish their papers in his journal. *VFR As a civil engineer in the service of the Prussian Government and worked on the construction and planning of roads and the first railway in Germany (completed in 1838). He founded (1826) the world's oldest mathematical periodical still in existence, Journal für die reine und angewandte Mathematik ("Journal for Pure and Applied Mathematics"), now known as Crelle's Journal,and edited it for the rest of his life. *TIS

1811 Urbain-Jean-Joseph Le Verrier (11 Mar 1811; 23 Sep 1877 at age 66) French astronomer who predicted by mathematical means the existence of the planet Neptune. He switched from his first subject of chemistry to to teach astronomy at the Ecole Polytechnique in 1837 and worked at the Paris Observatory for most of his life. His main activity was in celestial mechanics. Independently of Adams, Le Verrier calculated the position of Neptune from irregularities in Uranus's orbit. As one of his colleagues said, " ... he discovered a star with the tip of his pen, without any instruments other than the strength of his calculations alone. In 1856, the German astronomer Johan G. Galle discovered Neptune after only an hour of searching, within one degree of the position that had been computed by Le Verrier, who had asked him to look for it there. In this way Le Verrier gave the most striking confirmation of the theory of gravitation propounded by Newton. Le Verrier also initiated the meteorological service for France, especially the weather warnings for seaports. Incorrectly, he predicted a planet, Vulcan, or asteroid belt, within the orbit of Mercury to account for an observed discrepancy (1855) in the motion in the perihelion of Mercury. *TIS (A nice blog about Le Verrier is at the Renaissance Mathematicus blog.)
I was reminded that as much as we appreciate his work in discovering Neptune, we should not overlook that his very first paper on astronomy submitted to The Academy of sciences was on

Statue of Le Verrier at the Paris Observatory was On the Secular Variations of the Orbits of the Planets.  It was in this paper , presented on September 16, 1839 that he became the first person to compute the eigen vectors of a matrix. *Hat Tip to Alain Juhel

1822 Joseph-Louis-François Bertrand (11 Mar 1822; 5 Apr 1900 at age 78) was a French mathematician and educator and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. In 1845 Bertrand conjectured that there is at least one prime between n and (2n-2) for every n greater than 3, as proved five years later by Chebyshev. It is not clear to me if he was the one who suggested the jingle
I've told you once and I'll tell you again
There's always a prime between n and 2n.
In 1855 he translated Gauss's work on the theory of errors and the method of least squares into French. He wrote a number of notes on the reduction of data from observations. *TIS At age 11 he started to attend classes at the Ecole Polytechnique, where his Uncle Duhamel was a well-known professor of mathematics. At 17 he received his doctor of science degree. *VFR
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with greater than q, what is the probability that A will be strictly ahead of B throughout the count?" which Bertrand asked, and proved in 1887 in Comptes Rendus de l'Académie des Sciences.
The answer is   $\frac{p-q}{p+q}.$

1845 Eleanor Mildred (Balfour) Sidgwick, (11 March 1845 – 10 February 1936) was an activist for the higher education of women, Principal of Newnham College of the University of Cambridge and a leading figure in the Society for Psychical Research.
She was born in East Lothian, daughter of James Maitland Balfour and Lady Blanche Harriet. She was born into perhaps the most prominent political clan in nineteenth-century Britain, the 'Hotel Cecil': her brother Arthur would eventually himself become prime minister. Another brother, Frank, a biologist, died young in a climbing accident.
One of the first students at Newnham College in Cambridge, in 1876 she married (and became converted to feminism by) the philosopher Henry Sidgwick. In 1880 she became Vice-Principal of Newnham under the founding Principal Anne Clough, succeeding as Principal on Miss Clough's death in 1892. She and her husband resided there until 1900, the year of Henry Sidgwick's death. In 1894 Mrs Sidgwick was one of the first three women to serve on a royal commission, the Bryce commission on Secondary Education.
As a young woman, Eleanor had helped (John William Strutt, who was married to her sister, Evelyn) Lord Rayleigh improve the accuracy of experimental measurement of electrical resistance. She conducted several experiments in electricity and with him published three papers in the Philosophical Transactions of the Royal Society.
She subsequently turned her careful experimental mind to the question of testing the veracity of claims for psychical phenomena. She was elected President of the Society for Psychical Research in 1908 and named 'president of honour' in 1932. Her Husband, Henry, her brother and future Prime Minister, Arthur, and Lord Rayleigh all were also Presidents of the Society.)
She was a member of the Ladies Dining Society in Cambridge, with 11 other members.
In 1916 Mrs Sidgwick left Cambridge to live with one of her brothers near Woking; she remained there until her death in 1936.
She was awarded honorary degrees by the universities of Manchester, Edinburgh, St Andrews and Birmingham.Most of her writings related to Psychical Research, and are contained in the Proceedings of the Society for Psychical Research. However, some related to educational matters, and a couple of essays dealt with the morality of international affairs. *Wik & encyclopedia.com

1853 Salvatore Pincherle (11 March 1853 in Trieste, Austria (now Italy)-10 July 1936 in Bologna, Italy) worked on functional equations and functional analysis. Together with Volterra, he can claim to be one of the founders of functional analysis. Pincherle contributed to the development and dissemination of Weierstrass's development of a theory of analytic functions. He wrote an expository paper in 1880 which was published in the Giornale di Matematiche which was inspired by the lectures of Weierstrass. This work is important both in the development of analysis and in particular the progress of mathematics in Italy. *SAU

He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "Unione Matematica Italiana"), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.

1870 Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).
His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes. *Wik Bachelier is now recognised internationally as the father of financial mathematics, but this fame, which he so justly deserved, was a long time coming. The Bachelier Society, named in his honour, is the world-wide financial mathematics society and mathematical finance is now a scientific discipline of its own. The Society held its first World Congress on 2000 in Paris on the hundredth anniversary of Bachelier's celebrated PhD Thesis, Théorie de la Spéculation *SAU

1888 William Edward Hodgson Berwick (11 March 1888 in Dudley Hill, Bradford – 13 May 1944 in Bangor, Gwynedd) was a British mathematician, specializing in algebra, who worked on the problem of computing an integral basis for the algebraic integers in a simple algebraic extension of the rationals.*Wik

1890 Birthdate of Vannevar Bush (11 Mar 1890; 28 Jun 1974 at age 84), the electrical engineer who developed the differential analyzer in the 1930s. This was an analogue device for integrating second order differential equations. It provides a nice simple model of the deﬁnite integral. *VFR Pre-World-War II computer pioneer Vannevar (pronounced "Van-ee-ver") Bush, who also was deeply involved with wartime computer projects, invented an electromechanical differential analyzer that used mechanical integrators to help solve differential equations. Bush was a co-founder of Raytheon, a military contractor. He also became very interested in information retrieval, which led him to imagine a machine he called "memex" -- an electronic extension of an individual's mind and memory base -- that mimicked human associative linking of information, and anticipated hypertext research. *CHM
Reminded by a tweet from Chris Stokes, "@Nisaccom" that Bush drove a Stanley Steamer in his youth I found this nice anecdote.
He drove a steam car, a Stanley Steamer, for many years and came to an easy understanding of its workings. He mastered the art of coaxing it up icy hills to see his future wife and of avoiding major fires. One day when it flooded and caught fire he sat by the side of the road waiting for it to go out but a traffic cop turned up and complained that if he wanted to burn his car there was a municipal dump just up the road. He explained that it was only a matter of time but the traffic cop wasn't convinced. When the fire eventually went out he drove away on the full head of steam that had built up leaving behind a bewildered traffic cop.
*iprogrammer info web page

Differential analyzer in use at the Cambridge University Mathematics Laboratory, 1938

1915 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to foresee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*Wik

1920  Nicolaas Bloembergen (March 11, 1920 – September 5, 2017) Dutch-American physicist who shared (with Arthur L. Schawlow of the United States and Kai M. Siegbahn of Sweden) the 1981 Nobel Prize for Physics for their revolutionary spectroscopic studies of the interaction of electromagnetic radiation with matter. Bloembergen made a pioneering use of lasers in these investigations and developed three-level pumps used in both masers and lasers.*TIS

DEATHS
1849 Louis Paul Emile Richard (31 March 1795 in Rennes, France - 11 March 1849 in Paris, France) Richard perhaps attained his greatest fame as the teacher of Galois and his report on him which stated, "This student works only in the highest realms of mathematics.... "
It is well known. However, he also taught several other mathematicians whose biographies are included in this archive including Le Verrier, Serret and Hermite. He fully realised the significance of Galois' work and so, fifteen years after he left the college, he gave Galois' student exercises to Hermite so that a record of his school-work might be preserved. It is probably fair to say that Richard chose to give them to Hermite since in many ways he saw him as being similar to Galois. Under Richard's guidance, Hermite read papers by Euler, Gauss and Lagrange rather than work for his formal examinations, and he published two mathematics papers while a student at Louis-le-Grand.
Despite being encouraged by his friends to publish books based on the material that he taught so successfully, Richard did not wish to do so and so published nothing. This is indeed rather unfortunate since it would now be very interesting to read textbooks written by the teacher of so many world-class mathematicians.*SAU
Four of his students

1895 Daniel Friedrich Ernst Meissel (31 July 1826 in Neustadt-Eberswalde, Brandenburg, Prussia - 11 March 1895 in Kiel, Herzogtum Holstein, Prussia) Ernst Meissel's mathematical work covers number theory, work on Möbius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem. *SAU

1924 Niels Fabian Helge von Koch (Stockholm, January 25, 1870 – ibidem, March 11, 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described. Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a stronger form of the prime number theorem. He described the Koch curve in a 1904 paper entitled "On a continuous curve without tangents constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire"). *Wik

1967 Walter Andrew Shewhart (March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.
W. Edwards Deming said of him, "As a statistician, he was, like so many of the rest of us, self-taught, on a good background of physics and mathematics. "
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

Data have no meaning apart from their context.
Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Walter Shewhart visited India in 1947-48 under the sponsorship of P. C. Mahalanobis of the Indian Statistical Institute. Shewhart toured the country, held conferences and stimulated interest in statistical quality control among Indian industrialists
*SAU

1971  Philo Taylor Farnsworth (August 19, 1906 – March 11, 1971) American pioneer in the development of electronic television, taking all of the moving parts out of television inventions. Farnsworth was a 15-year-old high school student when he designed his first television system. Six years later he obtained his first patent. In 1935 he demonstrated his complete television system. Farnsworth's basic television patents covered scanning, focusing, synchronizing, contrast, controls, and power. He also invented the first cold cathode ray tubes and the first simple electronic microscope. The Philco TV manufacturing was named after him.

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