## Friday 15 March 2024

### On This Day in Math - March 15

 1659 title page of one of Argoli's books.*Wik

...there is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being ...
~James J Sylvester

The 74th day of the year.
74 is related to an open question in mathematics since 742 + 1 is prime. Hardy and Littlewood conjectured that asymptotic number of elements in this sequence, primes = n2 + 1, not exceeding n is approximately $c \frac {\sqrt{n}} {log(n)}$ for some constant c. There was a \$1000 prize for best solution to an open sequence during 2015 and submitting it to OEIS, details here

74 is the sum of the squares of two consecutive prime numbers.
A hungry number is number in the form 2n  that eats as much pi as possible, for example 25 is the smallest power of two that contains a 3.  The smallest power that contains the first three digits of pi, 314 is 27 4
(eating e seems much harder for powers of 2) Teachers might have students try "eating pi" with other bases

22796996699 is the 999799787th prime. Note that the sum of digits of the nth prime equals the sum of digits of n. The number 74 is the largest known digit sum with this property (as of August 2004). *Prime Curios

One of my new favorite expression of pi, $\sqrt{\frac{6}{1^2}+\frac{6}{2^2}+\frac{6}{3^2}+...}$ *@MathType

EVENTS
44 B.C. Julius Caesar assassinated on the Ides of March, a phrase which came to denote an ill omen. The word “ides” is from the Etruscan for one-half (it is the middle of the lunar month).

1590 On this day in 1590, François Viète cracked the code of a message from Philip II of Spain and sent it to Henry IV of France.
... when Philip, assuming that the cipher could not be broken, discovered that the French were aware of his military plans, he complained to the Pope that black magic was being employed against his country.  *MacTutor

1689 Christiaan Huygens writes to his brother Constantijn, secretary to the Prince of Orange who is about to be crowned William III: ‘It is a shame that the Prince has so little fondness for studies and the sciences, otherwise I would have greater hope [of royal patronage].’ * @Hoooaw, Hugh Aldersey-Williams

1758 March 15th was the earliest date in the prediction of the return of Halley's comet by the team of Clairaut, La Lande and Lepaute. After incremental computations of the gravitational influences and motion of Jupiter and Saturn on the predicted return of Halley's comet, Alexis-Claude Clairaut presents the results to the Academies de Sciences. The computational work of the team of Clairaut, with La Lande and Nicole-Reine Lepaute, (having removed Saturn from the last few months calculations to speed the results) had predicted a window of arrival between March 15 and May 15 (1758).
The unruly comet reached perihelion on the 13th of March, 1759 *David A Grier, When Computers Were Human.
Addendum:  The Renaissance Mathematicus writes about La a Landes support for female astronomers, "As a young man he{La Lande} assisted Alexis-Claude Clairaut in the recalculation of the orbit of Comet Halley. Lalande was ably assisted in this tedious but complex mathematical work by Nicole-Reine Lepaute (1723–1788). In his publication Clairaut did not acknowledge Lepaute’s contribution, which angered Lalande, who honoured her work so"

 *David Darling

In 1806, a 6-kg chondritemeteorite - carrying carbon-based, organic chemicals - was unequivocally identified for the first time. Its arrival on earth was noted at 5:30 pm, outside Alais, France. The organic chemicals it carried suggested the possibility of life on whatever body was the source, somewhere in the universe. According to the observations of Berzelius and a commission appointed by the French Academy it "emits a faint bituminous substance" when heated. Berzelius reported his analysis of the Alais meteorite in 1833 that destructive distillation yielded a blackish substance, indigenous water, carbon dioxide gas, a soluble salt containing ammonia, and a blackish-brown sublimate, which Berzelius confessed was unknown to him. *TIS

1871 James Clerk Maxwell in a letter to C. J. Monro comments on the fourth dimension, "The peculiarity of our space is that of its three dimensions, none is before or after another. As is x, so is y, and so is z."
Later in the same message he adds, "I am quite sure that the kind of continuity which has four dimensions all co-equal is not to be discovered by merely generalizing Cartesian space equations." Alfred M. Bork, The Fourth Dimensions in Nineteenth-Century Physics, Isis, Sept. 1964, pg 326-338
And yet, within two decades, the fourth power will be widely discussed.The fourth dimension in geometric thought became more popular after the publication of Flatland and more directly following the publication of work by Charles Hinton in 1888. According to OED, he first used the word tesseract in 1888 in his book A New Era of Thought. He also invented the words "kata" (from the Greek "down from") and "ana" (from the Greek "up toward") to describe the two opposing fourth-dimensional directions—the 4-D equivalents of left and right, forwards and backwards, and up and down.

Matt Parker's fun book on the Fourth Dimension

1873 Lewis Carroll in a letter to fourteen year old Helen Fielden offers a tempting geometric problem,
I don’t know if you’re fond of puzzles, or not. If you are, try this. If not, never mind. A gentlemen (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it — a square window, 3 feet high and 3 feet wide. Now, he had weak eyes, and the window gave too much light,  so (don’t you like “so” in a story?) he sent for the builder, and told him to alter it, so  as to give half the light. Only, he was to keep it square — he was to keep it 3 feet high — and he was to keep it 3 feet wide. How did he do it? Remember, he wasn’t allowed to use curtains, or shutters, or colored glass, or anything of that sort.

I must tell you an awful story of my trying to set a puzzle to a little girl the other day. It was at a dinner party, at dessert. I had never seen her before, but, as she was sitting next me, I rashly proposed to her to try the puzzle (I daresay you know of it) of “the fox, the goose, and bag of corn.” And I got some biscuits to represent the fox and the other things. Her mother was sitting on the other side, and said, “Now you take pains, my dear, and do it right!” The consequences were awful! She shrieked out, “I can’t do it! I can’t do it! Oh, Mamma! Mamma!” threw herself into her mother’s lap, and went off into a fit of sobbing which lasted several minutes! That was a lesson to me about trying children with puzzles. I do hope the square window won’t produce any awful effect on you! I am.

*Robin Wilson, Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life (If the puzzle stumps you, I put a helpful hint at the bottom after credits.)

1892 The earliest working type of escalator was patented in 1892 by Jesse W. Reno, and was actually introduced in 1896 as a novelty ride at Coney Island, a theme park in New York. Also during that decade George H. Wheeler patented a moving stairway with a moving handrail and flat steps that had to be boarded and exited from the side. Charles D. Seeberger bought Wheeler’s patent in 1898 and went to work at the Otis Elevator Company developing the first step-type moving stairway. It was Seeberger who created the name “escalator”, from the word scala (Latin for steps), and the word elevator, which was already in general use in the US by this time, and registered it as a trademark for a moving stairway.

The first escalator-like machine appeared in the mid 19th century, two years after the first passenger elevator. In 1859, Nathan Ames of the state of Michigan in the United States invented something he called Revolving Stairs, enshrined in history as US patent number 25,076, and generally acknowledged as the world’s first escalator. But Ames was unable to put the invention into practical use; he died in 1860, and in fact the thing was never built. The installation design formed an equilateral triangle that required passengers to jump on the stairway at the base and jump off at the top. *Mitsubishi

1933 Carl Anderson's discovery of the positron was published. Anderson had observed a new kind of particle, which he named the positron. It was soon to be identified as the first antiparticle, the antielectron. Anderson’s detailed findings were published #OTD. Although the scientific community expressed skepticism, the positron fitted with Paul Dirac's prediction in 1931 of the antielectron.
 @NobelPrize

"Cloud chamber photograph by Anderson, the first positron ever observed. The deflection and direction of the particle's ion trail indicate it is a positron." *@NobelPrize
1933 Winston Churchill was very interested in science and wrote often and popularly on the subject. He chaired a conference in on the atomic discoveries in the Cavendish Laboratory in Cambridge. On this date his scientific friend, Frederick Lindemann said of him, "All the qualities … of the scientist are manifest in him. The readiness to face realities, even though they contradict a favourite hypothesis; the recognition that theories are made to ﬁt facts, not facts to ﬁt the theories; the interest in phenomena and the desire to explore them, and above all the underlying conviction that the world is not just a jumble of events but that there must be some higher unity." *Graham Farmelo, Churchill's Bomb

1955 John von Neumann sworn in as one of the ﬁrst Atomic Energy Commissioners. In August he learned that he had bone cancer. *Goldstein, The Computer from Pascal to von Neumann

1994 Aldus Corporation and Adobe Systems Inc. Merge:
Aldus Corporation and Adobe Systems Inc. announce they will merge. Aldus revolutionized desktop publishing (DTP) when founder Paul Brainerd released the PageMaker program in 1985. Computer Scientists John Warnock and Charles Geschke applied knowledge learned in their graduate work to similar products and founded Adobe in 1982.CHM

2023 Every year on the Sunday on, or following March 15 since 1957, the city of Hinckley, Ohio has eagerly awaited the return of the buzzards at "Buzzards' Roost" at the Hinckley Reservation, part of the Cleveland Metroparks. *about.com Just as the swallows return to the Mission of Capistrano every year on March 19, St. Joseph’s Day, the buzzards return to Hinckley, Ohio, every year on March 15. Historical records dating to 1820 speak of the return of the buzzards.
If you are planning on going, don't miss the pancake breakfast/lunch at the elementary school.

BIRTHS
1570 Andrea Argoli a versatile Italian scholar. He was a jurist, mathematician, astronomer and astrologer, and medical writer.
He was professor of mathematics at the University of Rome La Sapienza, from 1622 to 1627, and then the University of Padua 1632 to 1657. His astrology pupils may have included Placido Titi, and Giambattista Zenno, astrologer to Wallenstein.*Wik
From 1622 to 1627 he held a chair of mathematics in Rome, but lost it because of his enthusiasm for astrology. *VFR

1713 Abbé Nicolas Louis de La Caille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS

 *Wik

1813 John Snow (15 March 1813 – 16 June 1858) was an English physician and a leader in the development of anesthesia and medical hygiene. He is considered one of the founders of modern epidemiology, in part because of his work in tracing the source of a cholera outbreak in Soho, London, in 1854, which he curtailed by removing the handle of a water pump. Snow's findings inspired the adoption of anesthesia as well as fundamental changes in the water and waste systems of London, which led to similar changes in other cities, and a significant improvement in general public health around the world.

Image, John Snow memorial and public house on Broadwick Street, Soho

The Ghost Map: The Story of London's Most Terrifying Epidemic – and How it Changed Science, Cities and the Modern World is a book by Steven Berlin Johnson.  Highly Recommended

1837 Esprit Jouffret (15 March 1837 – 6 November 1904) was a French artillery officer, insurance actuary and mathematician, author of Traité élémentaire de géométrie à quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions, 1903), a popularization of Henri Poincaré's Science and Hypothesis in which Jouffret described hypercubes and other complex polyhedra in four dimensions and projected them onto the two-dimensional page.

An illustration from Jouffret's Traité élémentaire de géométrie à quatre dimensions. The book, which influenced Picasso, was given to him by Princet.
Maurice Princet brought Traite to artist Pablo Picasso's attention. Picasso's sketchbooks for his 1907 painting Les Demoiselles d'Avignon illustrate Jouffret's influence on the artist's work. *Wik

 *Linda Hall Org

1855 Sir Charles Vernon Boys, FRS (15 Mar 1855; 30 Mar 1944 at age 88) English physicist and inventor of sensitive instruments. He graduated in mining and metallurgy, self-taught in a wide knowledge of geometrical methods. In 1881, he invented the integraph, a machine for drawing the antiderivative of a function. Boys is known particularly for his utilization of the torsion of quartz fibres in the measurement of minute forces, enabling him to elaborate (1895) on Henry Cavendish's experiment to improve the values obtained for the Newtonian gravitational constant. He also invented an improved automatic recording calorimeter for testing manufactured gas (1905) and high-speed cameras to photograph rapidly moving objects, such as bullets and lightning discharges. Upon retirement in 1939, he grew weeds.*TIS

A reproduction of his wonderful book, Soap-Bubbles: Their Colours and the Forces Which Mould Them : Being the Substance of Many Lectures Delivered to Juvenile and Popular Audiences with the Addition of Several New and Original Sections

1860 Walter Frank Raphael Weldon DSc FRS (Highgate, London, 15 March 1860 – Oxford, 13 April 1906) generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of Biometrika, with Francis Galton and Karl Pearson.*Wik Pearson said of him, "He was by nature a poet, and these give the best to science, for they give ideas." *SAU

1868 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany, where in 1895 she became the first woman to receive a doctorate in any field in that country. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik

DEATHS
1897 James Joseph,(Sylvester) (3 Sep 1814; 15 Mar 1897) youngest child of Abraham Joseph, born in London. The eldest son, an actuary, eventually migrated to the U.S. where, for unknown reasons, he took the surname Sylvester. The rest of the family soon followed suit, so that is how James Joseph Sylvester got his name. *VFR British mathematician who, with Arthur Cayley, founded the theory of algebraic invariants, algebraic-equation coefficients that are unaltered when the coordinate axes are translated or rotated. Beginning in 1833, he studied at St John's College, Cambridge. However, at this time signing a religious oath to the Church of England was required to graduate. Being Jewish, he refused and so he did not graduate. He taught physics at the University of London (1838-41), one of the few places which did not bar him because of his religion. Sylvester did important work on matrix theory, in particular, to study higher dimensional geometry. In 1851 he discovered the discriminant of a cubic equation. Earlier in his life, he tutored Florence Nightingale.*TIS (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)
James Joseph Sylvester died, at age 83, after earlier suffering a paralytic stroke while working at his mathematics. *VFR
I came across a nice story about Sylvester on the wonderful "Cut-the-Knot" blog of Alexander Bogomolny. He writes, "Sylvester was one the greatest British mathematicians of the 19th century. He was known for his absentmindedness and poor memory; on one occasion he even denied the truth of one of his own theorems."

1900 Elwin Bruno Christoffel (November 10, 1829 in Montjoie, now called Monschau – March 15, 1900 in Strasbourg) was a German mathematician and physicist. Christoffel worked on conformal maps, potential theory, invariant theory, tensor analysis, mathematical physics, geodesy, and shock waves. The Christoffel symbol, Riemann–Christoffel tensor, and Schwarz–Christoffel mapping are named after him. *Enotes.com

1960 Eduard Cech,(29 June 1893 in Stracov, Bohemia (now Czech Republic)- 15 March 1960 in Prague, Czechoslovakia (now Czech Republic)) Czech topologist. His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1955 Michele Angelo Besso (25 May 1873 Riesbach – 15 March 1955 Genoa) was a Swiss/Italian engineer of Jewish Italian (Sephardi) descent. He was a close friend of Albert Einstein during his years at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, and then at the patent office in Bern. Besso is credited with introducing Einstein to the works of Ernst Mach, the sceptical critic of physics who influenced Einstein's approach to the discipline. Einstein called Besso "the best sounding board in Europe" for scientific ideas.
In a letter of condolence to the Besso family Albert Einstein wrote his now famous quote "Now Besso has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion" *Wik

1962 Arthur Holly Compton (10 Sep 1892; 15 Mar 1962) American physicist and engineer. He was a joint winner, with C.T.R. Wilson of England, of the Nobel Prize for Physics (1927) for his discovery and explanation of the change in the wavelength of X rays when they collide with electrons in metals. This so-called Compton effect is caused by the transfer of energy from a photon to a single electron, then a quantum of radiation is re-emitted in a definite direction by the electron, which in so doing must recoil in a direction forming an acute angle with that of the incident radiation. During WW II, in 1941, he was appointed Chairman of the National Academy of Sciences Committee to Evaluate Use of Atomic Energy in War, assisting in the development of the atomic bomb.*TIS

1992 Deane Montgomery (2 Sept 1909 - 15 March 1992 in Chapel Hill, North Carolina, USA) was a mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.
Born in the small town of Weaver, Minnesota, he received his B.S. from Hamline University in St. Paul, MN and his Masters and Ph.D. from the University of Iowa in 1933; his dissertation advisor was Edward Chittenden.
In 1941 Montgomery was awarded a Guggenheim Fellowship. In 1988, he was awarded the American Mathematical Society Leroy P. Steele Prize for Lifetime Achievement.*Wik

2004 William Hayward Pickering (24 Dec 1910; 15 Mar 2004) Engineer and physicist, head of the team that developed Explorer 1, the first U.S. satellite. He collaborated with Neher and Robert Millikan on cosmic ray experiments in the 1930s, taught electronics in the 1930s, and was at Caltech during the war. He spent the rest of his career with the Jet Propusion Laboratory, becoming its Director (1954) with responsibility for the U.S. unmanned exploration of the planets and the solar system. Among these were the Mariner spacecraft to Venus and Mercury, and the Viking mission to Mars. The Voyager spacecraft yielded stunning photographs of the planets Jupiter and Saturn.*TIS
Photograph 11 of Mars surface, taken by Mariner 4, July 14, 1965, showing impact craters (Wikimedia commons)

2004 John A. Pople (31 Oct 1925; 15 Mar 2004) British mathematician and chemist who, (with Walter Kohn), received the 1998 Nobel Prize in Chemistry for his work on computational methodology to study the quantum mechanics of molecules, their properties and how they act together in chemical reactions. Using Schrödinger's fundamental laws of quantum mechanics, he developed a computer program which, when provided with particulars of a molecule or a chemical reaction, outputs a description of the properties of that molecule or how a chemical reaction may take place - often used to illustrate or explain the results of different kinds of experiment. Pople provided his GAUSSIAN computer program to researchers (first published in 1970). Further developed, it is now used by thousands of chemists the world over. *TIS

2006 George Whitelaw Mackey (February 1, 1916 in St. Louis, Missouri – March 15, 2006 in Belmont, Massachusetts) was an American mathematician.
Mackey's main areas of research were in the areas of representation theory, ergodic theory, and related parts of functional analysis. Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products.
He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularly quantum mechanics and statistical mechanics. He was among the first five recipients of William Lowell Putnam fellowships in 1938.*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

(Hint for the Lewis Carroll puzzle, think of diamonds.)