## Sunday 9 October 2022

### On This Day in Math - October 9

It is important that students bring a certain ragamuffin, barefoot, irreverence to their studies; they are not here to worship what is known, but to question it.
~Jacob Bronowski, The Ascent of Man

It is the perennial youthfulness of mathematics itself which marks it off
with a disconcerting immortality from the other sciences.
~Eric Temple Bell

No clearly nice place for this on any year date, but since I received it from Jim on my birthday, here it is:

The 282nd day of the year; there are 282 plane partitions of nine objects. (A plane partition is a -dimensionalq array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n.)
(That reads much harder than the idea, here is an image of a plane partition of 22 from Mathworld, which, as they say, is worth a thousand words:

282 is the smallest number between twin primes which is a palindrome. Can you find the next?

282 is the largest gap between two successive primes below one billion.

EVENTS

1410   The first known mention of the Prague astronomical clock. *The Painter Flynn
The Orloj is mounted on the southern wall of Old Town Hall in the Old Town Square. The clock mechanism has three main components – the astronomical dial, representing the position of the Sun and Moon in the sky and displaying various astronomical details; statues of various Catholic saints stand on either side of the clock; "The Walk of the Apostles", an hourly show of moving Apostle figures and other sculptures, notably a figure of a skeleton that represents Death, striking the time; and a calendar dial with medallions representing the months. According to local legend, the city will suffer if the clock is neglected and its good operation is placed in jeopardy; a ghost, mounted on the clock, was supposed to nod its head in confirmation. According to the legend, the only hope was represented by a boy born on New Year's night*Wik

1676 Leeuwenhoek writes to Oldenburg to describe the "little animals" he sees in his microscope.
The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite.
*The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 75.

1701 Yale College founded. Yale traces its beginnings to "An Act for Liberty to Erect a Collegiate School", passed by the General Court of the Colony of Connecticut on October 9, 1701 in an effort to create an institution to train ministers and lay leadership for Connecticut. Soon thereafter, a group of ten Congregationalist ministers: Samuel Andrew, Thomas Buckingham, Israel Chauncy, Samuel Mather, James Noyes, James Pierpont, Abraham Pierson, Noadiah Russell, Joseph Webb and Timothy Woodbridge, all of whom were alumni of Harvard, met in the study of Reverend Samuel Russell in Branford, Connecticut, to pool their books to form the school's first library. The group, led by James Pierpont, is now known as "The Founders". *Wik

1775 A paper by Euler, Speculationes circa quasdam insignes proprietates numerorum, was presented at the Saint-Petersburg Academy. In This paper, he revisits the idea that has come to be called Euler's Phi function. He first introduced the idea to the Academy on Oct 15,1759 but did not include a symbol or name. Euler defined the function as "the multitude of numbers less than D, and which have no common divisor with it." (This is slightly different than the current definition which used Greatest Common Divisor is one). In the earlier papers, he had not used a symbol but chose πD for a symbol. In 1801 Gauss's Disquisitiones Arithmeticae introduced the Phi notation, although Gauss didn't use parentheses around the argument and wrote φA. The term Totient was applied by J J Sylvester in 1879. So it's not Euler's Phi, and it's not Euler's Totient, and in fact, the function is now not exactly Euler's function. *Wik

In 1780, the first U.S. astronomy expedition to record an eclipse of the sun left on this day from Harvard College, Cambridge, Mass., for Penobscot Bay, led by Samuel Williams. A boat was supplied by the Commonwealth of Massachusetts with four professors and six students. Although the country was at war with Britain, the British officer in charge of Penobscot Bay permitted the expedition to land and observe the eclipse of 27 Oct 1780. The eclipse began at 11:11 am and ended at 1:50 pm. They set up equipment to observe the predicted total eclipse of the sun. A solar eclipse occurred, but the expedition was shocked to find itself outside the path of totality. They saw a thin arc of the sun instead of its complete obscuration by the moon. *TIS

1805  Carl Friedrich Gauss married Johanna Ostoff. Sadly, she died four years later. *Mathematics & Statistics St Andrews

In 1890, it is reported, however without evidence, French electrical engineer Clément Ader was the first person to actually fly an airplane, but his steam-powered bat-like plane, "Eole", only rose a few inches off the ground. (It was not a sustained flight like the Wright Brothers later flight.) Ader's 50-meter flight was cut short, said eyewitnesses, by trees at the end of the field. The plane's design flaw didn't show up in that minimal flight - Ader hadn't provided adequate control. He coined the French word "avion" for aircraft. It is said to mean Appareil Volant Imitant les Oisaux Naturels: Flying Machine Imitating Natural Birds. At the Paris Electrical Exhibition (1881), Ader showed a closed-circuit stereo audio system to a listening booth. *TIS

1926 Saturday Evening Post prints "Coconuts" story by Ben Ames Williams with a problem of five men and a monkey and a pile of coconuts. In the following week 2000 letters to the Post demand to know the answer. Editor-in-chief Horace Latimore send Williams an emphatic telegram, "FOR THE LOVE OF MIKE, HOW MANY COCONUTS? HELL POPPING AROUND HERE."
For those who seek the problem:
"Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food. Piled them all up together and then went to sleep for the night.
But when they were all asleep one man woke up, and he thought there might be a row about dividing the coconuts in the morning, so he decided to take his share. So he divided
the coconuts into five piles. He had one coconut left over, and he gave that to the monkey, and he hid his pile and put the rest all back together. By and by the next man woke up and did the same thing. And he had one left over, and he gave it to the monkey. And all five of the men did the same thing, one after the other; each one taking a fifth of the coconuts in the pile when he woke up, and each one having one left over for the monkey. And in the morning they divided what coconuts were left, and they came out in five equal shares. Of course each one must have known there were coconuts missing; but each one was guilty as the others, so they didn't say anything. How many coconuts were there in the beginning?"
*Martin Gardner, The Second Scientific American Book of Mathematical Puzzles and Diversions,

Professor David Singmaster credits the first problem of this type to Mahavira's "Ganita-sara-sangraha" in the year 850."
 850 Mahavira: Ganita-sara-sangraha - first 100 Fowls Problem with four
types; first Monkey and Coconuts Problem; first Selling Different Amounts at
the Same Prices; first Sharing Cost of Stairs."

In 1933, a great unpredicted meteor shower was seen from Europe that surprised astronomers. Dr. W.J. Fisher, a Harvard astronomer, identified the Giacobini-Zinner comet as the cause. This minor periodic comet was only sparsely the cause of meteors in the past, and would otherwise be little noticed by the astronomical observers. A hundred "shooting stars" a minute were reported from the Soviet observatory at Pulkovo, near Leningrad. Though short-lived, this exceeded in brilliance the showers of 1833 and 1866, Lasting only a few hours, its maximum came at about 20:00 GMT. It was regarded as one of the major meteoric displays of history, resulting from stray fragments of comet burning up in Earth's upper atmosphere. TIS

1947 A contract was signed to develop the BINAC. The BINary Automatic Computer was the only computer ever built by the Eckert-Mauchly Computer Co., founded by ENIAC pioneers J. Presper Eckert and John Mauchly. The company became a division of Remington Rand Corp. before completing its next project, the UNIVAC. The first electronic digital computer with a stored-program capability to be completed in the United States, the BINAC had a capacity of 512 words. At a price of \$278,000, the BINAC improved on the ENIAC primarily by improving speed and power with only 700 vacuum tubes instead of 18,000.*CHM

1972 On October 9, 1972, Dr. Jeffrey Hamilton from Warwick University wanted to show his students the effect of chance by tossing a coin. Taking a 2p coin out of his pocket, he tossed it, then watched as it hit the floor, spun around and came to rest on its edge.
Prof Hamilton tells me that dozens of students witnessed the amazing event, and after a stunned silence they all broke into wild applause. As well they might, for you don't need to be a distinguished Cambridge mathematician to postulate that none of them will see such an event again. *from my loose notes and credited to "Robert Matthews who apparently knows the professor in question."

1991
The Peekskill meteorite is among the most historic meteorite events on record. Sixteen separate video recordings document the meteorite burning through the Earth's atmosphere in October 1992, whereupon it struck a parked car in Peekskill, New York, United States. The Peekskill meteorite is an H6 monomict breccia; its filigreed texture is the result of the shocking and heating following the impact of two asteroids in outer space. The meteorite is of the stony variety and approximately 20% of its mass is tiny flakes of nickel-iron. When it struck Earth, the meteorite weighed 27.7 pounds (12.6 kg) and measured one foot (0.30 m) in diameter. The Peekskill meteorite is estimated to be 4.4 billion years old *Wikipedia

2014 October 9, 2014, the post office of Macau in the People's Republic of China issued a series of stamps based on magic squares. The figure below shows the six magic squares chosen to be in this collection. *Wik   The lues of the stamps range from 1 to 9 Patacas and the stamps are arranged so tht the nine stamps values  themselves form a magic square.

In 1992, a great meteor, seen from Kentucky to New York, was observed at 7:50 pm EDT. It landed as a stone (chondrite, Olivine-Bronzite, H6, brecciated) meteorite. Its 12.37 kg mass crashed onto the Chevrolet Malibu car of Mrs. Michelle Knapp of Wells Street in Peekskill, NY. The fireball was first seen over West Virginia and traveled about 700 km NE, before smashing into the parked car with a velocity of about 80 m/s. It is only the 4th recovered meteorite for which detailed data exist on its trajectory. Dark flight began about 30 km high when the velocity dropped below 3 km/s and it continued an additional 50 km without ablation. Since getting hit by the meteorite, the car has toured Germany, Switzerland, Japan, France, and the US.*TIS

2012 The Nobel Prize in Physics is awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems". Their work may eventually help make quantum computing possible. *Wik

BIRTHS

1581 Claude-Gaspar Bachet de M´eziriac (9 Oct 1581, 26 Feb 1638), noted for his work in number theory and mathematical recreations. He published a Latin translation of the Greek text of Diophantus’s Arithmetica in 1621. This is the translation that Fermat made his famous note that became the famous Fermat's Last Theorem. He asked the ﬁrst ferrying problem: Three jealous husbands and their wives wish to cross a river in a boat that will only hold two persons, in such a manner as to never leave a woman in the company of a man unless her husband is present. (With four couples this is impossible.)*VFR (Why First?? I admit that I don't know how this differs from the similar river crossings problems of Alcuin in the 800's, Help someone?)

1704 Johann Andreas von Segner (9 Oct 1704; 5 Oct 1777) German physicist and mathematician who recognized the surface tension of liquids. He discovered that every solid body has 3 axes of symmetry. He used Daniel Bernoulli's theoretical work on the "reaction effect" to produce a horizontal waterwheel the same principle which drives a modern lawn sprinkler, which influenced Euler to work on turbines. In 1751 Segner introduced the concept of the surface tension of liquids, likening it to a stretched membrane. His view that minute and imperceptible attractive forces maintain surface tension laid the foundation for the subsequent development of surface tension theory. He made an unsuccessful attempt to give a mathematical description of capillary action.*TIS

1801 Auguste-Arthur de La Rive (9 Oct 1801; 27 Nov 1873) Swiss physicist who was one of the founders of the electrochemical theory of batteries. He began experimenting with the voltaic cell (1836) and supported the idea of Michael Faraday that the electricity was the result of chemical reactions in the cell. He invented a prize-winning electroplating method to apply gold onto brass and silver. He determined the specific heat of various gases, examined the temperature of the Earth's crust, and made ozone from electrical discharge through oxygen gas. He was a contemporary of Faraday, Ampere, and Oersted, with whom he exchanged correspondence on electricity.*TIS

1873 Karl Schwarzschild (9 Oct 1873; 11 May 1916) German theoretical astrophysicist who made both practical and theoretical contributions to 20th-century astronomy. He developed the use of photography for measuring variable stars. He also investigated the geometrical aberrations of optical systems using ray optics by introducing a perturbation equation which he called the Seidel Eikonal. While on the Russian front during military service, he computed the first two exact solutions of the Einstein Field Equations of General Relativity, one in static isotropic empty space surrounding a massive body (such as a "black hole"), and one inside a spherically symmetric body of constant density - work which led directly to modern research on black holes.*TIS His grave is in Gottingen, shown at right.

1879 Max von Laue (9 Oct 1879; 23 Apr 1960) German physicist who was a recipient of the Nobel Prize for Physics in 1914 for his discovery of the diffraction of X-rays in crystals. This enabled scientists to study the structure of crystals and hence marked the origin of solid-state physics, an important field in the development of modern electronics. *TIS When Nazi Germany invaded Denmark in World War II, the Hungarian chemist George de Hevesy dissolved the gold Nobel Prizes of von Laue and James Franck in aqua regia to prevent the Nazis from discovering them. At the time, it was illegal to take gold out of the country and had it been discovered that Laue had done so, he could have faced prosecution in Germany. Hevesy placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then re-cast the Nobel Prizes using the original gold. *Wik

1898 Heinrich Behne (9 Oct 1898, 10 Oct 1979) In addition to his work on complex analysis, Behnke wrote many articles on mathematicians. For example, he published works on Weierstrass, Toeplitz, Reidemeister, Hopf, Aleksandrov, Klein, Blumenthal, von Neumann, and Lorey. He also was a leading expert on mathematical education publishing articles such as Freiheit und Autorität im mathematischen Leben (1972) which considers the professor-student relationship and the way in which a framework, like the Erlanger program, may be immensely stimulating and yet end by being stifling and having to be discarded. Also, Die Autonomie der Geometrie (1971) which considers the way that geometry is taught in schools. *SAU

1901 Winifred Deans (9 October 1901  New Milton, Hampshire, England - 7 Jun 1990  Milltimber, Peterculter, Aberdeenshire, Scotland) graduated from Aberdeen and Cambridge. After a period in teaching, she joined a Scottish publishing company and translated many important German scientific texts for them. After World War II she worked at the Commonwealth Bureau of Animal Nutrition in Aberdeen. *SAU

1911 Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanish mathematician.
He graduated from the University of Madrid and he studied at the University of Hamburg, where he received his Ph.D. in 1936. His advisor was Wilhelm Blaschke. Because of the Spanish Civil War, he moved to Argentina where he became a very famous mathematician.
He studied integral geometry and many other topics of mathematics and science.
He worked as a teacher in the National University of the Littoral, National University of La Plata and the University of Buenos Aires. *Wik

1949 Fan Rong K Chung Graham (October 9, 1949, ), known professionally as Fan Chung, is a mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős-Rényi model for graphs with general degree distribution (including power-law graphs in the study of large information networks). Since 1998 she has been the Akamai Professor in Internet Mathematics at the University of California, San Diego (UCSD). She received her doctorate from the University of Pennsylvania in 1974, under the direction of Herbert Wilf. After working at Bell Laboratories and Bellcore for nineteen years, she joined the faculty of the University of Pennsylvania as the first female tenured professor in mathematics. She serves on the editorial boards of more than a dozen international journals. Since 2003 she has been the editor-in-chief of Internet Mathematics. She has given invited lectures in many conferences, including the International Congress of Mathematicians in 1994, and a plenary lecture on the mathematics of PageRank at the 2008 Annual meeting of the American Mathematical Society. She was selected to be a Noether Lecturer in 2009.
Chung has two children, the first born during her graduate studies, from her first marriage. Since 1983 she has been married to the mathematician Ronald Graham. They were close friends of Paul Erdős, and have both published papers with him; thus, both have Erdős numbers of 1.
She has published more than 200 research papers and three books. *Wik

DEATHS

1253 Robert Grosseteste (1168, 9 Oct 1253) was an English bishop who worked on geometry, optics, and astronomy and made Latin translations of many Greek and Arabic scientific writings. He was educated at Oxford University. He became Chancellor of Oxford University in 1215 remaining in this post until about 1221. After this he held a number of ecclesiastical positions, then from 1229 to 1235, he was a lecturer in theology to the Franciscans.
He became Bishop of Lincoln in 1235 and remained in this position until his death. As Bishop of Lincoln, he attended the Council of Lyon (1245) and addressed the papal congregation at Lyon in 1250.
Grosseteste worked on geometry, optics, and astronomy. In optics he experimented with mirrors and with lenses. He believed that experimentation must be used to verify a theory by testing its consequences. In his work De Iride, he writes:-
This part of optics, when well understood, shows us how we may make things a very long distance off appear as if placed very close, and large near things appear very small, and how we may make small things placed at a distance appear any size we want, so that it may be possible for us to read the smallest letters at incredible distances, or to count sand, or seed, or any sort or minute objects.
Grosseteste realised that the hypothetical space in which Euclid imagined his figures was the same everywhere and in every direction. He then postulated that this was true of the propagation of light. He wrote the treatise De Luce on light.
In De Natura Locorum he gives a diagram which shows light being refracted by a spherical glass container full of water.
Grosseteste also made Latin translations of many Greek and Arabic scientific writings. He wrote a commentary on Aristotle's Posterior Analytics and Physics and many treatises on scientific subjects including De Generatione Stellarum, Theorica Planetarum, and De astrolabio. In an astronomy text, he claimed that the Milky Way was the fusion of light from many small close stars.
In 1225 in De Luce (On Light), four centuries before Isaac Newton proposed gravity and seven centuries before the Big Bang theory, Grosseteste describes the birth of the Universe in an explosion and the crystallization of matter to form stars and planets in a set of nested spheres around Earth.
To our knowledge, De Luce is the first attempt to describe the heavens and Earth using a single set of physical laws.
His student, Roger Bacon, called him “the greatest mathematician” of his time. Grosseteste's work on optical physics influenced mathematicians and natural philosophers for generations, notably in Oxford during the fourteenth century and in Prague during the fifteenth.. *SAU & *Nature.com

1806 Benjamin Banneker (9 Nov 1731, 9 Oct 1806). Black-American astronomer, inventor, and mathematician, compiler of almanacs and one of the first important black American intellectuals who was the self-educated son of a freed slave. He was the first to record the arrival of the "seventeen-year locusts" or periodical cicadas. In 1753, Banneker built a wooden clock that kept accurate time even though he had only previously seen a sundial and a pocket watch. He calculated the clock's gear ratios and carved them with a pocket knife. In 1789, he successfully predicted an eclipse. He helped survey the site of Washington D.C. (1791-3). Banneker was also an early antislavery publicist who worked to improve the lot of black people in the U.S.*TIS

1807 Gianfrancesco Malfatti (26 September 1731 – 9 October 1807) was an Italian mathematician who worked on geometry, probability, and mechanics and made contributions to the problem of solving polynomial equations. Malfatti wrote an important work on equations of the fifth degree. In 1802 he gave the first solution to the problem of describing in a triangle three circles that are mutually tangent, each of which touches two sides of the triangle, the so-called Malfatti problem. His solution was published in a paper of 1803 on un problema stereotomica. *SAU

1909 Bailie Hugh Blackburn (2 July 1823, Craigflower, Torryburn, Fife – 9 October 1909, Roshven, Inverness-shire) was a Scottish mathematician. A lifelong friend of William Thomson (later Lord Kelvin), and the husband of illustrator Jemima Blackburn, he was professor of mathematics at the University of Glasgow from 1849 to 1879. He succeeded Thomson's father James in the Chair of Mathematics.*Wik

1943 Pieter Zeeman (25 May 1865, 9 Oct 1943). Dutch physicist who was an authority on magneto-optics. In 1896, he discovered the "Zeeman effect," the "phenomena produced in spectroscopy by the splitting up of spectral lines in a magnetic field." He shared (with Hendrik A. Lorentz) the Nobel Prize for Physics in 1902 for his discovery of the Zeeman effect.*TIS

1948 Joseph Henry Maclagen Wedderburn (2 Feb 1882 in Forfar, Angus, Scotland
- 9 Oct 1948 in Princeton, New Jersey, USA) studied at Edinburgh, Leipzig, Berlin, and Chicago. He returned to Scotland to work at Edinburgh but then moved to a post at Princeton where he spent the rest of his career except for a break for service in World War I. He made far-reaching discoveries in the theory of rings, algebras, and matrices. He became an honorary member of the EMS in 1946. *SAU

1990 Georges de Rham (10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology.
In 1931 he proved de Rham's theorem, identifying the de Rham cohomology groups as topological invariants. This proof can be considered as sought-after since the result was implicit in the points of view of Henri Poincaré and Élie Cartan. The first proof of the general Stokes' theorem, for example, is attributed to Poincaré, in 1899. At the time there was no cohomology theory, one could reasonably say: for manifolds the homology theory was known to be self-dual with the switch of dimension to codimension (that is, from Hk to Hn-k, where n is the dimension). That is true, anyway, for orientable manifolds, an orientation being in differential form terms an n-form that is never zero (and two being equivalent if related by a positive scalar field). The duality can to great advantage be reformulated in terms of the Hodge dual—intuitively, 'divide into' an orientation form—as it was in the years succeeding the theorem. Separating out the homological and differential form sides allowed the coexistence of 'integrand' and 'domains of integration', as cochains and chains, with clarity. De Rham himself developed a theory of homological currents, that showed how this fitted with the generalised function concept.
The influence of de Rham’s theorem was particularly great during the development of Hodge theory and sheaf theory.
De Rham also worked on the torsion invariants of smooth manifolds. Wik

2006 Raymond Noorda (19 Jun 1924, 9 Oct 2006) American electrical engineer, known as "the father of computer networking" because he was primarily responsible for making widespread the business use of networked personal computers (PC's). He did not invent the local area network (LAN) by which computers share files and printers through interlinked nodes. However, as chief executive of Novell Inc (1983-94), his organization and marketing turned the company's NetWare brand software into the first major PC network operating system. It linked even previously incompatible computers, whether IBM-compatible, Apple or Unix. To establish standardization in the industry, he believed in working with competitors, for which he coined the term "co-opetition." *TIS

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