Friday, 9 October 2015

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

The 282nd day of the year; there are 282 plane partitions of nine objects. (A plane partition is a two-dimensional 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:


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

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

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 eye witnesses, 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 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 round 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."

2014 October 9, 2014 the post office of Macao 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

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


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 the Greek text of Diophantus’s Arithmetica in 1621. 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 (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 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


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 & *

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

Thursday, 8 October 2015

On This Day in Math - October 8

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

The 281st day of the year, 281 is a prime and is the sum of the first fourteen prime numbers. It is the sixth, and last, day of the year such that the sum of the first k primes is a prime.  (I just noticed that all of them except 2, is the smaller of pair of twin primes.  Unfortunately, the next one after that is not.)
281 appears in the sequence of primes generated by \(f(x)= x^2 + x + 41 \)  Which is often called the Euler Polynomial. (although Euler actually used  \(x^2 -x + 41\) which is prime for x values from 1 to 40.  Legendre noticed that the positive x form produced the same primes for values from 0 to 39.)


In 1604, the supernova now called "Kepler's nova" was first sighted in the constellation Ophiuchus, the Serpent Bearer. Johannes Kepler observed it from the time of its appearance as an apparently new star. It encouraged him to write The New Star in 1606.*TIS

1834 Jakob Steiner appointed extraordinary professor at the University of Berlin, a post he held until his death in 1863. *VFR

1996 The U.S. Postal Service issued a special "Computer Technology" stamp to mark the 50th anniversary of the ENIAC. In a ceremony at the Army’s Aberdeen Proving Ground, speakers paid tribute to computer pioneers with the image of a brain partially covered by small blocs that contain parts of circuit boards and binary language. The stamp was designed entirely on a computer. A Postal Service news release from Oct. 8 introduced the
stamp with a discussion of the ENIAC’s origins: "Long before PCs became standard office equipment and surfing on the information superhighway became a national obsession, calculations were done the ‘old-fashioned way’ by hand. And, as is often the case, it took a war to bring the world into the computer age specifically, the need for the United States Army to rapidly compute ballistic firing tables." *CHM
There also seems to be a US 3 cent stamp of the Eniac. The date on the page I saw has 1943, but on the stamp it says eniac was "completed in 1946"  . If someone knows the true date this stamp was released, please advise.  

2008 The Mathematics Library at Notre Dame was rededicated and named for Prof. O. Timothy O’Meara. Prof. O’Meara is a noted Mathematician, who has been on the faculty of the Mathematics Department since 1962, and twice served as its chairman. In 1976 he was named to the Kenna Endowed Chair in Mathematics. He is noted for serving as the first lay Provost of the University, 1978-1996. He is now an emeritus faculty member, but still very active and interested in the library *ND Web Site

2014 A total lunar eclipse will be visible, weather permitting, from much of North America, as well as to observers in Australia, western Asia and across the Pacific Ocean. Observers east of the Mississippi in the US may see the total eclipse of the moon and the rising sun simultaneously. The little-used name for this effect is called a "selenelion," a phenomenon that celestial geometry says cannot happen. But thanks to Earth's atmosphere, the images of both the sun and moon are apparently lifted above the horizon by atmospheric refraction. This allows people on Earth to see the sun for several extra minutes before it actually has risen and the moon for several extra minutes after it has actually set.


1561 Edward Wright (baptised 8 October 1561; November 1615) was an English mathematician and cartographer noted for his book Certaine Errors in Navigation (1599; 2nd ed., 1610), which for the first time explained the mathematical basis of the Mercator projection, and set out a reference table giving the linear scale multiplication factor as a function of latitude, calculated for each minute of arc up to a latitude of 75°. This was in fact a table of values of the integral of the secant function, and was the essential step needed to make practical both the making and the navigational use of Mercator charts.*Wik At his Renaissance Mathematicus blog, Thony Christie points out that "Mercator printed and published a world map constructed according to this method (cylindrical) of projection in 1569 but he did not explain the mathematical rules on which it was based. He was a professional cartographer and globe maker and he probably hoped that if he kept his method secret then the people who wished to take advantage of this new development would have to order their maps and charts from him.... John Dee and Thomas Harriott both independently solved the mathematical problem of the projection but like Mercator neither of them made the knowledge public. We can however assume that both of them made use of this knowledge when teaching navigation and cartography, Dee to the pilots of the Muscovy Company and Harriot to Walter Raleigh’s sea captains.
The first person to publish the mathematical method of constructing such a chart was another English mathematicus Edward Wright in his book Certaine Errors in Navigation, first published in 1599."

1850 Peter Scott Lang (8 Oct 1850, 5 July 1926) graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

1873 Ejnar Hertzsprung (8 Oct 1873; 21 Oct 1967) Danish astronomer who classified types of stars by relating their surface temperature (or colour) to their absolute brightness. A few years later Russell illustrated this relationship graphically in what is now known as the Hertzsprung-Russell diagram, which has become fundamental to the study of stellar evolution. In 1913 he established the luminosity scale of Cepheid variable stars.*TIS

1908 Hans Arnold Heilbronn (8 October 1908 – 28 April 1975) was a mathematicianb orn into a German-Jewish family. He was a student at the universities of Berlin, Freiburg and Göttingen, where he met Edmund Landau, who supervised his doctorate. In his thesis, he improved a result of Hoheisel on the size of prime gaps. *Wik

1932 Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. Their conclusion, that four colors would suffice for any map, depended on 1,200 hours of computer time — the equivalent of 50 days — and 10 billion logical decisions all made automatically and out of sight by the innards of an I.B.M. computer at the University of Illinois in Urbana.
He died of esophageal cancer on April 19, 2013. *Wik

1944 E. E. "Pat" Ballew , Whose greatest contribution to mathematics was in helping to educate many great young people who went on to be successful in numerous walks of life.  Editor/author of this blog. So "Happy Birthday to me". 


1647 Christian Longomontanus (4 Oct 1562, 8 Oct 1647) Byname of Christian Severin, a Danish astronomer and astrologer who is best known for his association with, and published support for, Tycho Brahe. He became the first professor of astronomy at the University of Copenhagen, and in 1610 he received funds for instruments and he probably constructed a small observatory at his home. Longomontanus used Tycho's data to compile the Astronomia danica (1622), an exposition of the Tychonic system, which holds that the Sun revolves around the Earth and the other planets revolve around the Sun. He began the construction of the Copenhagen Observatory in 1632, but died before its completion.*TIS

1652 John Greaves (1602, 8 Oct 1652) Greaves was appointed as Professor of Geometry at Gresham College, London, in February 1631. He was able to retain his fellowship at Merton College, Oxford. His main scientific aim was the "practical and sober project of standardizing and synchronizing the weights and measures of all ancient and modern nations."
His desire to find out about measurements in the ancient world led him to plan visits to Italy and Egypt, where he wanted to make measurements of the pyramids. As Shalev puts it "It is metrology which fuelled Greaves's fascination with ancient monuments, and with the Great Pyramid above all."
In 1649 he published A Discourse of the Roman Foot, and Denarius; from whence, as from two Principles, the Measures and Weights used by the Ancients may be deduced. In the same year he published Elementa Linguae Persicae.*SAU

1883 Professor Enoch Beery Seitz,(August 24, 1846 Rushcreek Township, Ohio – October 8, 1883 Kirksville, Mo.) of Missouri State Normal School(now Truman State University), was “stricken by that ‘demon of death.’ typhoid fever, and passed the mysterious shades, to be numbered with the silent majority.” “Prof. Seitz was in mathematics what Demosthenes was in oratory; Shakespeare in poetry; and Napoleon in war: the equal of the best, the peer of all the rest.” In case you have never heard him, see the biography in the first volume (1894) of the Americal Mathematical Monthly, pp. 3–6. *VFR
A nice problem from Professor Seitz, Perhaps inspired by the Greenville (Ohio) hometown legend Annie Oakly and her rifleman ship, Seitz offered the problem:
"A cube is thrown into the air and a random shot fired through it; find the chance that the shot passes through the opposite side." From a nice biography of the professor *by John E. Zimmerman, Washington & Jefferson College

1940 Robert Emden (4 Mar 1862, 8 Oct 1940) Swiss astrophysicist and mathematician who wrote Gaskugeln (Gas Spheres, 1907), giving a mathematical model of stellar structure as the expansion and compression of gas spheres, wherein the forces of gravity and gas pressure are in equilibrium. He expanded on earlier work by J. H. Lane (1869) and A. Ritter (1878-83) who first derived equations describing stars as gaseous chemical, spherical bodies held together by their own gravity and obeying the known gas laws of thermodynamics. For four decades, the Lane-Emden equation was the foundation of theoretical work on the structure of stars: their central temperatures and pressures, masses, and equilibria. Emden also devised a hypothesis, no longer taken seriously, to explain sunspots. *TIS

1973 Evan Tom Davies (24 Sept 1904, 8 Oct 1973) graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations. *SAU

2001 Caryl Parker Haskins (August 12, 1908 to October 8, 2001) was a scientist, author, inventor, philanthropist, governmental adviser and pioneering entomologist in the study of ant biology. In the 1930s he was inspired by Alfred Lee Loomis to establish his own research facility. Along with Franklin S. Cooper, he founded the Haskins Laboratories, a private, non-profit research laboratory, in 1935. Affiliated with Harvard University, MIT, and Union College in Schenectady, NY, Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of this program is now part of Pace University in New York. In the 1940s Luigi Provasoli joined the Laboratories to set up a research program in marine biology which disbanded with his retirement in 1978. Since the 1950s, the main focus of the research of Haskins Laboratories has been on speech and its biological basis. The main facility of Haskins Laboratories moved to New Haven, Connecticut in 1970 where it entered into affiliation agreements with Yale University and the University of Connecticut. Haskins Laboratories continues to be a leading, multidisciplinary laboratory with an international scope that does pioneering work on the science of the spoken and written word.
Haskins served as President, Research Director, and Chairman of the Board of Haskins Laboratories, 1935-'87; Director, E.I. du Pont de Nemours, 1971-'81 and Research Professor, Union College, 1937-'55. In 1956, he was appointed to the Presidency of the Carnegie Institution of Washington, a position he held until 1971. He was also President of the Sigma Xi society in 1967-'68. He remained a Trustee of Carnegie Institution and of Haskins Laboratories, as well as Trustee Emeritus of the National Geographic Society until his death. He also continued his research on entomology, working with his wife, Edna Haskins, and other colleagues. *Wik

2005 Alfred William Goldie (10 Dec 1920, 8 Oct 2005) was an English mathematician who proved an important result in Ring Theory. Goldie's first paper in this area Decompositions of semi-simple rings (1956) made an immediate impact since Jacobson included one of Goldie's theorems in his classic monograph Structure of Rings of 1956, acknowledging that it had been communicated by Goldie. Over the next few years Goldie's work on non-commutative Notherian rings would totally revolutionise the subject. He was able to prove totally unexpected structure theorems. Even his first steps towards these results were startling *SAU

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

Wednesday, 7 October 2015

On This Day in Math - October 7

Contraria sunt complementa.
Opposites are complementary.
Motif on Niels Bohr's coat of arms

The 280th day of the year; There are 280 plane trees with ten nodes. As a consequence of this, 18 people around a round table can shake hands without crossing arms in 280 different ways (up to rotations)
The sum of the first 280 consecutive primes mod 280 is prime. *Prime Curios

For more fun with daily calendar math see Dereks Daily Math
and Ben Vitale


1601 Baptismal date of Florimond DeBeaune whose fame rests on two brief notes published in Schooten’s Latin edition of Descartes (1649 and 1659–60). In the second of these he raised the first inverse tangent problem: determine a curve from a property of its tangent. *VFR (This is the first example of a first order differential equation problem.) This is often listed as his birth date (SAU and others) but appears not to have been.

1854 In an addendum to his paper An Introductory Memoir upon Quantics, Arthur Cayley would add a second differential equation and state that "a covariant is a expression which, if it satisfies one of these equations, it satisfies the other. This would be the backbone of his new formulation of covariants in his next paper, A second Memoire upon Quantics. *James Joseph Sylvester: Life and Work in Letters, edited by Karen Hunger Parshall

1864 The mathematical seminar at Berlin began. It was the oldest such seminar in Germany and the model for many others. Kummer, Weierstrass, and Kronecker ran it. One of its goals was to improve teaching. *ISIS 66(1975), p 584

1893 When the poet/mathematician Omar Khayyam died in 1123 he was buried in a spot where the North wind would scatter rose petals over his grave. On this date a rose tree started from those on Khayyam’s grave was transplanted to the grave of Edward FitzGerald (1809-1883), the Irish translator who made Khayyam’s poetry so famous in modern times. For Khayyam’s geometric solution to the cubic see Eves, Great Moments in Mathematics (before 1650), p. 155. *VFR (FitzGerald is buried in the churchyard of the small, isolated Church of St Michael and All Angels, Boulge, Suffolk, England (Near Ipswitch). Six more rose trees were planted around the grave in 1972.) If anyone has an image of the roses in bloom around his grave, I would appreciate a note.

1988 The Computer Bowl Begins. The first round of The Computer Bowl, an annual televised game show of computer trivia pitting the gurus of the East versus the wizards of the West, was held. Mitch Kapor and Bill Joy were the MVPs, winning a place on the all star team. *CHM

2014 Sky watchers heading to bed early tonight: Early tomorrow a total lunar eclipse, a "blood moon", will be visible, weather permitting, from much of North America, as well as to observers in Australia, western Asia and across the Pacific Ocean. Observers east of the Mississippi in the US may see the total eclipse of the moon and the rising sun simultaneously. The little-used name for this effect is called a "selenelion," a phenomenon that celestial geometry says cannot happen. But thanks to Earth's atmosphere, the images of both the sun and moon are apparently lifted above the horizon by atmospheric refraction. This allows people on Earth to see the sun for several extra minutes before it actually has risen and the moon for several extra minutes after it has actually set.
The phrase “blood moon” comes from an interpretation of a Biblical prophecy concerning the upcoming tetrad of total lunar eclipses. That is to say, the April 15, 2014 total lunar eclipse is one of four total lunar eclipses that will take place, with no partial lunar eclipses between them. As you might imagine, this is a relatively rare astronomical event. There are only 8 tetrads in the 21st century. In some centuries, a tetrad does not occur at all. The word “blood” comes into play presumably because at totality, the eclipsed moon appears reddish brown. You could even call it blood red.*


1858 Charles Marvin (October 7, 1858 – June 5, 1943) U.S. meteorologist who invented the clinometer that figures height of clouds over airports. He was Chief of the U.S. Weather Bureau (1913-34). He worked on, and wrote about, the Robinson cup anemometer, from early in his career with the Weather Bureau until years after his retirement. For early systematic investigations of the upper air, he designed and constructed kites and kite instruments. He also devised the Marvin pyrheliometer and inaugurated the regular measurement of solar radiation intensity by the Weather Bureau. Marvin designed a seismograph operated by the Weather Bureau. He was also particularly interested in the application of mathematical statistics to meteorological problems.*TIS (Teachers who have student's create clinometers with a straw, protractor and plumbline might include this historical artifact as a preliminary to the lesson.)

1875 Raymond Clare Archibald (7 Oct 1875, 26 July 1955) studied in Canada, at Harvard and at Strasbourg. He spent most of his career at Brown University in Rhode Island. His main interests were in the History of Mathematics. *SAU

1885 Niels Henrik David Bohr (7 Oct 1885, 18 Nov 1962) was a Danish physicist, born in Copenhagen, who was the first to apply the quantum theory, which restricts the energy of a system to certain discrete values, to the problem of atomic and molecular structure. For this work he received the Nobel Prize for Physics in 1922. He developed the so-called Bohr theory of the atom and liquid model of the nucleus. Bohr was of Jewish origin and when the Nazis occupied Denmark he escaped in 1943 to Sweden on a fishing boat. From there he was flown to England where he began to work on the project to make a nuclear fission bomb. After a few months he went with the British research team to Los Alamos in the USA where they continued work on the project. *TIS (Bohr and his brother, the mathematician Harald Bohr, were both outstanding athletes. An amusing anecdote about their sporting lives here.)

1899 Oystein Ore (7 October 1899 in Oslo, Norway – 13 August 1968 in Oslo) was a Norwegian mathematician. Ore is known for his work in ring theory, Galois connections, and most of all, graph theory. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then worked on noncommutative rings, proving his celebrated theorem on embedding a domain into a division ring. He then examined polynomial rings over skew fields, and attempted to extend his work on factorisation to non-commutative rings.
In 1930 the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject. Ore's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life.
Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel. *Wik

1939 Sir Harold W. Kroto (7 Oct 1939, )English chemist who, with Richard E. Smalley and Robert F. Curl, Jr., was awarded the 1996 Nobel Prize for Chemistry for their joint discovery of the carbon compounds called fullerenes. These new forms of the element carbon contain 60 or more atoms arranged in closed shells. The number of carbon atoms in the shell can vary, and for this reason numerous new carbon structures have become known. Formerly, six crystalline forms of the element carbon were known, namely two kinds of graphite, two kinds of diamond, chaoit (1968) and carbon(VI) (1972). Fullerenes are formed when vaporized carbon condenses in an atmosphere of inert gas. The carbon clusters can then be analyzed with mass spectrometry.*TIS


1719 Pierre Rémond de Montmort (27 Oct 1678, 7 Oct 1719) was a French mathematician who wrote an important work on probability. Montmort's reputation was made by his book on probability Essay d'analyse sur les jeux de hazard which appeared in 1708. The book, which is a collection of combinatorial problems, is a systematic study of games of chance and shows that there is important mathematics in this area. Montmort collaborated with Nicolaus(I) Bernoulli and he was also a friend of Taylor. At a time of high feelings in the Newton-Leibniz controversy it says a lot for Montmort that he could be friends with followers of both camps. In addition, Montmort corresponded with Craig, Halley, Hermann and Poleni. Montmort was elected to be a Fellow of the Royal Society in 1715, when he was on a trip to England. The following year he was elected to the Académie Royal des Sciences. *SAU

1903 Rudolf Otto Sigismund Lipschitz (14 May 1832, 7 Oct 1903) is remembered for the "Lipschitz condition", an inequality that guarantees a unique solution to the differential equation y' = f (x, y).*SAU

1965 Jesse Douglas (3 Jul 1897, 7 Oct 1965) American mathematician who was awarded one of the first two Fields Medals in 1936 for solving the Plateau problem. which had first been posed by the Italian-French mathematician Joseph-Louis Lagrange in 1760. The Plateau problem is one of finding the surface with minimal area determined by a fixed boundary. Experiments (1849) by the Belgian physicist Joseph Plateau demonstrated that the minimal surface can be obtained by immersing a wire frame, representing the boundaries, into soapy water. Douglas developed what is now called the Douglas functional, so that by minimizing this functional he could prove the existence of the solution to the Plateau problem. Douglas later developed an interest in group theory.*TIS

1992 Martin Eichler (29 March 1912 – 7 October 1992) was a German number theorist. He received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. He is linked with Goro Shimura in the development of a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.*Wik

1995 Gerard Henri de Vaucouleurs (25 Apr 1918, 7 Oct 1995) French-born U.S. astronomer whose pioneering studies of distant galaxies contributed to knowledge of the age and large-scale structure of the universe. He produced three Reference Catalogues of bright galaxies (1964, 1976, 1991). Each was a homogenization of data from widely different sources, so that the catalogues would not be merely finding lists or data collection lists, but astrophysically useful databases. Using data in the Reference Catalogues, he was able to develop new distance indicators and refine others. His unique philosophy on distance matters was "spreading the risks," that is, applying as many different and independent techniques as possible to check for scale and zero-point errors.*TIS

1995 Olga Taussky-Todd (August 30, 1906– October 7, 1995) was a Czech-American mathematician who worked first in algebraic number theory, with a doctorate at the University of Vienna supervised by Philipp Furtwängler. During that time in Vienna she also attended the meetings of the Vienna Circle. Later, she started to use matrices to analyze vibrations of airplanes during World War II, at the National Physical Laboratory in the United Kingdom. She became the torchbearer for matrix theory.
In 1938 she married another mathematician, John Todd and in 1945 the Todds immigrated to the United States and worked for the National Bureau of Standards. In 1957 they joined the faculty of California Institute of Technology in Pasadena, California.
She was a Fellow of the AAAS, a Noether Lecturer and a recipient of the Austrian Cross of Honour for Science and Art. She also supervised Caltech's first female Ph.D. in Math, Lorraine Foster. *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

Tuesday, 6 October 2015

On This Day in Math - October 6

[after proving Euler's formula e π i + 1 = 0 in a lecture]
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it is the truth.

~Benjamin Peirce

The 279th day of the year; Every positive integer is the sum of at most 279 eighth powers. See Waring's problem

279 = 3^2 + 3^3 + 3^5 (powers are consecutive primes). *Derek Orr

For more fun with daily calendar math see Dereks Daily Math
and Ben Vitale


1570 Cardano imprisoned for 87 days on charges of impiety (casting a horoscope of Christ). He spent the remaining five years of his life in Rome under the eye of a suspicious pope who nonetheless gave him a pension. See “Girolamo Cardano’s Horoscope of Christ,” pp. 53–90 in Renaissance Curiosa by Wayne Shumaker, especially p. 55 *VFR

1651 Sir Charles Cavendish writes to John Pell about Thomas Harriot’s Doctrine of Triangular Numbers; “Sr. Th Alesburie remembers him to you & desires to know if you would be pleased to shew the use of Mr. Harriots doctrine of triangulare numbers; which if you will doe, he will send you the original; I confess I was so farre in loue with it that I coppied it out; though I doute I vnderstand it not all; much less the many vses which I assure myself you will finde of it.” *Thomas Harriot’s Doctrine of Triangular Numbers, Beery &Stedall, pg 3

1668 (Oct 16 NS) Wallis writes to thank Oldenburg for gift of "Lalovera's book" (La Loubere), veterum geometria promota, in septem de cycloide libris. La Loubere is often cited as the first man to bring the "Siamese" method of solving nxn odd magic squares to the West. *Philip Beeley, Christoph J. Scriba; Correspondence of John Wallis

1729 The first known letter which contains an interpolating function for the factorials was written by Daniel Bernoulli on October 6, 1729. Bernoulli suggests for an arbitrary (positive) x and an infinite number A the infinite product $$ (A + \frac{x}{2})^{x-1} *((\frac{2}{1+x}) *(\frac{3}{2+x})* ... *(\frac{A}{A-1+x})$$

In 1783, the self-winding clock was patented by Benjamin Hanks.*TIS

1807 Humphry Davy first isolated potassium by electrolysis of molten KCl in the basement of Royal Institute.  *Anthony Hardwicke Tweet

1860 J. J. Sylvester, in a dinner invitation for Thomas Archer Hirst to join him with Arthur Cayley and Sylvester's "young French mathematical friend", (Camille Jordan); Sylvester entices him with a bit of mathematics, "I shall have something very striking to tell you about algebraic quantities of any order of irrationality and their representation by multiple definite integrals when we meet." *James Joseph Sylvester: Life and Work in Letters, edited by Karen Hunger Parshall

1983 Lotus Development Corp. went public after recording revenues of $12.8 million for the previous 12 months. The company, founded by Mitch Kapor and Jonathan Sachs in 1982, found its success with Kapor’s spreadsheet program, Lotus 1-2-3​. Lotus 1-2-3 bypassed the operating system of the IBM PC, making it much faster than its competitors. In addition, its combination of spreadsheet capabilities with graphics and data retrieval made the program popular. IBM acquired Lotus in 1995.*CHM

1994 Fermat confirmed, FINALLY. Wiles sends corrected proof. Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Andres Wiles had announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards.
(Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

In 1995, the first discovery of a planet around a star similar to the sun was announced (about 160 times the mass of the Earth around the star 51 Pegasus).*TIS

2008 First Space object observed before it hit the earth. At 06:38 UTC on October 6, astronomers at the University of Arizona discovered an object provisionally called 8TA9D69 that appeared to be on a collision course with Earth. Three other observatories reported sightings within the next few hours -- Sabino Canyon in Arizona and Siding Spring Observatory and a Royal Astronomical Society site, both in Australia. Together these four observers provided enough data on the object so that a Minor Planet Electronic Circular was issued at 14:59 UTC the same day, giving 8TA9D69 the more formal name 2008 TC3, and advising the astronomical community that "The nominal orbit given above has 2008 TC3 coming to within one earth radius around Oct. 7.1. The absolute magnitude indicates that the object will not survive passage through the atmosphere. Steve Chesley (JPL) reports that atmospheric entry will occur on 2008 Oct 07 0246 UTC over northern Sudan."
The object wouldn't be more than a big meteor, but even so, it represented the first time ever that an object had been observed before it was to hit Earth, and, clearly, astronomers around the world scrambled to their telescopes to observe it before it was to pass into Earth's shadow (and, therefore, invisibility) just before 01:50 UTC. *The Planetary Society


1552 Matteo Ricci (6 Oct 1552, 11 May 1610) Matteo Ricci was an Italian Jesuit who went to China as a missionary and introduced the Chinese to Western mathematics.*SAU More detail about this student of Clavius at the Renaissance Mathematicus

1732 Nevil Maskelyne (6 Oct 1732, 9 Feb 1811) (SAU gives 5 Oct for birhtdate)
British astronomer noted for his contribution to the science of navigation. In 1761 the Royal Society sent Maskelyne to the island of St Helena to make accurate measurements of a transit of Venus. This in turn gives the distance from the Earth to the Sun, and the scale of the solar system. During the voyage he also experimented with the lunar position method of determining longitude. In 1764 he went on a voyage to Barbados to carry out trials of Harrison's timepiece, followed by appointment as Astronomer Royal (1765). In 1774, he carried out an experiment on a Scottish mountain with the use of a plumb line to determine the Earth's density. He found it was approximately 4.5 times that of water. *TIS

1735 Jesse Ramsden (6 Oct 1735; 5 Nov 1800) British pioneer in the design of precision tools. At 23, Ramsden chose to apprentice to a maker of mathematical instruments. By age 27 he had his own business in London and was known as the most skilful designer of mathematical, astronomical, surveyingand navigationalinstruments in the 18th Century. He is best known for the design of a telescope and microscope eyepiece (ocular) still commonly used today and bearing his name. The French scientist N. Cassegrain proposed a design of a reflecting telescope in 1672, but Ramsden, however, 100 years later, who found that this design reduces blurring of the image caused by the sphericity of the lenses or mirrors. He also built lathes, barometers, manometers and assay balances.*TIS

1784 Pierre Charles François Dupin (6 Oct 1784, 18 Jan 1873) Dupin made contributions to differential geometry and in particular invented the 'Dupin indicatrix'.*SAU

1795 Benjamin Olinde Rodrigues (6 Oct 1795, 17 Dec 1851) was a French mathematician best known for his formula for the Legendre polynomials.*SAU

1831 (Julius Wilhelm) Richard Dedekind (6 Oct 1831, 12 Feb 1916 at age 84) German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern mathematics. *TIS A 1904 academic calendar marked September fourth, 1899 as the day Dedekind died. He wrote the publisher saying that while 4 September might be correct, 1899 certainly was not, for on that day he had enjoyed a stimulating mathematical discussion with his dinner guest and honored friend, Georg Cantor. *VFR

1866 Reginald Aubrey Fessenden (6 Oct 1866, 22 Jul 1932) Canadian inventor and engineer with 300 patents. He broadcast the first program of voice and music. In 1893, Fessenden moved to Pittsburgh as the head of electrical engineering at the university, Fessenden read of Marconi's work and began experimenting himself. Marconi could only transmit Morse code. But Fessenden's goal was to transmit the human voice and music. He invented the "continuous wave": sound superimposed onto a radio wave for transmission. A radio receiver extracts the signal so the listener with the original sound. Fessenden made the first long-range transmissions of voice on Christmas Eve 1906 from a station at Brant Rock, Massachusetts, heard hundreds of miles out in the Atlantic.*TIS

1903 Ernest Thomas Sinton Walton(6 Oct 1903; 25 Jun 1995) Irish physicist, who was corecipient, with Sir John Douglas Cockcroft of England, of the 1951 Nobel Prize for Physics for the development of the first nuclear particle accelerator, known as the Cockcroft-Walton generator. The accelerator was built in a disused room in the Cavendish Laboratory, and supplied with several hundred kilovolts from a voltage multiplier circuit designed and built by Cockroft and Walton. On 14 Apr 1932 Walton turned the proton beam on to a lithium target. Despite all the odds against them, they succeeded in being the first to split the atom, and Walton was the first to see the reaction taking place. They identified the disintegration products as alpha particles (helium nuclei). *TIS

1908 Sergei Lvovich Sobolev (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations.*Wik

1918 Abraham Robinson (October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics.*Wik

1936 Robert Phelan Langlands (October 6, 1936 - ) is a Canadian mathematician best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory. He is an emeritus professor at the Institute for Advanced Study. Langlands has received the 1996 Wolf Prize (which he shared with Andrew Wiles), the 2005 AMS Steele Prize, the 1980 Jeffery-Williams Prize, the 1988 NAS Award in Mathematics from the National Academy of Sciences, the 2006 Nemmers Prize in Mathematics, and the 2007 Shaw Prize in Mathematical Sciences (with Richard Taylor) for his work on automorphic forms. *Wik Langlands occupies the office formerly held by Albert Einstein at Princeton.  *Edward Frenkel, Love and Math

1950 Glen David Brin, (born October 6, 1950 - ) is an American scientist and award-winning author of science fiction. He has received the Hugo, Locus, Campbell and Nebula Awards.
Brin was born in Glendale, California in 1950. In 1973, he graduated from the California Institute of Technology with a Bachelor of Science in astrophysics. He followed this with a Master of Science in applied physics in 1978 and a Doctor of Philosophy in space science in 1981, both from the University of California, San Diego. He is a 2010 fellow of the Institute for Ethics and Emerging Technologies.*Wik


1809 Benjamin Peirce (4 Apr 1809, 6 Oct 1880) American astronomer, mathematician and educator who computed the general perturbations of the planets Uranus and Neptune. He was Harvard's Perkins Professor of Astronomy and Mathematics for nearly 40 years, and was largely responsible for introducing mathematics as a subject for research in American institutions. He is known especially for his contributions to analytic mechanics and linear associative algebra, but he is also remembered for his early work in astronomy and for playing a role in the discovery of Neptune. *TIS In number theory, he proved there is no odd perfect number with fewer than four prime factors. In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition. *Wik

1840 François Budan de Boislaurent (28 Sept 1761, 6 Oct 1840) was a Haitian born amateur mathematician best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan is considered an amateur mathematician and he is best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan's rule was in a memoir sent to the Institute in 1803 but it was not made public until 1807 in Nouvelle méthode pour la résolution des équations numerique d'un degré quelconque. In it Budan wrote, "If an equation in x has n roots between zero and some positive number p, the transformed equation in (x - p) must have at least n fewer variations in sign than the original." *SAU (Sounds like a nice followup extension to Descartes Rule of signs in Pre-calculus classes. Mention the history, how many times do your students hear about a Haitian mathematician?)

Crelle Memorial in his hometown
1855 August Leopold Crelle (11 Mar 1780; 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. In 1841, he was elected a foreign member of the Royal Swedish Academy of Sciences.*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