Sunday, 24 November 2019

On This Day in Math - November 24


Albertus Magnus

To call in the statistician after the experiment is done may be no more than asking hm to perform a postmortem examination: he may be able to say what the experiment died of.
~Fisher, Ronald Aylmer


The 328th day of the year; 328 is the sum of the first fifteen primes. No year day can has more.
It is also is a tau-number since it is divisible by the number of divisors it has.

328 reversed is prime, and it is the sum of the first 15 primes.  It is the last day of the year that will be the sun of the first n primes.


EVENTS

1639 British astronomers Jeremiah Horrocks and William Crabtree became the first observers to record a transit of Venus. Horrocks was just a teenager, and would die at the tender age of twenty-two, but before he did, he ran up several impressive notches in his scientific portfolio. For more on this event, see
this blog by The Renaissance Mathematicus. Applying Kepler's prediction that in 1631, Venus would transit the Sun, Horrocks calculated that these transits occurred not singly but in pairs eight years apart. Thus, Horrocks prepared his equipment for the next transit he had thus predicted for this day. His simple telescope was mounted on a wooden beam, so he could project a solar image onto a piece of paper marked with a six inch graduated circle. From this, he made measurements and calculated that the value for the solar parallax was smaller than previously recorded, and so concluded that the Sun was further away from the Earth than previously thought. *TIS As the image shows, the observation was made at Carr House where he lived at the time.  "Horrocks returned to Toxteth Park (Liverpool) sometime in the summer of 1640 and died suddenly and from unknown causes on 3 January 1641, aged only 22. As expressed by Crabtree, "What an incalculable loss!" *John Wallis  The image is from the lancashire.gov.uk

1713 As the 18th century began, even the devoted Newton supporters were finding themselves drawn to the Leibniz notation used on the continent, although the real break would not come for another hundred years.  But in 1713, even the most devout Newtonians were wavering.  On this date, John Kell, a bitter opponent of Leibniz, would use the \( \int \) for integration, but fiercely continued to use the "pricked numerals" of Newton.  \( \dot {x}\) .  *Philosophical Transactions


1759 Lagrange wrote Euler that he believes that he had developed the true metaphysics of the calculus; at that time he seems to have been convinced that the use of infinitesimals was rigorous. Lagrange attempted to prove Taylor’s theorem (the power of which he was the first to observe) and then to develop the entire calculus from it. (Cajori, History of Mathematics, 257) *VFR

1789 Lagrange finished his M´ecanique analytique. In this he lays down the law of virtual work, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole of mechanics, both of solids and fluids.
The object of the book is to show that the subject is implicitly included in a single principle, and to give general formulae from which any particular result can be obtained. The method of generalized co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he showed that, if we determine its configuration by a sufficient number of variables whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation. *Wik

1831 Michael Faraday reads the first of a series of papers on "Experimental Research into Electricity." *Phil. Trans. R. Soc. Lond. January 1, 1832 122:125-162;

1836 A total lunar eclipse occurred which Gauss had promised to show, through the observatory telescope to his friend Ribbentrop, confirmed bachelor, campus eccentric, and absent-minded professor of law. Although it was pouring rain that evening Ribbentrop appeared. Gauss explained that observation was impossible, but Ribbentrop countered, “No, I have my umbrella.” [Eves, Squared, 191◦] *VFR

1845 After Faraday’s discovery of the a between light and magnetism was announced in the papers, Mrs. Jane Marcet, whose book, Conversations on Chemistry, had been influential in Faraday's youth, wrote to ask Faraday for more information. " I have kept back the proof sheets of the ‘Conversation on Electricity,’ which I was this morning revising, until I receive your answer, in hopes of being able to introduce it in that sheet."
The two kept up correspondence throughout her life, and she would contact him for information on the most recent developments in order to update her "Conversations." The last new edition of Conversations on Chemistry came out in 1853, when Marcet was 84 years old!
A more complete story of the influence she had on Faraday, and their relationship is at the *skullsinthestars blogsite.

1847 Barrister to barrister math; 1837's second Wrangler to 1842's Senior Wrangler: J. J. Sylvester writes to Arthur Cayley to inform him that while reading the second volume of Theorie des Nombres that he had found two examples by Legendre that he thought might be "very congenial" to Cayley's present line of thought, "not doubting that it will turn to good account in your able hands." Although their communication was stil in the "My Dear Sir" stage, Sylvester felt he had found a kindred spirit. *Karen Hunger Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World

In 1859, The Origin of Species by Means of Natural Selection, Darwin's groundbreaking book, was published in England to great acclaim. The British naturalist, Charles Darwin detailed the scientific evidence he had collected since his voyage on the Beagle in the 1830's. He presented his idea that species are the result of a gradual biological evolution in which nature encourages, through natural selection, the propagation of those species best suited to their environments. He had been prompted to publish at this time by Charles Lyell, who advised him that Alfred Russel Wallace, a naturalist working in Borneo, was approaching the same conclusions. Lyell believed Darwin should publish without further delay to establish priority. *TIS

1864 So as not to miss a lecture, George Boole walked the three miles from his home in Ballintemple to Queen’s College in Cork, Ireland, in a pouring rain. He lectured in wet clothes, caught a cold, and died two weeks later at age 49. [MacHale, George Boole, His Life and Work, p 24]. *VFR

1858 Dedekind discovers his cuts and thereby provides the first correct definition of continuity. [Dauben, p. 48] *VFR

1888 On Thanksgiving Day, six members of the mathematics department at Columbia University met to form a society for the purpose of discussing mathematics and reading papers of mathematical interest. A month later they christened it the New York Mathematical Society. By 1894 the society had attained a national character, so its name was changed to the American Mathematical Society. The six were J. H. Van Amring, the first president, Thomas Scott Fiske, Rees (a professor), Jacoby and Stabler (fellow students with Fiske) and Maclay (a graduate student). *P. Duren (ed), A Century of Mathematics in America, vol. I, pp. 5, 13.

1918 Richard Courant sat down with Ferdinand Springer and signed a contract for the series of books now famous as the “Yellow Series.” *Constance Reid, Courant in Gottingen and New York, p. 72

1982 Sweden issued five stamps honoring Nobel Prize winners Niels Bohr, Erwin Schrodinger, Louis de Broglie, Paul Dirac and Werner Heisenberg. [Scott #1425-9] *VFR Bohr also appears on 500-krone banknote with the portrait of Bohr smoking a pipe since 1997.



2015 President Barack Obama awarded the presidential medal of freedom—America’s highest civilian honor—to a 97-year-old mathematician named Katherine Coleman Goble Johnson. You might not have heard her name in history class, but Katherine did some life-saving work back in 1962. In her job at NASA, she calculated the trajectory for astronaut John Glenn's pioneering space mission to orbit Earth. Katherine co-authored the research and equations that laid out how to send Glenn into orbit and how to bring him back home safely. Johnson is just one part of a cadre of African American women who did crucial calculations for the space workforce during the Cold War. */bitchmedia.org


BIRTHS

1879 Duncan MacLaren Young Sommerville (24 Nov 1879 in Beawar, Rajasthan, India - 31 Jan 1934 in Wellington, New Zealand) Sommerville studied at St Andrews and then had a post as a lecturer there. He left to become Professor of Pure and Applied mathematics at Victoria College, Wellington New Zealand. He worked on non-Euclidean geometry and the History of Mathematics. He became President of the EMS in 1911. *SAU

1909 Gerhard Gentzen (24 Nov 1909 in Greifswald, Germany - 4 Aug 1945 in Prague, Czechoslovakia) Gentzen invented a 'natural deduction' which provided a logic closer to mathematical reasoning than the systems proposed by Frege, Russell and Hilbert.*SAU

1912 Dr. Lyle B. Borst, (Nov 24, 1912 - July 30, 2002) was a nuclear physicist who helped build Brookhaven National Laboratory's nuclear reactor and was an early member of the Manhattan Project.
In 1950, Dr. Borst led the construction of the Brookhaven Graphite Research Reactor, which was the largest and most powerful reactor in the country and the first to be built solely for research and other peacetime uses of atomic energy.
Within the first nine months of operating the reactor, Dr. Borst announced that it had produced a new type of radioactive iodine, which is used in treating thyroid cancer.
In 1952, based on studies of new types of atomic nuclei created in the reactor, Dr. Borst helped explain the mystery behind giant stars, known as supernovae, that burst with the energy of billions of atomic bombs and flare for several years with the brilliance of several million suns.
Dr. Borst found that beryllium 7, an isotope of beryllium that does not occur naturally on earth, is formed in supernovae by the fusion of two helium nuclei. The fusion takes place after the star has used up its hydrogen supply. This reaction absorbs huge quantities of energy, causing the star to collapse in the greatest cosmic explosion known. *NY Times obit.

1925 Simon van der Meer (24 Nov 1925, )Dutch engineer and physicist who along with Italian physicist Carlo Rubbia, discovered the W particle and the Z particle by colliding protons and antiprotons, for which both men shared the Nobel Prize for Physics. These subatomic particles (units of matter smaller than an atom) transmit the weak nuclear force, one of four fundamental forces in nature. The discovery supported the unified electroweak theory put forward in the 1970's. Working at CERN in Switzerland, Van der Meer improved the design of particle accelerators used produce collisions between beams of subatomic particles. He invented a device that would monitor and adjust the particle beam with correcting magnetic fields by a system of 'kickers' placed around the accelerator ring.*TIS

1926 Tsung Dao Lee (24 Nov 1926, ) Chinese-born American physicist who received (with Chen Ning Yang) the 1957 Nobel Prize for Physics for their "penetrating investigation" of violations of the principle of parity conservation (the quality of space reflection symmetry of subatomic particle interactions), which has led to important discoveries regarding the elementary particles. Conservation of parity had previously been regarded as a "law" of nature. (Parity holds that the laws of physics are the same in a right-handed system of coordinates as in a left-handed system.) The theory was subsequently confirmed experimentally by Chien-Shiung Wu in observations of beta decay.*TIS

1944 Veerabhadran Ramanathan (24 Nov 1944, )Indian atmospheric scientist who in 1999 discovered the "Asian Brown Cloud" - wandering layers of air pollution as wide as a continent and deeper than the Grand Canyon. The dark particles in these brown clouds may reduce rainfall, dry the planet’s surface, cool the tropics and reduce sunlight - Global Dimming. In 1975, Ramanathan was the first to demonstrate that CFCs are major greenhouse gases. His calculations showed each CFC molecule in the atmosphere contributes more to the greenhouse effect that over 10,000 molecules of carbon dioxide. In the 1980s, he led a study discovering numerous trace gases contributing to global warming, and a NASA study that demonstrated that clouds had a net global cooling effect on the planet.*TIS



DEATHS
1930 Prosper-René Blondlot (3 July 1849 – 24 November 1930) was a French physicist, best remembered for his mistaken "discovery" of N rays, a phenomenon that subsequently proved to be illusory.
In order to demonstrate that a Kerr cell responds to an applied electric field in a few tens of microseconds, Blondlot, in collaboration with Ernest Bichat, adapted the rotating-mirror method that Léon Foucault had applied to measure the speed of light. He further developed the rotating mirror to measure the speed of electricity in a conductor, photographing the sparks emitted from two conductors, one 1.8 km longer than the other and measuring the relative displacement of their images. He thus established that the speed of electricity in a conductor is very close to that of light.
In 1891, he made the first measurement of the speed of radio waves, by measuring the wavelength using Lecher lines. He used 13 different frequencies between 10 and 30 MHz and obtained an average value of 297,600 km/s, which is within 1% of the current value for the speed of light. This was an important confirmation of James Clerk Maxwell's theory that light was an electromagnetic wave like radio waves.
In 1903, Blondlot announced that he had discovered N rays, a new species of radiation. The "discovery" attracted much attention over the following year until Robert W. Wood showed that the phenomena were purely subjective with no physical origin. The French Academy of Sciences awarded the Prix Leconte (₣50,000) for 1904 to Blondot, although they hedged on the reason, citing the totality of his work rather than the discovery of N-rays.
Little is known about Blondlot's later years. William Seabrook stated in his Wood biography Doctor Wood, that Blondlot went insane and died, supposedly as a result of the exposure of the N ray debacle: "This tragic exposure eventually led to Blondlot's madness and death." Using an almost identical wording this statement was repeated later by Martin Gardner, possibly without having investigated into the subject: "Wood's exposure led to Blondlot's madness and death." However, Blondlot continued to work as a university professor in Nancy until his early retirement in 1910. He died at the age of 81; at the time of the N-ray affair he was nearly 60 years old. *Wik

1978 Warren Weaver​ (b. July 17, 1894 in Reedsburg, Wisconsin d. November 24, 1978 in New Milford, Connecticut) was an American scientist, mathematician, and science administrator. He is widely recognized as one of the pioneers of machine translation, and as an important figure in creating support for science in the United States.*Wik

1980 Henrietta Hill Swope(26 October 1902; Saint Louis, Missouri - 24 November 1980; Pasadena, California)was an American astronomer. She was the eldest child of Gerard and Mary Dayton (Hill) Swope; her mother was the daughter of Thomas Hill, president of Harvard University, 1862-1868. She received her A.B. from Barnard College in 1926 and her A.M. from Radcliffe College in 1928. In 1936, while assistant at the Harvard Observatory (1928-1942), she was a member of the expedition sent jointly by the Harvard Observatory and the Massachusetts Institute of Technology to study the solar eclipse in Soviet Central Asia. During World War II she was staff member of the M.I.T. Radiation Laboratory and then served as a mathematician in the Hydrographic Office of the U.S. Department of the Navy. From 1947 to 1952 she taught astronomy at Barnard College and in 1952 was appointed assistant, later research fellow, at the Mt. Wilson and Palomar Observatories in California. After her retirement in 1968, she continued to work at the Observatories.
HHS was a member of the American Astronomical Society; she received the AAS Annie Jump Cannon Prize in 1968 for her research on photometry and variable stars. She was responsible for developing a new yardstick for measuring the universe: calibrating distance by determining the brightness of stars. She received the Distinguished Alumna Award of Barnard College in 1975 and the Barnard Medal of Distinction in 1980.
The Swope Telescope at the Las Campanas Observatory in Chile is named in her honor, as is asteroid 2168 Swope.

1987 Hans Herbert Schubert (1 May 1908 in Weida, Thüringen Germany - 24 Nov 1987 in Halle, Germany) Schubert was a German mathematician who worked on differential equations. *SAU

2008 John Robert Stallings Jr. (July 22, 1935 – November 24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967.  He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups. Stallings was born in the small town of Morrilton, Arkansas.*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

Saturday, 23 November 2019

On This Day in Math - November 23



Whereas Nature does not admit of more than three dimensions ...
it may justly seem very improper to talk of a solid ...
drawn into a fourth, fifth, sixth, or further dimension.

~John Wallis


The 327th day of the year; 327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once. (Students might search for a smaller number with that quantity) *What's Special About This Number

and from Jim Wilder @wilderlab:
For day 327: 327 is a perfect totient number- φ(327)=216, φ(216)=72, φ(72)=24, φ(24)=8, φ(8)=4, φ(4)=2, φ(2)=1, and 216+72+24+8+4+2+1=327.

The number 327 in base ten is equal to \( 57_{[64]} \) but also \( 75_{[46} \)


EVENTS

1654 From 10:30 to 12:30 in the evening Pascal experienced a religious ecstasy that called him to give up his intermittent interest in mathematics and to devote his time to religious contemplation. *VFR

1670 James Gregory writes to John Collins, with the first use of what will come to be called the Newton-Gregory interpolation formula. He includes in the letter two enclosures showing how to apply his method to series for sines and logarithms. *Thomas Harriot’s Doctrine of Triangular Numbers, Beery & Stedall, pg 51-52

1706 Jakob Hermann writes to Leibniz about proof that Machin's series converges to pi. *My uncredited notes (sorry)

1821 Thomas Jefferson writes to West Point Instructor Claudius Crozet to thank him for the gift of a copy of his A Treatise on Descriptive Geometry and praised the book, and the author. Jefferson pronounced Crozet, "by far the best mathematician in the United States." *Natl. Archives, Wik (Crozet is sometimes credited with introducing the blackboard into the US, but it seems to have been common at West Point before his arrival there.)

1823 Janos Bolyai wrote to his father “I have made such wonderful discoveries that I am myself lost in astonishment.” This refers to his discovery of Non-Euclidean Geometry that was published in 1833. *Kline, Mathematics. The Loss of Certainty, p. 83 via *VFR

1834 Astronomer Royal Airy Replies to suggestion that he begin a mathematical search for undiscovered planet that would be Neptune by the Reverend T.J. Hussey.
Hussey had mentioned in his letter how he has heard of a possible planet beyond Uranus and looked for it using a reflector telescope, but to no avail. He presented the idea of using mathematics as a tool in the search but admitted to Airy that he would not be of much help in that regard. On Novemeber 23rd Airy writes back to the reverend and admits he too has been preoccupied with a possible planet. He had observed that Uranus' orbit deviated the most in 1750 and 1834, when it would be at the same point. This was strong evidence for an object pulling on the planet, but Airy felt that until more observations were made no mathematical tools would be of help
*from http://theoriginal1701.hubpages.com/hub/The-Drama-of-Neptunes-Discovery

In 1889, the first jukebox was installed when an entrepreneur named Louis Glass and his business associate, William S. Arnold, placed a coin-operated Edison cylinder phonograph in the Palais Royale Saloon in San Francisco. The machine, an Edison Class M Electric Phonograph with oak cabinet, had been fitted locally in San Francisco with a coin mechanism invented and soon patented by Glass and Arnold. This was before the time of vacuum tubes, so there was no amplification. For a nickel a play, a patron could listen using one of four listening tubes. Known as "Nickel-in-the-Slot," the machine was an instant success, earning over $1000 in less than half a year. *TIS

1924 New York Times publishes Hubble's new universe: Between 1922–1923, Hubble's observations had proved conclusively that these nebulae were much too distant to be part of the Milky Way and were, in fact, entire galaxies outside our own. This idea had been opposed by many in the astronomy establishment of the time, in particular by the Harvard University-based Harlow Shapley. (Shapley wrote sarcastically that Hubble's letter informing him of his results was “the most entertaining piece of literature I have seen for a long time.” ) Despite the opposition, Hubble, then a thirty-five year old scientist, had his findings first published in The New York Times on November 23, 1924, and then more formally presented in the form of a paper at the January 1, 1925 meeting of the American Astronomical Society. Hubble's findings fundamentally changed the scientific view of the universe.*Wik

1982 Vatican City issued a set of three stamps commemorating the 400th anniversary of the Gregorian Calendar. The image on the Vatican stamp is from the tomb of Pope Gregory XIII in St. Peter's Basilica. The tomb, the work of Camillo Rusconi, includes a relief showing Clavius kneeling before the Pope, presenting his work as the Pope promulgates the new calendar in 1582. *VFR

1982 Poland issued stamps honoring the mathematicians StanisLlaw Zaremba (1863–1942), WacLlaw Sierpi´nski (1882–1969), Zygmunt Janiszewski (1888–1920), and Stefan Banach (1892-1945). [Scott #2542-5]. *VFR

1992 "Computer industry on the skids" With IBM projected to lose $5 billion in 1992, Business Week describes the computer business as "an industry on the skids." The magazine cited layoffs at most established computer companies, such as IBM, as well as newer firms like Sun Microsystems Inc., as evidence that the industry was saturated. A solution, the article concluded, would be for each business to find its proper niche.*CHM



BIRTHS

1221 Alfonso X of Castile (23 Nov 1221; 4 Apr 1284) Spanish monarch and astronomer who encouraged the preparation of revised planetary tables (1252), published on the day of his accession to the throne as king of Castile and León. These "Alfonsine Tables," a revision and improvement of the Ptolemaic tables, were the best available during the Middle Ages; they were not replaced by better ones for over three centuries. The astronomical data tabulating the positions and movements of the planets was compiled by about 50 astronomers he had assembled for this purpose. He questioned the complexity of the Ptolemaic model centuries before Copernicus. "If the Lord Almighty had consulted me before embarking on the Creation, I would have recommended something simpler." He also wrote a commentary on alchemy. *TIS

1616 John Wallis (23 Nov 1616, 28 Oct 1703) British mathematician who introduced the infinity math symbol $\infty$. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TIS

1820 Isaac Todhunter (23 Nov 1820 in Rye, Sussex, England - 1 March 1884 in Cambridge, England) Todhunter is best known for his textbooks and his writing on the history of mathematics. Among his textbooks are Analytic Statics (1853), Plane Coordinate Geometry (1855), Examples of Analytic geometry in Three Dimensions (1858). He also wrote some more elementary texts, for example Algebra (1858), Trigonometry (1859), Theory of Equations (1861), Euclid (1862), Mechanics (1867) and Mensuration (1869).
Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873). *SAU

1837 Johannes Diederik van der Waals (23 Nov 1837; 9 Mar 1923) Dutch physicist, winner of the 1910 Nobel Prize for Physics for his research on the gaseous and liquid states of matter. He was largely self-taught in science and he originally worked as a school teacher. His main work was to develop an equation (the van der Waals equation) that - unlike the laws of Boyle and Charles - applied to real gases. Since the molecules do have attractive forces and volume (however small), van der Waals introduced into the theory two further constants to take these properties into account. The weak electrostatic attractive forces between molecules and between atoms are called van der Waals forces in his honour. His valuable results enabled James Dewar and Heike Kamerlingh-Onnes to work out methods of liquefying the permanent gases. *TIS

1853 George Bruce Halsted (23 Nov 1853 in Newark, New Jersey, USA - 16 March 1922 in New York, USA) His main interests were the foundations of geometry and he introduced non-euclidean geometry into the United States, both through his own research and writings as well as by his many important translations. Halsted gave commentaries on the work of Lobachevsky, Bolyai, Saccheri and Poincaré and made translations of their works into English. His work on the foundations of geometry led him to publish Demonstration of Descartes's theorem and Euler's theorem in the Annals of Mathematics in 1885. His other main interest was in mathematical education and, as a mathematics educator, he criticised the careless way that mathematics was presented in the textbooks of the time. He contributed over ninety article to the American Mathematical Monthly and wrote many biographies of mathematicians such as Lambert, Farkas Bolyai, Lobachevsky, De Morgan, Sylvester, Chebyshev, Cayley, Hoüel and Klein. *SAU

1887 Henry Gwyn Jeffreys Moseley (23 Nov 1887; 10 Aug 1915) English physicist who experimentally demonstrated that the major properties of an element are determined by the atomic number, not by the atomic weight, and firmly established the relationship between atomic number and the charge of the atomic nucleus. He began his research under Ernest Rutherford while serving as lecturer at the Univ. of Manchester. Using X-ray photographic techniques, he determined a mathematical relation between the radiation wavelength and the atomic numbers of the emitting elements. Moseley obtained several quantitative relationships from which he predicted the existence of three missing elements (numbers 43, 61, and 75) in the periodic table, all of which were subsequently identified. Moseley was killed in action during WW I.*TIS

1917 Elizabeth Scott (November 23, 1917 – December 20, 1988) was an American mathematician specializing in statistics.
Scott was born in Fort Sill, Oklahoma. Her family moved to Berkeley, California when she was 4 years old. She attended the University of California, Berkeley where she studied mathematics and astronomy. There were few options for further study in astronomy, as the field was largely closed to women at the time, so she completed her graduate studies in mathematics. She received her Ph.D. in 1949, and received a permanent position in the Department of Mathematics at Berkeley in 1951.
She wrote over 30 papers on astronomy and 30 on weather modification research analysis, incorporating and expanding the use of statistical analyses in these fields. She also used statistics to promote equal opportunities and equal pay for female academics.
In 1957 Elizabeth Scott noted a bias in the observation of galaxy clusters. She noticed that for an observer to find a very distant cluster, it must contain brighter than normal galaxies and must also contain a large number of galaxies. She proposed a correction formula to adjust for (what came to be known as) the "Scott effect".
The Committee of Presidents of Statistical Societies awards a prize in her honour to female statisticians.*Wik



DEATHS

1604 Francesco Barozzi (in Latin, Franciscus Barocius) (9 August 1537 – 23 November 1604) was an Italian mathematician, astronomer and humanist. Barozzi helped in the general reappraisal of the geometry of Euclid, and corresponded with numerous mathematicians, including the German Jesuit Christopher Clavius. His original works include Cosmographia in quatuor libros distributa summo ordine, miraque facilitate, ac brevitate ad magnam Ptolemaei mathematicam constructionem, ad universamque
astrologiam institutens (1585), which he dedicated to the Duke of Urbino. This work concerns the cosmography and mathematic systems of Ptolemy. Barozzi also discussed 13 ways of drawing a parallel line in his Admirandum illud geometricum problema tredecim modis demonstratum quod docet duas lineas in eodem plano designare, quae nunquam invicem coincidant, etiam si in infinitum protrahantur: et quanto longius producuntur, tanto sibiinuicem propiores euadant (1586).
In his Opusculum: in quo una Oratio et due Questiones, altera de Certitude et altera de Medietate Mathematicarum continentur, Barozzi stressed that "the certitude of mathematics is contained in the syntactic rigor of demonstrations." Barozzi dedicated this work to Daniele Barbaro.
He also wrote Rythmomachia (1572), which he dedicated to Camille Paleotti, a Senator of Bologna, a work that is based on the mathematical game of the same name, also known as "The Philosophers' Game."
As an antiquarian, he copied many Greek inscriptions on Crete. His collection of inscriptions was later inherited by his nephew Iacopo Barozzi (1562–1617), who edited and expanded it. This collection was later acquired in 1629 by the University of Oxford. They are wide-ranging in date and subject-matter and can still be found in the Bodleian Library.*Wik

1817 James Glenie (Oct 1750 in Leslie, Fife, Scotland - 23 Nov 1817 in Chelsea, London, England ) He was an artillery officer when his regiment was sent out to North America in 1775 at the start of the American War of Independence. During his time in North America with the army Glenie worked on mathematics. In fact, even before being sent to North America, he had discovered what he called the antecedental calculus in 1774. The was an attempt to base Newton's fluxional calculus on the binomial theorem rather than on the concept of motion. He published a number of papers on this and other topics; The division of right lines, surfaces and solids being published in the Philosophical Transactions of the Royal Society in 1776 while The general mathematical laws which regulate and extend proportion universally was published in the same journal in the following year. In 1778 the Royal Society published Glenie's paper on the antecedental calculus. In addition to these papers he had also published a book on gunnery entitled The History of Gunnery with a New Method of Deriving the Theory of Projectiles in 1776. For his achievements in mathematics and its applications he was elected a fellow of the Royal Society on 18 March 1779 while he was still based with the army in Quebec.
He died in poverty. *SAU

1826 Johann Elert Bode (19 Jan 1747, 23 Nov 1826) German astronomer best known for his popularization of Bode's law. In 1766, his compatriot Johann Titius had discovered a curious mathematical relationship in the distances of the planets from the sun. If 4 is added to each number in the series 0, 3, 6, 12, 24,... and the answers divided by 10, the resulting sequence gives the distances of the planets in astronomical units (earth = 1). Also known as the Titius-Bode law, the idea fell into disrepute after the discovery of Neptune, which does not conform with the 'law' - nor does Pluto. Bode was director at the Berlin Observatory, where he published Uranographia (1801), one of the first successful attempts at mapping all stars visible to the naked eye without any artistic interpretation of the stellar constellation figures. *TIS

1844 Thomas Henderson (28 Dec 1798, 23 Nov 1844) Scottish astronomer, the first Scottish Astronomer Royal (1834), who was first to measure the parallax of a star (Alpha Centauri, observed at the Cape of Good Hope) in 1831-33, but delayed publication of his results until Jan 1839. By then, a few months earlier, both Friedrich Bessel and Friedrich Struve had been recognized as first for their measurements of stellar parallaxes. Alpha Centauri can be observed from the Cape, though not from Britain. It is now known to be the nearest star to the Sun, but is still so distant that its light takes 4.5 years to reach us. As Scottish Astronomer Royal in 1834, he worked diligently at the Edinburgh observatory for ten years, making over 60,000 observations of star positions before his death in 1844.*TIS

1864 Friedrich Georg Wilhelm von Struve (15 Apr 1793, 23 Nov 1864) German-Russian astronomer, one of the greatest 19th-century astronomers and the first in a line of four generations of distinguished astronomers. He founded the modern study of binary (double) stars. In 1817, he became director of the Dorpat Observatory, which he equipped with a 9.5-inch (24-cm) refractor that he used in a massive survey of binary stars from the north celestial pole to 15°S. He measured 3112 binaries - discovering well over 2000 - and cataloged his results in Stellarum Duplicium Mensurae Micrometricae (1837). In 1835, Czar Nicholas I persuaded Struve to set up a new observatory at Pulkovo, near St. Petersburg. There in 1840 Struve became, with Friedrich Bessel and Thomas Henderson, one of the first astronomers to detect parallax. *TIS

1910 Octave Chanute(18 Feb 1832, 23 Nov 1910) U.S. aeronaut whose work and interests profoundly influenced Orville and Wilbur Wright and the invention of the airplane. Octave Chanute was a successful engineer who took up the invention of the airplane as a hobby following his early retirement. Knowing how railroad bridges were strengthened, Chanute experimented with box kites using the same basic strengthening metod, which he then incorporated into wing design of gliders. Through thousands of letters, he drew geographically isolated pioneers into an informal international community. He organized sessions of aeronautical papers for the professional engineering societies that he led; attracted fresh talent and new ideas into the field through his lectures; and produced important publications. *TIS The town of Chanute, Kansas is named after him, as well as the former Chanute Air Force Base near Rantoul, Illinois, which was decommissioned in 1993. The former Base, now turned to peacetime endeavors, includes the Octave Chanute Aerospace Museum, detailing the history of aviation and of Chanute Air Force base. He was buried in Springdale Cemetery, Peoria, Illinois. *Wik

1942 Stanisław Saks (December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Café circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*Wik

1942 Stanisław Zaremba (October 3, 1863 – November 23, 1942) was a Polish mathematician. His research in differential equations, applied mathematics, classical analysis, particularly on harmonic analysis, was widely recognized. He was a mathematician who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Zaremba wrote a number of university textbooks and monographies.*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

Friday, 22 November 2019

On This Day in Math - November 22


Ulam Spiral
PrimeSpiral_1000.gif
mathworld.wolfram.com


I believe there are
15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,
914,527,116,709,366,231,025,076,185,631,031,296
protons in the universe,
and the same number of electrons.
— Sir Arthur Stanley Eddington

The 326th day of the year; 326 is the maximum number of pieces that may be produced in a pizza with 25 straight cuts. These are sometimes called "lazy caterer numbers" and more generally they are centered polygonal numbers.

326 is also the sum of the first 14 consecutive odd primes: 326 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47. *MAA

326 prefixed or followed by any digit still remains composite.  *Derek's Daily Math


EVENTS



1850 J J Sylvester called to the Bar. Rather than practicing law he gave private instruction in mathematics, and counted among his pupils Florence Nightingale. [Osiris, 1(1936), 102] *VFR (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)

1906 An International Radiotelegraphic Convention adopted the S.O.S radio distress signal, ... The Convention met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals".
The first well documented use of the SOS distress call is by the Arapahoe on August 11, 1909, when it suffered a broken shaft in the Atlantic Ocean, near Cape Hatteras, North Carolina. However, an article titled "Notable Achievements of Wireless" in the September, 1910 Modern Electrics suggests that an earlier SOS distress call was transmitted by the Cunard liner Slavonia, on June 10, 1909.
[The wireless operator aboard S.S. Arapahoe, T. D. Haubner, radioed for help. A few months later, Haubner on the S.S. Arapahoe received an SOS from the SS Iroquois, the second use of SOS in America.(*TIS)]
The first radio distress call to be adopted appears to have been "CQD", by the Marconi International Marine Communication Company​, for Marconi-operated shipboard stations. It was announced on January 7, 1904 by the company's "Circular 57" that "...on and after the 1st February, 1904, the call to be given by ships in distress or in any way requiring assistance shall be 'C.Q.D.'." ("CQ" was a general call to all stations; amateur or "ham" radio operators still use it today when soliciting a contact with any station that hears the call.) *Citizens Compendium



BIRTHS

1796 Charles Bonnycastle (22 Nov 1796 - 31 Oct, 1840). The University of Virginia's second Professor of Mathematics, Charles Bonnycastle, was born in Woolwich, England. His father, John, was Professor of Mathematics at the Royal Military Academy there, and so Charles grew up and received his education in an environment that very much influenced his own subsequent career. The contributions that the son made to the thirteenth edition of his father's textbook, Introduction to Algebra (1824), in fact, augmented the credentials he presented to Francis Walker Gilmer, agent for the newly forming University of Virginia.
Bonnycastle actually came to the University at its opening in 1825 as the first professor, not of mathematics, but of natural philosophy (as physics was then called). When Thomas Key, the first Professor of Mathematics, resigned to return to his native England, Bonnycastle shifted over to the mathematical chair and remained in that post until his untimely death on 31 October 1840 at the age of only forty-three. "Old Bonny," as he was fondly called by the students, moved away from what was increasingly becoming the antiquated synthetic approach to mathematical pedagogy that had been so typical of Oxbridge mathematical teaching in the eighteenth and early nineteenth centuries and introduced the more avant-garde analytic approach of late eighteenth-century French authors such as Silvestre Lacroix. In 1834, he published his own textbook, Inductive Geometry, in which he aimed to unite the best of the synthetic and the analytic approaches to geometry for the college- and university-level audience. Bonnycastle also contributed works on mathematical and physical topics to the Transactions of the American Philosophical Society, one of the few venues available in early nineteenth-century America for the publication of original work in the sciences.
Bonnycastle apparently also entrusted a number of mathematical papers to his friend, Princeton physics professor and (after 1846) first Secretary of the Smithsonian Institution, Joseph Henry. Shortly before his death in 1878, Henry deposited these in the library at the University of Virginia. They did not survive the infamous Rotunda fire of 1895. *History of the U V Math Dept. He was buried in University of Virginia Cemetery, Charlottesville, Virginia. His gravestone reads:
Sacred to the memory of
Charles Bonnycastle
late Professor of Mathematics
in the University of Virginia
who was born in London
on the 22nd day of November 1796
was made professor in the University in 1825
and continued in this station until his death
on the 31st of October 1840.
For Michigan residents around Kalamazoo, Charles Bonnycastle's brief stay in the area with his brother Humphrey is still marked by Bonniecastle Lake west of the city.  

1803 Giusto Bellavitis (22 Nov 1803 in Bassano, Vicenza, Italy - 6 Nov 1880 in Tezze (near Bassano) Italy ) Bellavitis solved various mechanical problems by original methods, among them Hamilton's quaternions. He developed very personal critical observations about the calculus of probabilities and the theory of errors. He also explored physics, especially optics and electrology, and chemistry. As a young man, Bellavitis weighted the problem of a universal scientific language and published a paper on this subject in 1863. He also devoted time to the history of mathematics and, among other things, he vindicated Cataldi by attributing the invention of continued fractions to him. *SAU

1840 Émile Michel Hyacinthe Lemoine (22 Nov 1840 in Quimper, France - 21 Feb 1912 in Paris, France) Lemoine work in mathematics was mainly on geometry. He founded a
new study of properties of a triangle in a paper of 1873 where he studied the point of intersection of the symmedians of a triangle. He had been a founder member of the Association Française pour l'Avancement des Sciences and it was at a meeting of the Association in 1873 in Lyon that he presented his work on the symmedians.
A symmedian of a triangle from vertex A is obtained by reflecting the median from A in the bisector of the angle A. He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point. Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex A cuts the side BC of the triangle in the ratio of the squares of the sides AC and AB. He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle. Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle. Lemoine gave up active mathematical research in 1895 but continued to support the subject. He had helped to found a mathematical journal, L'intermédiaire des mathématiciens., in 1894 and he became its first editor, a role he held for many years. *sau

1904 Louis-Eugène-Félix Néel (22 Nov 1904; 17 Nov 2000) French physicist, corecipient (with the Swedish astrophysicist Hannes Alfvén) of the Nobel Prize for Physics in 1970 for his pioneering studies of the magnetic properties of solids. His contributions to solid-state physics have found numerous useful applications, particularly in the development of improved computer memory units. About 1930 he suggested that a new form of magnetic behavior might exist - called antiferromagnetism. Above a certain temperature (the Néel temperature) this behaviour stops. Néel pointed out (1947) that materials could also exist showing ferrimagnetism. Néel has also given an explanation of the weak magnetism of certain rocks, making possible the study of the past history of the Earth's magnetic field.*TIS



DEATHS

1784 Paolo Frisi (13 Apr 1728, 22 Nov 1784) Italian mathematician, astronomer, and physicist who is best known for his work in hydraulics (he designed a canal between Milan and Pavia). He was, however, the first to introduce the lightning conductor into Italy. His most significant contributions to science, however, were in the compilation, interpretation, and dissemination of the work of other scientists, such as Galileo Galilei and Sir Isaac Newton. His work on astronomy was based on Newton's theory of gravitation, studying the motion of the earth (De moto diurno terrae). He also studied the physical causes for the shape and the size of the earth using the theory of gravity (Disquisitio mathematica, 1751) and tackled the difficult problem of the motion of the moon. *TIS

1880 James Craig Watson (January 28, 1838 – November 22, 1880) was a Canadian-American astronomer born in the village of Fingal, Ontario Canada. His family relocated to Ann Arbor, Michigan in 1850.
At age 15 he was matriculated at the University of Michigan, where he studied the classical languages. He later was lectured in astronomy by professor Franz Brünnow.
He was the second director of Detroit Observatory (from 1863 to 1879), succeeding Brünnow. He wrote the textbook Theoretical Astronomy in 1868.
He discovered 22 asteroids, beginning with 79 Eurynome in 1863. One of his asteroid discoveries, 139 Juewa was made in Beijing when Watson was there to observe the 1874 transit of Venus. The name Juewa was chosen by Chinese officials (瑞華, or in modern pinyin, ruìhuá). Another was 121 Hermione in 1872, from Ann Arbor, Michigan, and this asteroid was found to have a small asteroid moon in 2002.
He was a strong believer in the existence of the planet Vulcan, a hypothetical planet closer to the Sun than Mercury, which is now known not to exist (however the existence of small Vulcanoid planetoids remains a possibility). He believed he had seen such two such planets during a July 1878 solar eclipse in Wyoming.
He died of peritonitis at the age of only 42. He had amassed a considerable amount of money through non-astronomical business activities. By bequest he established the James Craig Watson Medal, awarded every three years by the National Academy of Sciences for contributions to astronomy.
The asteroid 729 Watsonia is named in his honour, as is the lunar crater Watson. *Wik

1907 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1944 Sir Arthur Stanley Eddington (28 Dec 1882, 22 Nov 1944) English astrophysicist, and mathematician known for his work on the motion, distribution, evolution and structure of stars. He also interpreted Einstein's general theory of relativity. He was one of the first to suggest (1917) conversion of matter into radiation powered the stars. In 1919, he led a solar eclipse expedition which confirmed the predicted bending of starlight by gravity. He developed an equation for radiation pressure. In 1924, he derived an important mass-luminosity relation. He also studied pulsations in Cepheid variables, and the very high densities of white dwarfs. He sought fundamental relationships between the prinicipal physical constants. Eddington wrote many books for the general reader, including Stars And Atoms  . *TIS  One of my favorite stories about Eddington is this one: Ludwick Silberstein approached Eddington and told him that people believed he was one of only three people in the world who understood general relativity, and that included Einstein. When Eddington didn't respond for a moment he prodded, come on, don't be modest, and Eddington replied, "Oh, no.  It's not that.  I was just trying to figure out who the third was?"  *Mario Livio, Brilliant Blunders

1986 Nikolai Grigor'evich Chudakov (14 Dec 1904 in Lysovsk, Novo-Burassk, Saratov, Russia - 22 Nov 1986 in Saratov, Russia) Chudakov established a number of important results in number theory. He gave an estimate for the bounds of the zeta-function in the critical strip using techniques which had been introduced a few years earlier by Vinogradov. As a consequence of this work he was able to give a substantially improved remainder term in the asymptotic formula for the number of primes less than a fixed number N. Also, by these method, he improved the estimate for the difference between two consecutive primes. In his later work he extended these results to apply to arbitrary arithmetic progressions. In 1947 Chudakov published On Goldbach-Vinogradov's theorem in the Annals of Mathematics. In this paper he proves Vinogradov's theorem that every large odd integer is representable as a sum of three odd primes. *SAU

1996 Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA – November 22, 1996, Water Mill, New York, USA) was an American mathematician. He is best known for his work in lattice theory.During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines.
The mathematician George Birkhoff (1884–1944) was his father.*Wik

2007 Andrew Ronald Mitchell (22 June 1921 – 22 November 2007), popularly known as Ron Mitchell, was a British applied mathematician and numerical analyst. He was a professor of mathematics at the University of St Andrews, Dundee, Scotland. He was known for his contribution to the field of numerical analysis of partial differential equations in general and finite difference method and finite element method in particular. Mitchell has authored several influential books on numerical solution of partial differential equations, including "The Finite Element Analysis in Partial Differential Equations" with Richard Wait and "The Finite Difference Method in Partial Differential Equations" with David F. Griffiths.*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

Thursday, 21 November 2019

Notes on the History of the Pigeonhole Theorem

This is an update of several posts I wrote as late as 2009, and some additional information acquired since then.


Sometimes problems that seem very hard, can be very easy if they are viewed in the right way, and one of those easy ways to make some hard problems manageable is the Pigeon-Hole Principle. Over the last few weeks seems like lots of problems invovling this idea have shown up, so I thought I would bring it to you.
The basic idea is so easy any sixth grader would agree; if you have two boxes, and you are going to put three balls in the boxes, then at least one box will get more than one ball..... "well, Duh!" they answer... and yet... it seems easier to apply than it might be. Now that you know the secret, try these two problems. I'll post the answer down lower on the page where you must not look until you take a few minutes to ponder the problems.
Here is the first from a recent blog I read: "39 people are attending a large, formal dinner, which must of course occur at a single, circular table. The guests, after milling about for a while, sit down to eat. It is then pointed out to them that there are name cards labeling assigned seats, and not a single one has sat in the seat assigned to them. Prove that there is some way to rotate the table so that at least two people are in the correct seats."
This one seems tougher, but really isn't, it just requires a different way of thinking. "Suppose you pick six unique integers from 1 to 1000. Prove that at least two of them must have a difference that is a multiple of five.

I'll give you the proofs of each of these, and then get to the main topic of the history of this important theorem in discrete mathematics

Ok, The Proofs... for number one... Suppose you handed each person a number that was how many seats they needed to move to the right to find their assigned seat. Since no one is at the right seat, the number can not be zero or thirty-nine. SO each of the people has a number between 1 and 38...wait, there are 39 people...two of them (at least) must be the same distance away from their assigned seats.... admit it…..that’s pretty cool.
For number two it is sort of the same idea, but you have to think about how much each number would have for a remainder if you divided them by five. The only possible choices are 0, 1, 2, 3, or 4... but there are six numbers, so two of them have the same remainder...and two numbers that have the same remainder on division by five, are a multiple of five apart.... think of 1,6, 11, etc for remainders of one. If you want to read more about how remainders can play a part in solving problems, see my blog on "casting out sevens"


The basic idea behind this mathematical principle is what students would call common sense; if there are n objects to be placed in m receptacles (with m less than n), at least two of the items must go into the same container. While the idea is common sense, in the hands of a capable mathematician it can be made to do uncommon things. Here is a link to an article by Alexander Bogomolny in which he uses the principle to argue that there must be at least two persons in New York City with the same number of hairs on their head. This "counting hairs" approach dates back to the earliest version of the principal I have ever seen.

The same axiom is often named in honor of Dirichlet who used it in solving Pell's equation. The pigeon seems to be a recent addition, as Jeff Miller's web site on the first use of some math words gives, "Pigeon-hole principle occurs in English in Paul Erdös and R. Rado, A partition calculus in set theory, Bull. Am. Math. Soc. 62 (Sept. 1956)" (although they credit Dedekind for the principle). In a recent discussion on a history group Julio Cabillon added that there are a variety of names in different countries for the idea. His list included "le principe des tiroirs de Dirichlet", French for the principle of the drawers of Dirichlet, and the Portugese "principio da casa dos pombos" for the house of pigeons principle and "das gavetas de Dirichlet" for the drawers of Dirichlet. It also is sometimes simply called Dirichlet's principle and most simply of all, the box principle. Jozef Przytycki wrote me to add, "In Polish we use also:"the principle of the drawers of Dirichlet"
that is 'Zasada szufladkowa Dirichleta' ". I received a note that said, "Dirichlet first wrote about it in Recherches sur les formes quadratiques à coefficients et à indéterminées complexes (J. reine u. angew. Math. (24 (1842) 291 371) = Math. Werke, (1889 1897), which was reprinted by Chelsea, 1969, vol. I, pp. 533-618. On pp. 579-580, he uses the principle."


He doesn't give it a name. In later works he called it the "Schubfach Prinzip" [which I am told means "drawer principle" in German]

The idea has been around much longer than Dirichlet, however, as I found out in June of 2009 when Dave Renfro sent me word that the idea pops up in the unexpected (at least by me) work, "Portraits of the seventeenth century, historic and literary", by Charles Augustin Sainte-Beuve. During his description of Mme. de Longuevillle, who was Ann-Genevieve De Bourbon, and lived from 1619 to 1679 he tells the following story:
"I asked M. Nicole (See below for description of M. Nicole) one day what was the character of Mme. de Longueville's mind; he told me she had a very keen and very delicate mind in knowledge of the character of individuals, but that it was very small, very weak, very limited on matters of science and reasoning, and on all speculative matters in which there was no question of sentiment ' For example,' added he, ' I told her one day that I could bet and prove that there were in Paris at least two inhabitants who had the same number of hairs upon their head, though I could not point out who were those two persons. She said I could not be certain of it until I had counted the hairs of the two persons. Here is my demonstration/ I said to her: M lay it down as a fact that the best-fiimbhed (not sure what this word was supposed to be, ..Plumed??) head does not possess more than 200,000 hairs, and the most scantily furnished head b that which has only 1 hair. If, now you suppose that 200,000 heads all have a different number of hairs, they must each have one of the numbers of hairs which are between 1 and 200,000; for if we suppose that there were 2 among these 200,000 who had the same number of hairs, I win my bet But suppose these 200,000 inhabitants all have a different number of hairs, if I bring in a single other inhabitant who has hairs and has no more than 200,000 of them, it necessarily follows that this number of hairs, whatever it b, will be found between 1 and 200,000, and, consequently, b equal in number of hairs to one of the 200,000 heads. Now, as instead of one inhabitant more than 200,000, there are, in all, nearly 800,000 inhabitants in Paris, you see plainly that there must be many heads equal in number of hairs, although I have not counted them.' Mme. de Longuevillle still could not understand that demonstration could be made of the equality in number of hairs, and she always maintained that the only way to prove it was to count them. "
The M. Nicole who demonstrated the principal was Pierre Nicole, (1625 -1695), one of the most distinguished of the French Jansenist writers, sometimes compared more favorably than Pascal for his writings on the moral reasoning of the Port Royal Jansenists. It may be that he had picked up the principal from Antoine Arnauld, another Port Royal Jansenist who was an influential mathematician and logician. Here is a segment from his bio at the St. Andrews Math History site.
-------------------------
He published Port-Royal Grammar in 1660 which was strongly influenced by Descartes' Regulae. In Port-Royal Grammar Arnauld argued that mental processes and grammar are virtually the same thing. Since mental processes are carried out by all human beings, he argued for a universal grammar. Modern linguistic theorists consider this work as the beginnings of the modern approach their subject. Arnauld's next work was Port-Royal Logic which was another book of major importance. It was also strongly influenced by Descartes' Regulae and also gave a first hand account of Pascal's Méthode. This work presented a theory of ideas which remained important in philosophy courses until comparatively recent times. In 1667 Arnauld published New Elements of Geometry. This work was based on Euclid's Elements and was intended to give a new approach to teaching geometry rather than new geometrical theorems."
He was a correspondent of Gottfried Wilhelm Leibniz, and of course Pascal, who wrote the Pascal "Provincial Letters" in support of Arnauld. I enjoyed the quote about him from the Wikipedia bio: "His inexhaustible energy is best expressed by his famous reply to Nicole, who complained of feeling tired. 'Tired!' echoed Arnauld, 'when you have all eternity to rest in?"
I have not been able to find any thing in Arnauld's personal writing at this time to confirm that he was aware of or used the Pigeon-hole Principle. I have also seen a comment that there is a book by Henry (or Henrik) van Etten (pseudonym of Jean Leurechon, who coined the term thermometer) , circa 1624, which uses the method for problems involving "if there are more pages than words on any page" and various other illustrations. The writer suggests that the problem is in the French version but not the English translation. Would love to hear from someone who can confirm, and perhaps send a digital image.

Around five years after I wrote the above, I was advised of a paper published by A. Heeffer and B. Rittaud that mentioned this Leurechon (They give the date as 1622) contained a single line about the principle, and amazingly, that involved the idea of proving two men had equal hairs on their heads.  " “It is necessary that two men have the same number of hairs, gold, and others.”
Later the authors add, "It is now established that an immensely popular work published at Pont-`a-Mousson in 1624 resulted from these disputationes. Entitled R´ecr´eation mathematicque, this French work is commonly attributed to Jean Leure-chon, but there are good reasons to believe that this attribution is wrong."  This book goes on to explain the solution from the idea posed in the 1622 book.  They say there is an English translation from 1633, which is [Jean Appier Hanzelet],Mathematicall Recreations , T. Cotes (1633).


After the fact

Shortly after I wrote the original post, I had a classroom encounter with a student who presented me with another teaching moment.

A young man in one of my classes, obviously trying to improve his A+ by sucking up to the teacher, mentioned that he had read my recent blog on the pigeon-hole principle. He went on to suggest that he really doubted the idea that 39 people could randomly seat themselves and ALL be in the wrong seat. "It just seems VERY unlikely." he suggested.

Rather than tell him the answer, I set him the task of simulating the activity with a deck of cards. Pull out any suit, say the spades, and really shuffle the remaining cards well. Now we need to decide on an order for the remaining suits, so let clubs be the numbers one to thirteen in order from Ace, two, up to King for thirteen. Then the ace of diamonds can be 14, up through the King of diamonds for 26. Finally the ace of hearts is 27 up to the king of hearts for 39. Now turn over the cards and as you do count, one, two, etc... and if you get a card that is where it should be, stop.. they didn't all sit in the wrong chairs. You need not go on forever, just ten or so trials should give you an idea of whether the event is really, really uncommon, or not so very uncommon. (I now realize an easier way to do this would be to have two decks of cards, lay 39 out in one row in order, then from the shuffled deck, lay the cards one at a time under where they should appear.)

I didn't tell him that I knew the probability (or a good approximation), and that he should probably get three or four trials in a string of ten shuffles in which none of the cards landed in the right place. Such a mis-ordering of the cards was just the idea behind the first critical study of the idea we now call derangements by Leonhard Euler, the great Swiss mathematician. Euler was studying the probability of winning in the game of rencontre, now called "coincidences" in his paper "Calcul de la Probabilite dans le jeu de Rencontre", published around 1751.

So what did Euler discover? Well for larger values of N, say 39 or so, the probability of having a perfect mis-sorting of the items approaches 1/e, or about 36.8%, more than a third of the time. It is not an unusual event at all. For smaller numbers you can find the probability by using the idea shown here for six items..
. This can be rewritten more easily using the factorial notation as P= 1/2! - 1/3! + 1/4! - 1/5! + 1/6! which is only a tiny bit above 36.8%, already very close to the 1/e value given above for the limiting value. If the number of items is even, the series will be a little more than 1/e, and if it is odd (and the last term is subtracted) then the probability will be a little below 1/e, with the propbability approaching 1/e as a limit as n gets greater and greater.

My student got two completely mismatched sets of 39, and expressed surprise that it was higher than he would have thought, but he didn't sound convinced that what had occurred was not just an unusual anomaly (or else he thought I might have rigged it somehow?)

I decided to simulate a lot more times than would be practical with a deck of cards, so I cranked up Fathom, a wonderful simulation software by the folks at Key Curriculum, and had it repeat the experiment of seating the 39 people at random 1000 times, and then count how many landed in the right place. The results are shown in the graph below.

It happened that no one landed in the right place 371 times.... Hmmmm, I guess Euler got it right.

Comments about additional sources related to this are always welcomed.