## Monday, 26 January 2015

### On This Day in Math - January 26

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
~Arthur Cayley

The 26th day of the year; 26 is the smallest non-palindrome with a palindromic square. (676). (What's the next smallest?)
Fermat's sandwich theorem states that 26 is the only number sandwiched between a perfect square number $5^2=25$ and a perfect cubic number $3^3 = 27$. According to Singh (1997), after challenging other mathematicians to establish this result while not revealing his own proof, Fermat took particular delight in taunting the English mathematicians Wallis and Digby with their inability to prove the result.*Wolfram Mathworld

When the single digits are raised to 26th power, only 526 contains all ten digits.  526 = 1490116119384765625  (As numbers get very large, counter intuitively, numbers that do not contain all the digits become very rare)

EVENTS
1126 Adelard of Bath translates Muhammad ibn Mˆusˆa al-Khwˆarizmˆı’s Astronomical Tables into Latin. *VFR

1678 Phillipe de LaHire nominated to the Academy of Sciences. This geometer was so adept at synthetic techniques that he, together with Rolle, was hostile to the inﬁnitesimal calculus when discussions of its value were raised in the Academy beginning in 1701*VFR (Kids studying the theorem bearing his name in intro calc seem fascinated to learn that Rolle was opposed to Calculus.)

In 1697, Isaac Newton received and solved Jean Bernoulli's brachistochrone problem. The swiss mathematician Bernouilli had challenged his colleagues to solve it within six months. Newton not only solved the problem before going to bed that same night, but in doing so, invented a new branch of mathematics called the calculus of variations. He had resolved the issue of specifying the curve connecting two points displayed from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time. Newton, age 55, sent the solution to be published, at his request, anonymously. But the brilliant originality of the work betrayed his identity, for when Bernoulli saw the solution he commented, "We recognize the lion by his claw." *TIS

1738 Frederick the Great wrote Voltaire of his plan of study, “to take up again philosophy, history, poetry, music. As for mathematics, I confess to you that I dislike it; it dries up the mind. We Germans have it only too dry; it is a sterile ﬁeld which must be cultivated and watered constantly, that it may produce”. Nonetheless, Frederick supported Euler at the Berlin Academy from 1741 to 1766.*VFR

1750 Danial Bernoulli writes to Euler to complain that d'Alembert's work on the wind had no experimental basis and ..his abstract speculations brought more shame than honor to mathematics. "After one has read his paper, one knows no more about the wind than he did before." * Thomas L. Hankins, Jean d'Alembert: science and the Englightenment; pg 3

1784 The idea that Benjamin Franklin preferred the turkey as the national bird of the United States comes from a letter he wrote to his daughter Sarah Bache on January 26, 1784, criticizing the choice of the Bald Eagle as the national bird and suggesting that a turkey would have made a better alternative. This letter to Franklin's daughter was written after Congress had spent six years choosing the eagle as the emblem of the newly formed country. Franklin's disapproval of the choice of the Bald Eagle appears evident, but may have been made with mock indignation, since it is not apparent that he ever officially advocated the use of the turkey as a national emblem. *Wik

1802 Congress passed an act calling for a library to be established within the U. S. Capitol. The collection was the forerunner of the Library of Congress. *VFR

1946: The 1st astronomical radio interferometer observation was made by Ruby-Payne Scott * David Dickinson@Astroguyz

1949, the Hale telescope at Palomar Observatory sees first light under the direction of Edwin Hubble *Yovista

1952 EDVAC demonstrated. John Von Neumann was instrumental in designing this machine, which used the stored program concept. *VFR @rmathematicus disagrees and Tweets, " One of the biggest myths in comp hist. JvN only analyzed the design created by others, principally Eckert & Mauchly."

1963 France issued a stamp picturing the bathyscaph “Archimede.” Do you know why this name is appropriate? [Scott #1052] *VFR (image at top) On 15 July 1962, Archimede descended to 31,350 feet (9,560 m) into the Kurile-Kamchatcha Trench, making it the second deepest dive ever, at that point in time.

1984 The Fredkin Foundation announced it will award a prize of \$100,000 for the ﬁrst major mathematical discovery made by a computer. [News release at the Louisville AMS meeting] *VFR (Fredkin Foundation was established by Edward Fredkin, an artificial-intelligence expert at MIT. They offered another large prize for the first computer program which could defeat a Chess Grand Master)

1997 Electronic vs. Paper Books in S.F. Library
The New York Times chronicles the debate between electronic and paper books in an article about the new San Francisco public library. Critics complained that the library sacrificed too much book space for computer terminals and too many books for online information, lamenting as well the end of the traditional card catalogue that has marked a move to the information age for many libraries.*CHM (Twenty-five years later such discussions continue as Kindle and on-line texts start to replace traditional paper.)

2015 Asteroid 2004 BL86 will make a close pass by the earth on this night. Although there’s no danger of impact, this one is huge; twice as big as a cruise ship! It will be the closest of any known space rock this large until asteroid 1999 AN10 flies past Earth in 2027. A telescope of the Lincoln Near-Earth Asteroid Research (LINEAR) survey in White Sands, New Mexico initially discovered asteroid 2004 BL86 on January 30, 2004. *http://earthsky.org

BIRTHS
1862 Eliakim Hastings Moore (January 26, 1862 – December 30, 1932) was an American mathematician. He discovered mathematics through a summer job at the Cincinnati Observatory while in high school. When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University.
Moore first worked in abstract algebra, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points were the only primitive notion, thus turning Hilbert's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics and model theory. After 1906, he turned to the foundations of analysis. The concept of closure operator first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry, number theory, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.
The American Mathematical Society established a prize in his honor in 2002. *Wik

1911 Polykarp Kusch (26 Jan 1911; 20 Mar 1993) German-American physicist who shared the Nobel Prize for Physics in 1955 for his accurate determination that the magnetic moment of the electron is greater than its theoretical value. This he deduced from researching the hyperfine structure of the energy levels in certain elements, and in 1947 found a discrepancy of about 0.1% between the observed value and that predicted by theory. Although minute, this anomaly was of great significance and led to revised theories about the interactions of electrons with electromagnetic radiation, now known as quantum electrodynamics. (He shared the prize with Willis E. Lamb, Jr. who performed independent but related experiments at Columbia University on the hyperfine structure of the hydrogen atom.)*TIS

1945 John Henry Coates, FRS (born 26 January 1945) is a mathematician who holds (since 1986) the position of Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom. He was elected a fellow of the Royal Society of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The latter organisation awarded him the Senior Whitehead Prize in 1997, for "his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally".
Since 1986 Coates has worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory, for instance, the study of the arithmetic of elliptic curves in nonabelian infinite extensions.*Wik

DEATHS
1630 Henry Briggs (Feb ? 1561, 26 Jan 1630) English mathematician who constructed the decimal-based common (Briggsian) logarithms that use base 10, and popularized them in Europe. John Napier had already introduced “natural” logarithms (1614) that use the base e (2.71...) [I think this is an error. Napier's log tables were not base e, nor any other particular base as they produced smaller log values for larger numbers, with log(107=0.]. Briggs visited Napier in 1616, and they agreed on the merit of using base 10. By 1624, Briggs had calculated logarithm tables to 14 decimal places, published in Arithmetica Logarithmica. These tables vastly simplified the task of mathematicians, astronomers and other scientists making otherwise long and tedious calculations. Briggs was professor of astronomy at Oxford from 1619. He is also credited with developing the modern method of long division. Briggs was strongly opposed to astrology, at a time when it was otherwise widely accepted by many scholars, including Napier. *TIS A story is told that when Briggs first journeyed to Scotland to meet Napier, after he was shown into the room they stood in silence for almost a quarter of an hour, "each beholding the other with admiration".

1697  Georg Mohr, (April 1, 1640 – January 26, 1697) (also Jorgen)Danish mathematician His only original contribution to geometry was the proof that any geometric construction which can be done with compass and straightedge can also be done with compasses alone, a result now known as the ohr–Mascheroni theorem. He published his proof in the book Euclides Danicus, Amsterdam, 1672.

1721 Pierre-Daniel Huet (8 Feb 1630, 26 Jan 1721) French scholar, antiquary, scientist, and bishop whose incisive skepticism, particularly as embodied in his cogent attacks on René Descartes, greatly influenced contemporary philosophers. Huet wrote a number of philosophical works that asserted the fallibility of human reason in addition to scientific work in the fields of astronomy, anatomy, and mathematics. *TIS

1895 Arthur Cayley (16 Aug 1821, 26 Jan 1895)English mathematician who played a leading role in founding the modern British school of pure mathematics. He trained first as a lawyer, and from 1849, spent 14 years at the bar, during which time he maintained an interest in mathematics and published about 250 mathematical papers. In 1863, Cayley followed his passion and commenced a new career as professor of Pure Mathematics at Cambridge and during his tenure published 900 papers and notes covering nearly every aspect of modern mathematics. The legacy of his work in n-dimensional geometry was later applied in physics to the study of the space-time continuum. His work on matrices served as a foundation for quantum mechanics developed by Werner Heisenberg in 1925.*TIS Cayley died, at age 74, after a long illness that he bore with courage and resignation. He continued his creative activity up to the week of his death. *VFR

1929 Constantin Marie Le Paige (9 March 1852 in Liège, Belgium - 26 Jan 1929 in Liège, Belgium) worked on the theory of algebraic forms, a topic whose study was initiated by Boole in 1841 and then developed by Cayley, Sylvester, Hermite, Clebsch and Aronhold. In particular Le Paige studied the geometry of algebraic curves and surfaces, building on this earlier work. He is best known for his construction of a cubic surface given by 19 points.
Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.
The history of mathematics was another topic which interested Le Paige. He published Sluze's correspondence with Pascal, Huygens, Oldenburg and Wallis. *SAU

1942 Felix Hausdorff (8 Nov 1868 in Breslau, Germany (now Wrocław, Poland)
- 26 Jan 1942 in Bonn, Germany) worked in topology creating a theory of topological and metric spaces. He also worked in set theory and introduced the concept of a partially ordered set.
As a Jew his position became more and more difficult. In 1941 he was scheduled to go to an internment camp but managed to avoid being sent.
Bonn University requested that the Hausdorffs be allowed to remain in their home and this was granted. By October 1941 they were forced to wear the "yellow star" and around the end of the year they were informed that they would be sent to Cologne.
They were not sent to Cologne but in January 1942 they were informed that they were to be interned in Endenich. Together with his wife and his wife's sister, he committed suicide on 26 January. He wrote to a friend on Sunday 25 January:
Dear Friend Wollstein
By the time you receive these lines, we three will have solved the problem in another way - in the way which you have continually attempted to dissuade us. ...
What has been done against the Jews in recent months arouses well-founded anxiety that we will no longer be allowed to experience a bearable situation. ...
Forgive us, that we still cause you trouble beyond death; I am convinced that you will do what you are able to do (and which perhaps is not very much). Forgive us also our desertion! We wish you and all our friends will experience better times
Yours faithfully
Felix Hausdorff
On the night of Sunday 25 January all three took barbiturates. Both Hausdorff and his wife Charlotte were dead by the morning of the 26 January. Edith, Charlotte's sister, survived for a few days in a coma before dying. *SAU

1952 James Ireland Craig (24 Feb 1868 in Buckhaven, Fife, Scotland - 26 Jan 1952 in Cairo, Egypt) graduated from Edinburgh and Cambridge. He taught at Eton and Winchester and then went to work on the Nile Survey for the Egyptian government. He made some significant inventions in map projections. He was killed when a mob attacked the Turf Club in Cairo.*SAU

2007 Gregory Maxwell Kelly (5 June 1930 in Bondi, New South Wales, Australia - 26 Jan 2007 in Sydney, Australia) founded the thriving Australian school of category theory. With Samuel Eilenberg he formalized and developed the notion of an enriched category based on intuitions then in the air about making the homsets of a category just as abstract as the objects themselves. He subsequently developed the notion in considerably more detail in his 1981 monograph Basic Concepts of Enriched Category Theory. The explicitly foundational role of the category Set in his treatment is noteworthy in view of the folk intuition that enriched categories liberate category theory from the last vestiges of Set as the codomain of the ordinary external hom-functor.
In 1967 Kelly was appointed Professor of Pure Mathematics at the University of New South Wales. In 1972 he was elected a Fellow of the Australian Academy of Science. He returned to the University of Sydney in 1973, serving as Professor of Mathematics until his retirement in 1994. In 2001 he was awarded the Australian government's Centenary Medal. He continued to participate in the department as Professorial Fellow and Professor Emeritus until his death at age 76.
Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of fruitful collaborations. His Ph.D. student Ross Street is himself a noted category theorist and early contributor to the Australian category theory school.*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