## Tuesday, 29 May 2012

### On This Day in Math - May 29

No matter how correct a mathematical theorem
may appear to be, one ought never to be satisfied
that there was not something imperfect
about it until it also gives
the impression of being beautiful.
~ George Boole

The 150th day of the year; 150 is the largest gap between consecutive twin prime pairs less than a thousand. It occurs between {659, 661} and {809, 811}. *Prime Curios

EVENTS
1733  Euler names the "Pell Equations" and gives a method of multiple solutions. "Euler’s first excursion into Pell’s equation was his 1732 paper E-29, bearing a title that translates
as “On the solution of problems of Diophantus about integer numbers.” The main result of this paper is to show how certain quadratic Diophantine equations can be reduced to the Pell equation. In particular, he shows that if we can find a solution to the Diophantine equation y2 = an2 + bn + c and we can find solutions to the Pell equation, q2 = ap2 +1, then we can use the solutions to the Pell equation to construct more solutions to the original Diophantine equation. He also shows how to use two solutions to a Pell equation to construct more solutions, and notes that solutions to a Pell equation give good rational approximations for the square root of a.  (Ed Sandifer, Euler and Pell, How Euler DId It. MAA) .

1832 Almost certain that he would die in a dual the next day, Evariste Galois ﬁrst wrote “Letter to all Republicans,” and then wrote to a friend (Auguste Chevalier) describing his mathematics. It ended: “Eventually there will be, I hope, some people who will ﬁnd it proﬁtable to decipher this mess.” [Burton, History of Mathematics, p. 322]. See Smith, Source Book, pp. 278–285 for the letter. *VFR

The appropriate pages from Smith's book is below:

1898 the heirs of Alfred Nobel sign a "reconciliation agreement" so that lawyers and accountants can execute his will. The will's major bequest was to create the Nobel Prizes, but first, there were disputes to be settled.*TIS

1919 São Tomé and Príncipe, officially the Democratic Republic of São Tomé and Príncipe, is a Portuguese-speaking island nation in the Gulf of Guinea, off the western equatorial coast of Central Africa. Príncipe was the site where astronomical observations of the total solar eclipse of 29 May 1919 confirmed Einstein's prediction of the curvature of light. The expedition was sponsored by the Royal Society and led by Sir Arthur Stanley Eddington. A solar eclipse permitted observation of the bending of starlight passing through the sun's gravitational field, as predicted by Einstein's theory of relativity. Separate expeditions of the Royal Astronomical Society travelled to Brazil and off the west coast of Africa. Both made measurements of the position of stars visible close to the sun during a solar eclipse. These observations showed that, indeed, the light of stars was bent as it passed through the gravitational field of the sun. The verification of predictions of Einstein's theory, proved during the solar eclipse was a dramatic landmark scientific event. *Wik

1957 Romania issued two stamps picturing a slide rule to publicize the 2nd Congress of the Society of Engineers and Technicians, which began in Bucharest on this day. [Scott #1159-60].
For the younger set... If you never used (saw) a slide rule, there is actually an online java app that you can simulate the use of one at this page.

BIRTHS
1675 Humphry Ditton (May 29, 1675 – October 15, 1715) was born at Salisbury and died in London in 1715 at Christ's Hospital, where he was mathematical master. He does not seem to have paid much attention to mathematics until he came to London about 1705. W. W. Rouse Ball states that Ditton's 1706 book on fluxions occupied a place in English education equivalent to L'Hospital's book in France.

1794 Johann Heinrich von Mädler (May 29, 1794 – March 14, 1874)  German astronomer who (with Wilhelm Beer) published the most complete map of the Moon of the time, Mappa Selenographica, 4 vol. (1834-36). It was the first lunar map to be divided into quadrants, and it remained unsurpassed in its detail until J.F. Julius Schmidt's map of 1878. Mädler and Beer also published the first systematic chart of the surface features of the planet Mars (1830).*TIS

1882 Harry Bateman (29 May 1882 – 21 January 1946) He spent much of his life collecting special functions and integrals that solved partial diﬀerential equations. He kept the references on index cards stored in shoe boxes—eventaully these began to crowd him out of his oﬃce. [DSB 1, 500] *SAU

1885 Finlay Freundlich (May 29, 1885 – July 24, 1964) was a distinguished German astronomer who worked with Einstein on measurements of the orbit of Mercury to confirm the general theory of relativity. He left Germany to avoid Nazi rule and became the Napier Professor of Astronomy at St Andrews.

1929 Peter Ware Higgs (29 May 1929 -  ) is an English theoretical physicist, the namesake of the Higgs boson. In the late 1960s, Higgs and others proposed a mechanism that would endow particles with mass, even though they appeared originally in a theory - and possibly in the Universe! - with no mass at all. The basic idea is that all particles acquire their mass through interactions with an all-pervading field, called the Higgs field. which is carried by the Higgs bosons. This mechanism is an important part of the Standard Model of particles and forces, for it explains the masses of the carriers of the weak force, responsible for beta-decay and for nuclear reactions that fuel the Sun. No Higgs boson has yet been detected; its mass (over 1 TeV) exceeds the capacity of any current accelerator. *TIS

1911 George Szekeres (29 May 1911 – 28 August 2005) was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics*SAU

1957 Jean-Christophe Yoccoz ( May 29, 1957 -   )  French mathematician who was awarded the Fields Medal in 1994 for his work in dynamical systems. Such studies began with Poincaré about the turn of the 20th century, who considered the stability of the solar system. It evolves according to Newton's laws but will it remain stable or, might a planet be ejected from the system? The techniques apply also in biology, chemistry, mechanics, and ecology where stability is an issue. This work also produces aesthetically appealing objects, such as the Julia and Mandelbrot fractal sets. Yoccoz was primarily concerned with establishing criteria that gave precise bounds on the validity of stability theorems. A combinatorial method for studying the Julia and Mandelbrot sets was named "Yoccoz puzzles." *TIS

DEATHS
1660 Frans van Schooten (1615 in Leiden – 29 May 1660 in Leiden) was a Dutch mathematician who was one of the main people to promote the spread of Cartesian geometry. Van Schooten's father was a professor of mathematics at Leiden, having Christiaan Huygens, Johann van Waveren Hudde, and René de Sluze as students.
Van Schooten read Descartes' Géométrie (an appendix to his Discours de la méthode) while it was still unpublished. Finding it hard to understand, he went to France to study the works of other important mathematicians of his time, such as François Viète and Pierre de Fermat. When Frans van Schooten returned to his home in Leiden in 1646, he inherited his father's position and one of his most important pupils, Huygens.
Van Schooten's 1649 Latin translation of and commentary on Descartes' Géométrie was valuable in that it made the work comprensible to the broader mathematical community, and thus was responsible for the spread of analytic geometry to the world. Over the next decade he enlisted the aid of other mathematicians of the time, de Beaune, Hudde, Heuraet, de Witt and expanded the commentaries to two volumes, published in 1659 and 1661. This edition and its extensive commentaries was far more influential than the 1649 edition. It was this edition that Gottfried Leibniz and Isaac Newton knew.
Van Schooten was one of the first to suggest, in exercises published in 1657, that these ideas be extended to three-dimensional space. Van Schooten's efforts also made Leiden the centre of the mathematical community for a short period in the middle of the seventeenth century. *Wik    Thony Christie (aka The Renaissance Mathematicus) sent me a comment to tell me that it was van Schooten who first used rectangular coordinates in his translations and extensions of Descartes Geometry.  The MAA Digital Library has seven images from van Schooten's "Exercitationes mathematicae". The copy was once the property of his student, Johann Hudde, and include problems from the book of another of his famous students, Christian Huygen's Ludo aleae.

If you read La Géométrie you will search for rectangular co-ordinates in vain, Descartes did not use them. (Neither did Fermat who developed/invented algebraic geometry independently from Descarte). The first person to use them was van Schooten in his extended translation of Descartes work. (Thanks Thony)

1829 Sir Humphrey Davy (Baronet) (17 December 1778 – 29 May 1829) English chemist who discovered several chemical elements and compounds, invented the miner's safety lamp, and epitomized the scientific method. With appointment to the Pneumatic Institution to study the physiological effects of new gases, Davy inhaled gases (1800), such as nitrous oxide (laughing gas) and a nearly fatal inhalation of water gas, (a mixture of hydrogen and carbon monoxide). Davy discovered alkali metals, potassium and sodium, an isolation made with electric current for the first time (1807); as well as alkaline earth metals: calcium, strontium, barium, and magnesium (1808). He discovered boron at the same time as Gay-Lussac. He recognized chlorine as an element, which prior workers confused as a compound. *TIS Davy died in Switzerland in 1829 of heart disease inherited from his father's side of the family. He spent the last months of his life writing "Consolations In Travel", an immensely popular, somewhat freeform compendium of poetry, thoughts on science and philosophy (and even speculation concerning alien life) which became a staple of both scientific and family libraries for several decades afterward. He is buried in the Plainpalais Cemetery in Geneva.

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*SAU=St Andrews Univ. Math History
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell