On This Day in Math - July 5

There is no smallest among the small and no largest among the large,

But always something still smaller and something still larger.

Quoted in E Maor, To Infinity and Beyond: a Cultural History of the Infinite

EVENTS
In 1643, an exceptionally strong wind occurred in Essex County, Mass. The description by Governor John Winthrop is the first record suggestive of a tornado in the U.S.: "There arose a sudden gust so violent for one-half hour as it blew down multitudes of trees. It lifted up their meeting house at Newbury, the people being in it. It darkened the air with dust, yet through God’s great mercy it did no hurt, but only killed one Indian with the fall of a tree." However, no tornado-like funnel shape - so likely to be noted, if seen - was not included in his log. So, it was likely not a tornado, in fact, but a severe straight-line squall with strong downburst winds. Reverend Increase Mather cited a likely tornado in Jul 1680 storm at Cambridge, Mass*TIS

1687 Halley wrote to Newton that his Principia was finally published. [Westfall, p. 468] *VFR 1687 – ushering in a tidal wave of changes in thought that would significantly accelerate the already ongoing scientific revolution by giving it tools that produced technologically valuable results, which had theretofore been otherwise unobtainable.

1698 Johann Bernoulli, in a letter to Leibniz, defined the notion of a function. The term “function” is due to Leibniz. [Cajori, Historical Introduction to the Mathematical Literature, p. 96]*VFR

1951 – William Shockley invents the junction transistor. *Wik

BIRTH
1820 William John Macquorn Rankine, Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. As the chair (1855) of civil engineering and mechanics at Glasgow, he developed methods to solve the force distribution in frame structures. Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853. Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. *TIS While many students never encounter it, there is a temperature scale named after Rankine. It is the Fahrenheit scale equivalent of the Kelvin scale for Celsius.

1867 Andrew Ellicott Douglass American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS



DEATHS
1865 Oskar Bolza died. Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Bolza published The elliptic s-functions considered as a special case of the hyperelliptic s-functions in 1900 which related to work he had been studying for his doctorate under Klein. However, he worked on the calculus of variations from 1901. Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907). His text Lectures on the Calculus of Variations published by the University of Chicago Press in 1904,[3] became a classic in its field and was republished in 1961 and 2005.[4] After the death of his friend Maschke in 1908, Bolza became unhappy in the United States and, in 1910, he and his wife returned to Freiburg in Germany where he was appointed as an honorary professor. Chicago gave him the title of 'non-resident professor of mathematics' which he retained for the rest of his life.*Wik He returned to Germany in 1910, where he researched function theory, integral equations and the calculus of variations. In 1913, he published a paper presenting a new type of variational problem now called "the problem of Bolza." The next year, he wrote about variations for an integral problem involving inequalities, which later become important in control theory. Bolza ceased his mathematical research work at the outbreak of WW I in 1914.*TIS

1911 George Johnstone Stoney Irish physicist who introduced the term electron for the fundamental unit of electricity. At the Belfast meeting of the British Association in Aug 1874, in a paper: On the Physical Units of Nature, Stoney called attention to a minimum quantity of electricity. He wrote, "I shall express 'Faraday's Law' in the following terms ... For each chemical bond which is ruptured within an electrolyte a certain quantity of electricity traverses the electrolyte which is the same in all cases." Stoney offered the name electron for this minimum electric charge. When J.J. Thomson identified cathode rays as streams of negative particles, each carrying probably Stoney's minimum quantity of charge, the name was applied to the particle rather than the quantity of charge.*TIS
1926 Peter Scott Lang graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

1932 Rene Louis Baire died. a French mathematician most famous for his Baire category theorem, which helped to generalize and prove future theorems. His theory was published originally in his dissertation Sur les fonctions de variable réelles ("On the Functions of Real Variables") in 1899.*Wik French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

1977 Henry Scheffé worked in several different areas of Statistics, including linear models, analysis of variance and nonparametrics.*SAU


Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History