**Perhaps... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, in the same way, so to speak, as he calculates the motions of celestial bodies.**

~Antoine-Laurent Lavoisier

The 238th day of the year; 238 is an untouchable number, The untouchable numbers are those that are not the sum of the proper divisors of any number. 2 and 5 are untouchable, can you find the next one? (four is not untouchable, for example since 1+3=4 and they are the proper divisors of 9)

**EVENTS**

**1735**Euler’s Konisburg bridge solution, "The Solution of a problem related to the Geometry of Position", was presented to the St. Petersburg Academy on August 26, 1735. He showed that there were no continuous walks across the seven bridges across the Pregel River in Konisburg. It is often cited as the earliest paper in both topology and graph theory.*VFR

**1768**Capt. James Cook began the ﬁrst circumnavigation of the globe. *VFR Cook and his ninety-eight foot bark, Endeavour, carried the Venus transit observation crew mounted by the Royal Society, led by a future Royal Soc. President, Joseph Banks. They would erect an observation station at Point Venus in Tahiti to observe the June 3, 1769 observation under clear blue skys. *Timothy Ferris, Coming of Age in the Milky Way

**1770**Lagrange, in a letter to d’Alembert, ﬁrst uses the notation f‘ (x) for the derivative. He ﬁrst used it in print in a paper published in 1772. Although Lagrange used the notation in his diagramless Mecanique Analytique (1788), it did not catch on until after he used it in his Theorie de functions analytiques (1797). *Oeuvres de Lagrange, 13, p. 181.

**1774**John Adams notes in his diary that he had toured Princeton’s library with Professor Euston (William Churchill Houston, first professor of mathematics and natural philosophy) and then into the “apparatus room” where he saw the “most beautiful machine”. It was an orrey made by Rittenhouse. Professor Houston served in combat in the revolution when Princeton was closed by the occupation of the British. After the college was reopened, he returned to teaching but was soon selected to represent New Jersey as a representative to the Continental Congress, and then to the Constitutional Convention. He died shortly after the close of the Constitutional Convention. *The Teaching and History of Mathematics in The United States, F. Cajori (pgs 71-72)

**In 1895**, electricity was first transmitted commercially from the first large-scale utilization of Niagara Falls power, the current being used by the Pittsburgh Reduction Company in the electrolytic production of aluminium metal from its ore. Buffalo subsequently received power for commercial use on 15 Nov 1896. The equipment was the result of a contract made on 24 Oct 1893 whereby Westinghouse Electric and Manufacturing Company of Pittsburgh, Pa., would install three 5,000-hp generators producing two-phase currents at 2,200 volts, 25 hertz. The first such tuboalternator unit was completed within 18 months. Prior capacity had been limited to generators no larger than 1,000 hp.*TIS

**1966**Professor Stephen Smale, who received the Fields medal ten days earlier, condemned American military intervention in Vietnam and Soviet intervention in Hungary at a news conference in Moscow. For Smale’s fascinating personal account see “On the Steps of Moscow University,” The Mathematical Intelligencer, 6, no. 2, pp. 21–27. *VFR

**1984**Miss Manners addresses computer correspondence

Miss Manners confronts a new realm of etiquette in her August 26 column as she responded to a reader's concern about typing personal correspondence on a personal computer. The concerned individual said that using the computer was more convenient but that they were worried about the poor quality of her dot-matrix printer and about copying parts of one letter into another.

Miss Manners replied that computers, like typewriters, generally are inappropriate for personal correspondence. In the event a word processor is used, she warned, the recipient may confuse the letter for a sweepstakes entry. And, she noted, if any one of your friends ever sees that your letter to another contains identical ingredients, you have will no further correspondence problems.*CHM

**BIRTHS**

**1728 Johann Heinrich Lambert**was born in Mulhouse, Alsace. His most famous results are the proofs of the irrationality of π and e *VFR In 1766, Lambert wrote Theorie der Parallellinien, a study of the parallel postulate. By assuming that the parallel postulate was false, he deduced many non-euclidean results. He noticed that in this new geometry the sum of the angles of a triangle increases as its area decreases. Lambert conjectured that e and p are transcendental, though this was not proved for another century. He is responsible for many innovations in the study of heat and light, devised a method of measuring light intensity, as well as working on the theory of probability.*TIS (Lambert's credit for a vigorous proof of the irrationality of π is generally agreed to, but Euler Scholar Ed Sandifer has written that Euler's proof was fully rigorous prior to Lambert. *How Euler Did It, Feb 2006).

**1740 Joseph-Michel Montgolfie**r (26 Aug 1740; 26 Jun 1810)French balloon pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep 1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world.*TIS

**1743 Antoine-Laurent Lavoisier**born. French scientist, the "father of modern chemistry," was a brilliant experimenter also active in public affairs. An aristocrat, he invested in a private company hired by the government to collect taxes. With his wealth he built a large laboratory. In 1778, he found that air consists of a mixture of two gases which he called oxygen and nitrogen. By studying the role of oxygen in combustion, he replaced the phlogiston theory. Lavoisier also discovered the law of conservation of mass and devised the modern method of naming compounds, which replaced the older nonsystematic method. During the French Revolution, for his involvement with tax-collecting, he was guillotined.*TIS

1875 Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain D⊂ℂ to a holomorphic function on D. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on. *Wik

**1882 James Franck**(26 Aug 1882; 21 May 1964) German-born American physicist who shared the Nobel Prize for Physics in 1925 with Gustav Hertz for research on the excitation and ionization of atoms by electron bombardment that verified the quantized nature of energy transfer.*TIS

**1886 Jerome C. Hunsake**r (26 Aug 1886; 10 Sep 1984)American aeronautical engineer who made major innovations in the design of aircraft and lighter-than-air ships, seaplanes, and carrier-based aircraft. His career had spanned the entire existence of the aerospace industry, from the very beginnings of aeronautics to exploration of the solar system. He received his master's degree in naval architecture from M.I.T. in 1912. At about the same time seeing a flight by Bleriot around Boston harbour attracted him to the fledgling field of aeronautics. By 1916, he became MIT's first Ph.D. in aeronautical engineering. He designed the NC (Navy Curtiss) flying boat with the capability of crossing the Atlantic. It was the largest aircraft in the world at the time, with four engines and a crew of six.*TIS

**1899 Wolfgang Krull**proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring.*SAU

**1951 Edward Witten**(26 Aug 1951, )American mathematical physicist who was awarded the Fields Medal in 1990 for his work in superstring theory. This is work in elementary particle theory, especially quantum field theory and string theory, and their mathematical implications. He elucidated the dynamics of strongly coupled supersymmetric field. The deep physical and mathematical consequences of the electric-magnetic duality thus exploited have broadened the scope of Mathematical Physics. He also received the Dirac Medal from the International Centre for Theoretical Physics (1985) and the Dannie Heineman Prize from the American Physical Society (1998), among others.*TIS

**DEATHS**

**1349 Thomas Bradwardine**, archbishop of Canterbury, died of the plague. This medieval mathematical physicist studied the notion of change. *VFR Bradwardine was a noted mathematician as well as theologian and was known as 'the profound doctor'. He studied bodies in uniform motion and ratios of speed in the treatise De proportionibus velocitatum in motibus (1328). This work takes a rather strange line between supporting and criticising Aristotle's physics. Perhaps it is not really so strange because Aristotle views were so fundamental to learning at that time that perhaps all that one could expect of Bradwardine was the reinterpretation of Aristotle's views on bodies in motion and forces acting on them. It is likely that his intention was not to criticise Aristotle but rather to justify mathematically a reinterpretation of Aristotle's statements. He was also the first mathematician to study "star polygons". They were later investigated more thoroughly by Kepler *SAU

**1572 Peter Ramus**was cruelly murdered, by hired assassins, during the St. Bartholomew’s Day Massacre. He was an early opponent of the teachings of Aristotle. *VFR Peter Ramus was a French mathematician who wrote a whole series of textbooks on logic and rhetoric, grammar, mathematics, astronomy, and optics. His assassination was due to religious conflict.

**1865 Johann Encke**(23 Sep 1791, 26 Aug 1865) German astronomer who established the period of Encke's Comet at 3.3 years (shortest period of any known). *TIS

1929 Thomas John l'Anson Bromwich (8 Feb 1875 in Wolverhampton, England - 26 Aug 1929 in Northampton, England) He worked on infinite series, particularly during his time in Galway. In 1908 he published his only large treatise An introduction to the theory of infinite series which was based on lectures on analysis he had given at Galway. He also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest. In a series of papers he put Heaviside's calculus on a rigorous basis treating the operators as contour integrals*SAU G. H. Hardy described him as the “best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians.” *VFR

**1961 Howard Percy Robertson**1903 Howard Percy Robertson (27 Jan 1903 in Hoquiam, Washington, USA - 26 Aug 1961) made outstanding contributions to differential geometry, quantum theory, the theory of general relativity, and cosmology. He was interested in the foundations of physical theories, differential geometry, the theory of continuous groups, and group representations. He was particularly interested in the application of the latter three subjects to physical problems.

His contributions to differential geometry came in papers such as: The absolute differential calculus of a non-Pythagorean non-Riemannian space (1924); Transformation of Einstein space (1925); Dynamical space-times which contain a conformal Euclidean 3-space (1927); Note on projective coordinates (1928); (with H Weyl) On a problem in the theory of groups arising in the foundations of differential geometry (1929); Hypertensors (1930); and Groups of motion in space admitting absolute parallelism (1932). *SAU

**1977 Robert Schatten**-- principal mathematical achievement was that of initiating the study of tensor products of Banach spaces. The concepts of crossnorm, associate norm, greatest crossnorm, least crossnorm, and uniform crossnorm, all either originated with him or at least first received careful study in his papers. He was mainly interested in the applications of this subject to linear transformations on Hilbert space. In this subject, the Schatten Classes perpetuate his name. Schatten had his own way of making abstract concepts memorable to his elementary classes. Who could forget what a sequence was after hearing Schatten describe a long corridor, stretching as far as the eye could see, with hooks regularly spaced on the wall and numbered 1, 2, 3, ...? "Then," Schatten would say, "I come along with a big bag of numbers over my shoulder, and hang one number on each hook." This of course was accompanied by suitable gestures for emphasis. *SAU

**1998 Frederick Reines**(16 Mar 1918, 26 Aug 1998) American physicist who was awarded the 1995 Nobel Prize for Physics for his detection in 1956 of neutrinos, working with his colleague Clyde L. Cowan, Jr. The neutrino is a subatomic particle, a tiny lepton with little or no mass and a neutral charge which had been postulated by Wolfgang Pauli in the early 1930s but had previously remained undiscovered. (Reines shared the Nobel Prize with physicist Martin Lewis Perl, who discovered the tau lepton.)*TIS

Credits:

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum

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