## Tuesday, 8 May 2012

### On This Day in Math - May 8

I have no certainties,
at most probabilities
Renato Caccioppoli

The 129th day of the year; 129 is the smallest number that can be written as the sum of 3 squares in 4 ways. 129 is the smallest number with four representations as a sum of three positive (but not necessarily distinct) squares: 129 = 12 + 82 + 82 = 22 + 22 + 112 = 22 + 52 + 102 = 42 + 72 + 82 .
129 is also the sum of the first ten primes.

EVENTS
1654 Otto von Guericke demonstrates the Magdenburg hemispheres in front of the imperial Diet, and the Emperor Ferdinand IIII in Regensburg.
The Magdeburg hemispheres, around 50 cm (20 inches) in diameter, were designed to demonstrate the vacuum pump that Guericke had invented. One of them had a tube connection to attach the pump, with a valve to close it off. When the air was sucked out from inside the hemispheres, and the valve was closed, the hose from the pump could be detached, and they were held firmly together by the air pressure of the surrounding atmosphere.
Thirty horses, in two teams of fifteen, could not separate the hemispheres until the valve was opened to equalize the air pressure. In 1656 he repeated the demonstration with sixteen horses (two teams of eight) in his hometown of Magdeburg, where he was mayor. He also took the two spheres, hung the two hemispheres with a support, and removed the air from within. He then strapped weights to the spheres, but the spheres would not budge.Gaspar Schott was the first to describe the experiment in print in his Mechanica Hydraulico-Pneumatica (1657).
In 1663 (or, according to some sources, in 1661) the same demonstration was given in Berlin before Frederick William, Elector of Brandenburg with twenty-four horses. It is unclear how strong a vacuum Guericke's pump was able to achieve, but if it was able to evacuate all of the air from the inside, the hemispheres would have been held together with a force of around 20 000 N (4400 lbf, or 2.2 short tons), equivalent to lifting a car or small elephant; a dramatic demonstration of the pressure of the atmosphere. *Wik

1661 “On 8 May 1661 the Society’s Journal Book notes that ‘a motion was made for the erecting of a library’, and later in the same month ‘it was resolved that every member, who hath published or shall publish any work, give the Society one copy’.” (from Emma Davidson at RSI)

1790 The Assembly (French) ordered the Académie des Sciences to standardize weights and measures on 8 May 1790. The Académie appointed a Commission of Lagrange, Borda, Condorcet, Laplace and Tillet to compare the decimal and duodecimal systems. Another Commission, with Monge instead of Tillet, was to examine how to make a standard of length. The Commissions continued functioning through the Revolution.

1794 Lavoisier Guillotined along with twenty-seven other members of the Ferme Générale, including his father-in-law. See Deaths below

In 1886, Coca-Cola, the soft drink, was first sold to the public at the soda fountain in Jacob's Pharmacy in Atlanta, Georgia. It was invented by pharmacist, John Stith Pemberton, who mixed it in a 30-gal. brass kettle hung over a backyard fire. Until 1905, the drink, marketed as a "brain and nerve tonic," contained extracts of cocaine as well as the caffeine-rich kola nut. The name, using two C's from its ingredients, was suggested by his bookkeeper Frank Robinson, whose excellent penmanship provided the first scripted "Coca-Cola" letters as the famous logo. Asa Candler marketed Coke to world after buying the company from Pemberton. *TIS

1961 President J. F. Kennedy presented astronaut Alan B. Shepard the ﬁrst National Aeronautics and Space Administration Distinguished Flying Medal for making America’s ﬁrst space ﬂight on May 5, 1961.*VFR

BIRTHS
1859 Johan Ludwig William Valdemar Jensen (8 May 1859 – 5 March 1925) contributed to the Riemann Hypothesis, proving a theorem which he sent to Mittag-Leffler who published it in 1899. The theorem is important, but does not lead to a solution of the Riemann Hypothesis as Jensen had hoped. It expresses
... the mean value of the logarithm of the absolute value of a holomorphic function on a circle by means of the distances of the zeros from the centre and the value at the centre.
He also studied infinite series, the gamma function and inequalities for convex functions.*SAU

1905 Karol Borsuk (May 8, 1905, Warsaw – January 24, 1982, Warsaw) Polish mathematician. His main interest was topology.
Borsuk introduced the theory of absolute retracts (ARs) and absolute neighborhood retracts (ANRs), and the cohomotopy groups, later called Borsuk-Spanier cohomotopy groups. He also founded the so called Shape theory. He has constructed various beautiful examples of topological spaces, e.g. an acyclic, 3-dimensional continuum which admits a fixed point free homeomorphism onto itself; also 2-dimensional, contractible polyhedra which have no free edge. His topological and geometric conjectures and themes stimulated research for more than half a century. *Wik

DEATHS
1794 Antoine Laurent Lavoisier (26 August 1743 – 8 May 1794) after a trial that lasted less than a day, a revolutionary tribunal condemned Antoine Laurent Lavoisier to death. He was 51 and guillotined on the same afternoon.  " It took only a moment to cause this head to fall and a hundred years will not suffice to produce its like." Joseph Louis Lagrange, the day of Lavoisier’s execution.
Lavoisier was guillotined in the terror following the French Revolution. 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. Under the Reign of Terror, despite his eminence and his services to science and France, he came under attack as a former Ferme Générale. In November 1793, all former members of the Ferme Générale including Lavoisier and his father-in-law, were arrested and imprisoned. After a trial that lasted less than a day, they were all found guilty of conspiracy against the people of France and condemned. When Lavoisier requested time to complete some scientific work, the presiding judge was said to have answered "The Republic has no need of scientists." He was guillotined and thrown in a common grave in the Cimetière de Picpus. Mathematician Joseph Louis Lagrange lamented the execution: "It took them only an instant to cut off that head, but France may not produce another like it in a century." About eighteen months following his death, Lavoisier was exonerated by the French government. When his belongings were delivered to his widow, a brief note was included reading "To the widow of Lavoisier, who was falsely convicted."
For more about Lavoisier see SomeBeans blog

1853 John Farrar (July 1, 1779 – May 8, 1853) died at Cambridge, Massachusetts.His translations from the French, including Legendre’s Elements of Geometry (Boston, 1819),were widely used in the U. S. *VFR
He first coined the concept of hurricanes as “a moving vortex and not the rushing forward of a great body of the atmosphere”, after the Great September Gale of 1815. Farrar
remained Professor of Mathematics and Natural Philosophy at Harvard University between 1807 and 1836. During this time, he introducedmodern mathematics into the curriculum. He was
also a regular contributor to the scientific journals. *Wikipedia He is buried in MountAuburn Cemetery Cambridge, Massachusetts,USA.*Wik

1904 Eadweard Muybridge English photographer important for his pioneering work in photographic studies of motion and in motion-picture projection. For his work on human and animal motion, he invented a superfast shutter. Leland Stanford, former governor of California, hired Muybridge to settle a hotly debated issue: Is there a moment in a horse’s gait when all four hooves are off the ground at once? In 1972, Muybridge took up the challenge. In 1878, he succeeded in taking a sequence of photographs with 12 cameras that captured the moment when the animal’s hooves were tucked under its belly. Publication of these photographs made Muybridge an international celebrity. Another noteworthy event in his life was that he was tried (but acquitted) for the murder of his wife's lover. *TIS

1951 Gilbert Ames Bliss, (9 May 1876, Chicago – 8 May 1951, Harvey, Illinois), was an American mathematician, known for his work on the calculus of variations. Bliss once headed a government commission that devised rules for apportioning seats in the U.S. House of Representatives among the several states. *Wikipedia

1959 Renato Caccioppoli (20 January 1904 – 8 May 1959) His most important works, out of a total of around eighty publications, relate to functional analysis and the calculus of variations. Beginning in 1930 he dedicated himself to the study of differential equations, the first to use a topological-functional approach. Proceeding in this way, in 1931 he extended the Brouwer fixed point theorem, applying the results obtained both from ordinary differential equations and partial differential equations.
In 1932 he introduced the general concept of inversion of functional correspondence, showing that a transformation between two Banach spaces is invertible only if it is locally invertible and if the only convergent sequences are the compact ones.
Between 1933 and 1938 he applied his results to elliptic equations, establishing the majorizing limits for their solutions, generalizing the two-dimensional case of Felix Bernstein. At the same time he studied analytic functions of several complex variables, i.e. analytic functions whose domain belongs to the vector space Cn, proving in 1933 the fundamental theorem on normal families of such functions: if a family is normal with respect to every complex variable, it is also normal with respect to the set of the variables. He also proved a logarithmic residue formula for functions of two complex variables in 1949.
In 1935 Caccioppoli proved the analyticity of class C2 solutions of elliptic equations with analytic coefficients.
The year 1952 saw the publication of his masterwork on the area of a surface and measure theory, the article Measure and integration of dimensionally oriented sets (Misura e integrazione degli insiemi dimensionalmente orientati, Rendiconti dell'Accademia Nazionale dei Lincei, s. VIII, v.12). The article is mainly concerned with the theory of dimensionally oriented sets; that is, an interpretation of surfaces as oriented boundaries of sets in space. Also in this paper, the family of sets approximable by polygonal domains of finite perimeter, known today as Caccioppoli sets or sets of finite perimeter, was introduced and studied.
His last works, produced between 1952 and 1953, deal about a class of pseudoanalytic functions, introduced by him to extend certain properties of analytic functions.
In his last years, the disappointments of politics and his wife's desertion, together perhaps with the weakening of his mathematical vein, pushed him into alcoholism. His growing instability had sharpened his "strangenesses", to the point that the news of his suicide on May 8, 1959 by a gunshot to the head did not surprise those who knew him. He died at his home in Palazzo Cellammare
In 1992 his tormented personality was remembered in a film directed by Mario Martone, The Death of a Neapolitan Mathematician (Morte di un matematico napoletano), in which he was portrayed by Carlo Cecchi. * Wik

1953 Benjamin Fedorovich Kagan (10 March 1869 in Shavli, Kovno (now Kaunas, Lithuania)
- 8 May 1953 in Moscow, USSR) Kagan worked on the foundations of geometry and his first work was on Lobachevsky's geometry. In 1902 he proposed axioms and definitions very different from Hilbert. Kagan studied tensor differential geometry after going to Moscow because of an interest in relativity.
Kagan wrote a history of non-euclidean geometry and also a detailed biography of Lobachevsky. He edited Lobachevsky's complete works which appeared in five volumes between 1946 and 1951. *SAU
1960 Henry Whitehead was a topologist and differential geometer who is best remembered for his work on homotopy equivalence. *SAU

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