A mathematician's reputation rests on the number of bad proofs he has given.

~Abram S Besicovitch

The 24th day of the year; 24! (6.2044840173323943936 10

^{23})is almost equal to Avogadro's Number, (6.022141×10^23). Also 1

^{2}+ 2

^{2}+...+ 24

^{2}= 70

^{2}the

**only**pyramidal number that is a square.

**EVENTS**

In 1925, a motion picture of a solar eclipse was taken by the U.S. Navy from the dirigible Los Angeles. The craft was at an elevation of about 4,500-ft and positioned about 19 miles east of Montauk Point, Long Island, NY. This give a view of a total eclipse of the sun that lasted just over 2-min. Four astronomical cameras and a spectrograph were used as well as two moving picture cameras. This was the first time in the U.S. that a dirigible had been used as a platform for observation of a total eclipse of the sun. The first U.S. attempt to photograph one from an aircraft 10 Sep 1923 was unsuccessful due to cloudy conditions, but on 28 Apr 1930, a flight over California sponsored by the U.S. Naval Observatory recorded a total solar eclipse. *TIS

1948 IBM dedicates the Selective Sequence Electronic Calculator (SSEC). Later the SSEC was put on public display near the company's Manhattan headquarters so passers-by could watch its operational speed. Before its decommissioning in 1952, the SSEC produced the moon-position tables used for plotting the course of the 1969 Apollo flight to the moon. *CHM

**BIRTHS**

*TIS

1798 Karl George Christian von Staudt (24 Jan 1798; 1 Jun 1867)German mathematician who developed the first complete theory of imaginary points, lines, and planes in projective geometry. His early work was on determining the orbit of a comet and, based on this work, he received his doctorate. He showed how to construct a regular inscribed polygon of 17 sides using only compasses. He turned to projective geometry and Bernoulli numbers (discovered by Jacob Bernoulli). An important work on projective geometry, Geometrie der Lage was published in 1847. It was the first work to completely free projective geometry from any metrical basis. He also gave a geometric solution to quadratic equations. *TIS (*Wik gives birthdate as Jan 23)

1801 Joseph Piazzi sends letters to Bode in Berlin, Oriani in Milan, and Lelande in Paris regarding a newly sighted "comet without tail and envelope". To Oriani he admits that :

I have announced this star as a comet, but since it is not accompanied by any nebulosity and, further, since its movement is so slow and rather uniform, it has occurred to me several times that it might be something better than a comet. But I have been careful not to advance this supposition to the public.*Wik

1863 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.

Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.

This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU

1872 Morris William Travers (24 Jan 1872; 25 Aug 1961)

English chemist who, while working with Sir Willam Ramsay in London, discovered the element krypton (30 May 1898). The name derives from the Greek word for "hidden." It was a fraction separated from liquified air, which when placed in a Plücker tube connected to an induction coil yielded a spectrum with a bright yellow line with a greener tint than the known helium line and a brilliant green line that corresponded to nothing seen before.*TIS

1882 Harold Delos Babcock (24 Jan 1882(Edgerton,Wisconsin) - 8 Apr 1968) American astronomer who with his son, Horace, invented the solar magnetograph (1951), for detailed observation of the Sun's magnetic field. With their magnetograph the Babcocks measured the distribution of magnetic fields over the solar surface to unprecedented precision and discovered magnetically variable stars. In 1959 Harold Babcock announced that the Sun reverses its magnetic polarity periodically. Babcock's precise laboratory studies of atomic spectra allowed others to identify the first "forbidden" lines in the laboratory and to discover the rare isotopes of oxygen. With C.E. St. John he greatly improved the precision of the wavelengths of some 22,000 lines in the solar spectrum, referring them to newly-determined standards.*TIS

1891 Abram Samoilovitch Besicovitch (24 Jan 1891 in Berdyansk, Russia -2 Nov 1970 in Cambridge, Cambridgeshire, England) Besicovitch left Petrograd for Copenhagen in 1924 and there worked with Harald Bohr. He had been awarded a Rockefeller Fellowship but his applications for permission to work abroad had been refused. He escaped across the border with a colleague J D Tamarkin under the cover of darkness. He managed to reach Copenhagen where he was supported financially for a year with the Rockefeller Fellowship. His interest in almost periodic functions came about through this year spent working with Harald Bohr. After he visited Oxford in 1925 Hardy, who quickly saw the mathematical genius in Besicovitch, found a post for him in Liverpool. At Cambridge Besicovitch lectured on analysis in most years but he also gave an advanced course on a topic which was directly connected with his research interests such as almost periodic functions, Hausdorff measure, or the geometry of plane sets. Besicovitch was famous for his work on almost periodic functions, his interest in which, as we mentioned above, came from his time in Copenhagen with Harald Bohr. In 1932 he wrote an influential text Almost periodic functions covering his work in this area.

One of the achievements, with which he will always be associated, was his solution of the Kakeya problem on minimising areas. The problem had been posed in 1917 by a Japanese mathematician S Kakeya and asked what was the smallest area in which a line segment of unit length could be rotated through 2p. Besicovitch proved in 1925 that given any e, an area of less than e could be found in which the rotation was possible. The figures that resulted from Besicovitch's construction were highly complicated, unbounded figures.

Other areas on which Besicovitch worked included geometric measure theory, Hausdorff measure, real function theory, and complex function theory. In addition to this work on deep mathematical theories, Besicovitch loved problems, particularly those which could be stated in elementary terms but which proved resistant to attack. Often he showed that the "obvious solution" to certain problems is false. An example of such a problem is the Lion and the Man problem posed by Richard Rado in the mid 1920s. *SAU

1902 Oskar Morgenstern (24 Jan 1902; 26 Jul 1977) German-American economist and mathematician who popularized "game theory" which mathematically analyzes behaviour of man or animals in terms of strategies to maximize gains and minimize losses. He coauthored Theory of Games and Economic Behavior (1944), with John von Neumann, which extended Neumann's 1928 theory of games of strategy to competitive business situations. They suggested that often in a business situation ("game'), the outcome depends on several parties ("players"), each estimating what all of the others will do before determining their own strategy. Morgenstern was a professor at Vienna University, Austria, from 1931 until the Nazi occupation in 1938), when he fled to America and joined the faculty at Princeton University. His later publications included works on economic prediction and aspects of U.S. defence.*TIS

1914 Vladimir Petrovich Potapov (24 Jan 1914 in Odessa, Ukraine - 21 Dec 1980 in Kharkov, Russia) In 1948 Potapov was invited to the Pedagogical Institute at Odessa. He soon became Head of Mathematics and, from 1952, Dean of the Faculty of Physics and Mathematics. He used his position to invite Livsic and others to the Institute.

During the 1950s Potapov worked on the theory of J-contractive matrix functions and the analysis of matrix functions became his main work. He published papers on the multiplicative theory of analytic matrix functions in the years 1950-55 which contain work from his doctoral thesis. He also worked on interpolation problems.

From 1974 Potapov lectured at Odessa Institute of National Economy, then he went to Kharkov to head the Department of Applied Mathematics at the Institute for low temperature physics. *SAU

1931 Lars V. Hörmander (24 Jan 1931 - ) Swedish mathematician who was awarded the Fields Medal in 1962 for his work on partial differential equations. Spending five years in writing, he produced a text The analysis of linear partial differential operators, in four volumes (1983-85). Between 1987 and 1990 he served as a vice president of the International Mathematical Union. In 1988 Hörmander was awarded the Wolf Prize. Hörmander's text, An Introduction to Complex Analysis in Several Variables, has become a classic dealing with the theory of functions of several complex variables. It developed from lecture notes of a course which he gave in Stanford in 1964 and published in book form two years later, with updates in 1973 and 1990.*TIS

1947 Michio Kaku (January 24, 1947 - ) is an American theoretical physicist, the Henry Semat Professor of Theoretical Physics in the City College of New York of City University of New York, the co-founder of string field theory, and a "communicator" and "popularizer" of science. He has written several books about physics and related topics; he has made frequent appearances on radio, television, and film; and he writes extensive online blogs and articles.*Wik

**DEATHS**

1914 Sir David Gill (12 Jun 1843, 24 Jan 1914) Scottish astronomer known for his measurements of solar and stellar parallax, showing the distances of the Sun and other stars from Earth, and for his early use of photography in mapping the heavens. His early training in timekeeping as a watchmaker led to astronomy and he designed, equipped, and operated a private observatory near Aberdeen. To determine parallaxes, he perfected the use of the heliometer, a telescope that uses a split image to measure the angular separation of celestial bodies. In 1877, Gill and his wife measured the solar parallax by observing Mars from Ascension Island. He was appointed Her Majesty's Astronomer at the Cape of Good Hope (1879-1906). Gill also made geodetic surveys of South Africa. In fact he carried out all of the observations to measure the distances to stars in terms of the standard meter. His precise redetermination of the solar parallax was used for almanacs until 1968. *TIS

1930 Adolf Kneser (19 March 1862 in Grüssow, Mecklenburg, Germany - 24 Jan 1930 in Breslau, Germany (now Wrocław, Poland)) He is remembered most for work mainly in two areas. One of these areas is that of linear differential equations; in particular he worked on the Sturm-Liouville problem and integral equations in general. He wrote an important text on integral equations. The second main area of his work was the calculus of variations. He published Lehrbruch der Variationsrechnung (Textbook of the calculus of variations) (1900) and he gave the topic many of the terms in common use today including 'extremal' for a resolution curve, 'field' for a family of extremals, 'transversal' and 'strong' and 'weak' extremals *SAU

1955 Percy John Heawood (8 September 1861 Newport, Shropshire, England[1] - 24 January 1955 Durham, England) was a British mathematician. He devoted essentially his whole working life to the four color theorem and in 1890 he exposed a flaw in Alfred Kempe's proof, that had been considered as valid for 11 years. With the four color theorem being open again he established the five color theorem instead. The four color theorem itself was finally established by a computer-based proof in 1976. *Wik

1961 Albert Carlton Gilbert (15 Feb 1884, 24 Jan 1961) was an American inventor who patented the Erector set after he founded the A.C. Gilbert Co. New Haven, Connecticut (1908) to manufacture boxed magic sets. In 1913, he introduced Erector Sets. Similar construction toys then existed, such as Hornby's Meccano set made in England. Meccano sets included pulleys, gears, and several 1/2" wide strips of varying length with holes evenly spaced on them. Gilbert needed something unique for his Erector sets, so he created the square girder, made using several 1" wide strips with triangles cut in them. These had their edges bent over so 4 strips could be screwed together to form a very sturdy square girder. Over the next 40 years, some 30 million Erector Sets were sold.*TIS

1982 Karol Borsuk (8 May 1905 in Warsaw, - 24 Jan 1982 in Warsaw) Borsuk introduced the important concept of absolute neighbourhood retracts in his doctoral dissertation, published in 1931, which was to lead to new and fruitful ideas in metric differential geometry. In 1936 he introduced the notion of cohomotopy groups, which could be said to mark the beginning of stable homotopy theory. Shape theory grew up at the same time as infinite-dimensional topology and the interaction between the two fields was of great mutual benefit. He was important for the many deep questions which Borsuk posed which stimulated most of the top mathematicians working in the area. *SAU

Credits

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts