**Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.**

~Leonhard Euler

The 284th day of the year; 284 is an amicable (or friendly) number paired with 220. The divisors of 220 add up to 284 and the divisors of 284 add up to 220. Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. A general formula by which some of these numbers could be derived was invented circa 850 by Thābit ibn Qurra (826-901).(Can you find the next pair?)

jim wilder @wilderlab pointed out a variation of friendly numbers in degree three...

Along the lines of friendly numbers... 136 = 2³ + 4³ + 4³ and 244 = 1³ + 3³ + 6³

So what should we call them? Third Cousins? Your suggestions?

1580 John Dee became one of the few commoners visited by Queen Elizabeth. Just hours after the death of his second wife the Queen and her entire privy council showed up at his door. Dee tried to entertain her using the "magical mirror" he had been given by William Pickering who had once been Elizabeth's suitor. The mirror, made of highly-polished obsidian (volcanic glass), was one of many Mexica cult objects and treasures brought to Europe after the conquest of Mexico by Cortés between 1527 and 1530. It is now in the British Museum. *Benjamin Wooley, The Queen's Conjuror

In

**1796**, according to tradition, the metric system was born. The Oct 10 (10/10) date was chosen since it seems to signify the base 10 way of using measurements.*TIS

*(tradition perhaps, but I can find no event that took place regarding metric system on this date. France would adopt system on Dec 10th of 1796. Can anyone verify a reason for this "traditional" date.)*

**1845**Naval School (now Naval Academy) opened at Annapolis, MD. *VFR

In

**1846**, Neptune's moon, Triton, is discovered by William Lassell while he was observing the newly discovered planet Neptune. He was attempting to confirm his observation of the previous week, that Neptune had a ring. Instead he discovered that Neptune had a satellite, Triton. Lassell soon proved that the ring he thought he had seen was a product of his new telescope's distortion. This picture of Triton was taken in 1989 by the only spacecraft ever to pass Triton: Voyager 2, which found fascinating terrain, a thin atmosphere, and even evidence for ice volcanoes on this world of peculiar orbit and spin. Ironically, Voyager 2 also confirmed the existence of complete thin rings around Neptune - but these would have been quite invisible to Lassell! *TIS

**1931**Spain issued a stamp picturing the Fountain of Lions at the Alhambra in Granada. The Alhambra is famous for its use of tesselations. [Scott #491] *VFR

**1971**The rebuilt London Bridge was completed and dedicated in Arizona. In 1831, New London Bridge had opened to traffic in London. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendour by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for $2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971.*TIS

**In 1986**, a tiny asteroid, Asteroid 3753, was found orbitting the Earth - a body in addition to the Moon - by J. D. Waldron at Siding Spring Observatory. It was called Cruithne, (pronounced "Croo-een-ya") after Celtic tribes who came to Britain between about 880 and 500 BC. It is pulled alternately by the Sun and Earth. When viewed from the Earth, its 770-year orbit appears to be horseshoe shaped, but this is an effect of viewing an orbit from a rotating planet. It actually passes closer to the Earth than the Moon. At its closest approach it only gets to within about 15 million km (9 million miles) of our planet. Its diameter ranges between 2.9 - 6.4 km diameter wide. Cruithne will remain in a suspended state around Earth for at least 5,000 years. *TIS

In

**2001**, construction on the Viaduc de Millau (Millau Viaduct) began to bridge the River Tarn in Southern France. Finished in 38 months, it was opened 14 Dec 2004. The Millau Viaduct, designed by Sir Norman Foster, is the longest cable-stayed bridge in the world. Taller than the Eiffel Tower, the tallest pylon is 340m high, making it the world's highest road bridge. It carries the A75 motorway from Clermont-Ferraud south to Beziers, crosses 2.5-km and rises 270m above the valley. It was to replace the motor route through the town of Millau with continual traffic jams, shorten the journey by 100 km and save 4 hours of driving time. It was built using a steel deck, rather than concrete roadbed. *TIS

**1731 Henry Cavendish**(10 Oct 1731; 24 Feb 1810) English chemist and physicist who conducted experiments with diverse interests in his private laboratory. Most notably, he determined the mass and density of the Earth. He investigated the properties of hydrogen and carbon dioxide, including comparing their density to that of air. Cavendish also showed that water was a compound and measured the specific heat of various substances. His manuscripts (published 1879) revealed discoveries he made in electrostatics before Coulomb, Ohm and Faraday - including deducing the inverse square law of electrostatic attraction and repulsion. He also found specific inductive capacity. His family name is attached to the Cavendish Laboratory (founded 1871, funded by a later family member) at Cambridge University. *TIS Cavendish was supposedly so shy that for his only portrait the artist painted his coat from a hook in the hall, then painted Cavendish body from memory. *"Shock and Awe", BBC broadcast on the history of electricity)(

**1817 Christophorus Henricus Didericus Buys Ballot**(10 Oct 1817; 3 Feb 1890) was a Dutch meteorologist who is remembered for his observation in 1857 that the wind blows at right angles to the atmospheric pressure gradient. He showed that northern hemisphere winds circulate counter-clockwise around low pressure areas and clockwise around high pressure areas. The reverse is true in the southern hemisphere. Although not the first to make this discovery, his name remains attached to it as Buys Ballot's law. He studied and taught at the University of Utrecht, and founded the Royal Netherlands Meteorological Institute in 1854. He was the inventor of the aeroklinoscope and of a system of weather signals.*TIS

**1861 Heinrich Friedrich Karl Ludwig Burkhardt**(10 Oct 1861, 2 Nov 1914) His main work was in analysis, particularly the theory of trigonometric series, and on the history of mathematics. Other topics on which Burkhardt published papers included groups, differential equations, differential geometry and mathematical physics.*SAU

**1896 Lester Halbert Germer**(10 Oct 1896; 10 Mar 1971) was a American physicist who, with his colleague Clinton Joseph Davisson, conducted an experiment (1927) that first demonstrated the wave properties of the electron. They showed that a beam of electrons scattered by a crystal produces a diffraction pattern characteristic of a wave. This experiment confirmed the hypothesis of Louis-Victor de Broglie, a founder of wave mechanics, that the electron should show the properties of an electromagnetic wave as well as a particle. He also studied thermionics, erosion of metals, and contact physics.*TIS

**1919 William Henry Kruskal**(October 10, 1919 – April 21, 2005) was an American mathematician and statistician. He is best known for having formulated the Kruskal–Wallis one-way analysis of variance (together with W. Allen Wallis), a widely-used nonparametric statistical method.

Kruskal was born in New York City to a successful fur wholesaler. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of Origami during the early era of television. He was the oldest of five children, three of whom, including himself, became researchers in mathematics and physics; see Joseph Kruskal and Martin Kruskal. Kruskal left Antioch College to attend Harvard University, receiving Bachelor's and Master's degrees in mathematics in 1940 and 1941. He pursued a Ph. D. in Mathematical Sciences at Columbia University, graduating in 1955.

During the Second World War, Kruskal served at the U.S. Naval Proving Ground in Dahlgren, Virginia. After brief stints working for his father and lecturing at Columbia, he joined the University of Chicago faculty as an instructor in statistics in 1950. He edited the Annals of Mathematical Statistics from 1958 to 1961, served as president of the Institute of Mathematical Statistics in 1971, and of the American Statistical Association in 1982. Kruskal retired as Professor Emeritus in 1990. He died in Chicago.*Wik

**1708 David Gregory**(3 Jun 1659, 10 Oct 1708) Scottish mathematician and astronomer. In 1702 he published a book Astronomiae physicae et geometricae elementa, an effort in the popularization of Newtonian science. However, in the matter of chromatic aberration, Gregory noted something that Newton had missed. Different kinds of glass spread the colours of the spectrum by different amounts. He suggested a suitable combination of two different kinds of glass might eliminate chromatic aberration. (A half century later, Dollond accomplished this result.) Telescopes were a special interest of his, and Gregory also experimented with making an achromatic telescope. Gregory also did important work on series.*TIS

**1925 Andrew Gray**(2 July 1847, 10 Oct 1925) graduated from Glasgow University and was appointed assistant and secretary to Lord Kelvin. He became Professor of Physics at University College Bangor and then returned to Glasgow as Kelvin's successor. He produced many books and papers in both mathematics and physics.*SAU

**1940**Vito Volterra (1860–1940) died in Rome. Best known for his early contributions to functional analysis: he introduced the concept of functional in 1887. He also gave an example of a function with a bounded derivative that is not Riemann integrable. He took a prominent role in public life, being President of the Accademia dei Lincei and also a Senator. When the Fascists’ came to power he opposed them and so lost his positions. Consequently his death was not announced in Italian newspapers. This had an ironic sequel: In October 1943 an SS detachment called at his house to arrest him and send him to a concentration camp. *VFR

**1971 Sir Cyril Burt**(3 Mar 1883, 10 Oct 1971) British psychologist who was a leader in developing methods of statistical data analysis, particularly factor analysis, in psychological testing. He investigated the role of heredity in intelligence with twin studies and the role of nuture in juvenile deliquency. In 1913, he was appointed thea school psychologist for the schools administered by the London County Council (LCC) This was the first appointment of this kind in the U.K. In 1926, he proposed a national testing program of intelligence tests on children at about age 11. Subsequently, the national "Eleven-Plus" exam was used to identify whether children were high scorers suitable for education at a grammar schools, or not. After Burt's death his later work on twins was questioned as flawed or fraud.*TIS

**1975 Norman Levinson**(August 11, 1912, Lynn, Massachusetts – October 10, 1975, Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.

He received both his bachelor's degree and his master's degree in electrical engineering from MIT in 1934, where he had studied under Norbert Wiener and took almost all of the graduate-level courses in mathematics. He received the MIT Redfield Proctor Traveling Fellowship to study at the University of Cambridge, with the assurance that MIT would reward him with a PhD upon his return regardless of whatever he produced at Cambridge. Within the first four months in Cambridge, he had already produced two papers. In 1935, MIT awarded him with the PhD in mathematics.

His death in 1975 was caused by a brain tumor.*Wik

**2007 Karl Walter Gruenberg**, (3 June 1928; 10 October 2007) Emeritus Professor of Pure Mathematics of Queen Mary, London University, was a much respected algebraist, being a leading light in the London algebra research community, with many professional contacts across the globe.

For his PhD he worked under Philip Hall, the UK's leading algebraist at the time, submitting a thesis in the theory of groups (a branch of algebra concerned with an abstract study of symmetry). He moved to Queen Mary College, London University, temporarily in 1953 and permanently in 1957. There Kurt Hirsch was slowly building up a world-class algebra research centre and Gruenberg rapidly became a leading member of this group.

Gruenberg remained at Queen Mary all his working life, apart from leaves of absence mostly taken at North American universities. He was made Professor in 1967, and was Head of the Pure Mathematics Department from 1973 until 1978.

After leaving Cambridge he continued his research in abstract group theory into the 1960s, becoming a leading expert at the time on the Engel theory of groups, which is concerned with extracting global information from certain types of local data.

From about 1960 or so, his main research interest moved into homological algebra and its applications, particularly to group theory. In mathematics, frequently unsuspected connections arise between quite separate and apparently unrelated areas. In this work Gruenberg was concerned with applying to group theory techniques originally developed for the "geometry of continuity". In this field he was a major, in many ways the major, pioneer. This work led him over the years towards representation theory, especially integral representation theory, and more latterly number theory. He published many research articles both singularly and jointly.

He was a talented and very successful teacher, especially of graduate students and his many innovative graduate courses were regularly attended by students, visitors and staff from Queen Mary and other London institutions. His books, Linear Geometry (1967, an undergraduate text written with Alan Weir), Cohomological Topics in Group Theory (1970) and Relation Modules of Finite Groups (1976), were all very well received. He continued his research to the end. He published a joint paper with Alfred Weiss in the Journal of Algebra in 2006, was working on further joint work with Weiss in the summer of 2007 both at Queen Mary and at the University of Alberta in Canada. He had been due to address the Queen Mary Pure Mathematics Seminar.* B.A.F. Wehrfritz Obituary in The Independent

Credits

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*SAU=St Andrews Univ. Math History

*TIA= Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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