Thursday 7 May 2020

On This Day in Math - May 7

Scientists study the world as it is,
engineers create the world that never has been
~Theodore Von Karman

The 128th day of the year; 128 is The largest known even number that can be expressed as the sum of two primes in exactly three ways. (Find them) *Prime Curios   How many smaller numbers (and which) are there that can be so expressed?

128 is also the largest number that cannot be expressed as the sum of distinct squares. *Number Gossip. (Surprisingly, there are only 31 numbers that can not be expressed as the sum of distinct squares. )

128 can be expressed by a combination of its digits with mathematical operators thus 128 = 28 - 1, making it a Friedman number in base 10 (Friedman numbers are named after Erich Friedman, as of 2013 an Associate Professor of Mathematics and ex-chairman of the Mathematics and Computer Science Department at Stetson University, located in DeLand, Florida.)

128 the sum of the factorials of the first three prime numbers, 2! + 3! + 5! =128.


1526 The first circumnavigation of the globe took place in 1519. In 1539 Cardano asked for the number of days spent if a ship sailed westward on January 1, 1517, and went three times around the earth, returning on May 7, 1526. See Sanford, History, pp. 214 and 377. *VFR

1660 Isaack B Fubine of Savoy, in The Hague, patents macaroni *TIS (as soon as someone invents cheese, the fun eating will begin)

1747 Johann Sebastian Bach visits King Frederick II of Prussia, the visit resulting in his Musikalische Opfer (Musical offering). See D. R. Hofstadter’s Godel, Escher, Bach, p. 4. [Manson]*VFR

1772 Read before the Royal Society, May 7, The Sieve of Eratosthenes. Being an Account of His Method of Finding All the Prime Numbers, by the Rev. Samuel Horsley, F. R. S.

1895 Steiger Gets "Millionaire" Patent:
Otto Steiger was issued a patent for his Millionaire calculating machine. For the next 40 years, Switzerland's Hans Egli manufactured 4,700 machines, which weighed 120 pounds each. The Millionaire was notable in its ability to perform direct multiplication, which meant a user could multiply a number by a single digit with a single rotation of the handle.*CHM

In his German Patent of 1892 Steiger describes a machine which uses a mechanical representation of the multiplication table to form partial products, in the same way that a human "calculator" uses a
multiplication table committed to memory. The partial products are then transferred via a "transmitting mechanism" to a "combining and registering mechanism" for display to the operator. The Steiger's machine is to be regarded as a proper multiplication machine in that it solves problems of multiplication directly on the basis of the multiplication table, whereas other types of calculating machines are only adding machines and, as such, carry out multiplication by a continued series of additions. *Georgi Dalakov, History of Computers

In 1952, the concept of the integrated circuit chip was first presented, at a Symposium on Progress in Quality Electronic Components in Washington DC., by radar scientist Geoffrey W.A. Dummer. His small team of researchers at the Royal Radar Establishment of the British Ministry of Defence, based at Malvern, Worcestershire, was working on the task of improving the reliability of the Royal Air Force's radar equipment.. He believed that it would be possible to fabricate multiple circuit elements on and into a block of silicon half an inch square. In 1956, his initial attempts to build such a circuit failed, and thereafter could get no further support for his idea. Britain lost the commercial lead. A few years later, in America, Jack Kilby of Texas Instruments was awarded a U.S. patent for essentially the same idea.*TIS


Alexis Clairaut (sometimes Clairault) (7 May 1713; 17 May 1765 at age 51) was a French mathematician who worked to confirm the Newton-Huygens belief that the Earth was flattened at the poles. He was a child prodigy was studying calculus at age 10 and was admitted to the Academy of Sciences at age 18. He was the first person to estimate the mass of Venus to a close value. He also calculated the return date of Halley's comet. In about 1737, Pierre de Maupertuis led an expedition (including Clairaut) to measure a degree along a meridian in Lapland, while Bouguer and La Condamine went to Peru.  The results, even before the Peru expedition had returned, showed that Newton was correct in predicting that the earth was flattened at the poles .(various) A nice brief summary of Clairaut's life and works is here.

1774 Sir Francis Beaufort (7 May 1774; 17 Dec 1857 at age 83)British naval officer, who devised (1805) a scale of wind force from 0 (calm) to 12 (hurricane) which was based on observation and so required no special instruments. [Chase]*VFR The initial scale of thirteen classes (zero to twelve) did not reference wind speed numbers but related qualitative wind conditions to effects on the sails of a man-of-war, then the main ship of the Royal Navy, from "just sufficient to give steerage" to "that which no canvas sails could withstand".
Although he devised the scale in 1805, it would not be adopted by the Royal Navy until 1830 when was an administrator. The first official use of the scale in a ships log was on December 22, 1831 by Robert Fitzroy on the first day of Darwin's voyage on the Beagle.
In 1829 Beaufort became the British Admiralty Hydrographer of the Navy. He remained at the post for 25 years. Beaufort converted what had been a minor chart repository into the finest surveying and charting institution in the world. Some of the excellent charts the Office produced are still in use today.

During his tenure, he took over the administration of the great astronomical observatories at Greenwich, England, and the Cape of Good Hope, Africa. Beaufort directed some of the major maritime explorations and experiments of that period. For eight years, Beaufort directed the Arctic Council during its search for the explorer, Sir John Franklin, lost in his last polar voyage to search for the legendary Northwest Passage. *Wik

1832 Carl Gottfried Neumann (May 7, 1832 - March 27, 1925) He worked on a wide range of topics in applied mathematics such as mathematical physics, potential theory and electrodynamics. He also made important pure mathematical contributions. He studied the order of connectivity of Riemann surfaces.
During the 1860s Neumann wrote papers on the Dirichlet principle and the 'logarithmic potential', a term he coined. In 1890 Émile Picard used Neumann's results to develop his method of successive approximation which he used to give existence proofs for the solutions of partial differential equations.*SAU

1854 Giuseppe Veronese (7 May 1854 – 17 July 1917) invented non-Archimedean geometries which he proposed around 1890. However Peano strongly criticised the notion due to the lack of rigor of Veronese's description and also for the fact that he did not justify his use of infinitesimal and infinite segments. The resulting argument was extremely useful to mathematics since it helped to clarify the notion of the continuum. Any fears that non-Archimedean systems would not be consistent were shown to unnecessary soon after this when Hilbert proved that indeed they were consistent.*SAU

1880 Oskar Perron(7 May 1880 – 22 February 1975) was a German mathematician best known for the Perron paradox:
Suppose the largest natural number is N. Then if N is greater than 1 we have N2 greater than  N contradicting the definition.  *SAU

1911 Raymond Arthur Lyttleton (7 May 1911; 16 May 1995 at age 83) English mathematician and theoretical astronomer who researched stellar evolution and composition. In 1939, with Fred Hoyle, he demonstrated the large scale existence of interstellar hydrogen, refuting the existing belief of that space was devoid of interstellar gas. Together, in the early 1940's, they applied nuclear physics to explain how energy is generated by stars. In his own mongraph (1953) Lyttleton described stability of rotating liquid masses, which he extended later to explain that the Earth had a liquid core resulting from a phase change associated with a combination of intense pressure and temperature. With Hermann Bondi, in 1959, he proposed the electrostatic theory of the expanding universe. He authored various astronomy books.*TIS

1927 Allen Shields (7 May 1927 New York – 16 September 1989 Ann Arbor, Michigan, USA) worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory.*Wik


1617 David Fabricius, (March 9, 1564 – May 7, 1617)a Protestant minister, was killed by a parishioner angered upon being accused by him as a thief.   A German astronomer, friend of Tycho Brahe and Kepler, and one of the first to follow Galileo in telescope observation of the skies. He is best known for a naked-eye observation of a star in Aug 1596, subsequently named Omicron Ceti, the first variable star to be discovered, and now known as Mira. Its existence with variable brightness contradicted the Aristotelian dogma that the heavens were both perfect and constant. With his son, Johannes Fabricius, he observed the sun and noted sunspots. For further observations they invented the use of a camera obscura and recorded sun-spot motion indicating the rotation of the Sun. *TIS  [re: invented, The Camera Obscura (Latin for dark room) was a dark box or room with a hole in one end. If the hole was small enough, an inverted image would be seen on the opposite wall. Such a principle was known by thinkers as early as Aristotle (c. 300 BC). It is said that Roger Bacon invented the camera obscura just before the year 1300, but this has never been accepted by scholars; more plausible is the claim that he used one to observe solar eclipses. In fact, the Arabian scholar Hassan ibn Hassan (also known as Ibn al Haitam), in the 10th century, described what can be called a camera obscura in his writings..]

1934 Karl Friedrich Geiser (26 Feb 1843 in Langenthal, Bern, Switzerland, 7 May 1934 in Küsnacht, Zürich, Switzerland) Swiss mathematician who worked in algebraic geometry and minimal sufaces. He organised the first International Mathematical Congress in Zurich.*SAU

1963  Theodore von Karman (May 11, 1881 – May 7, 1963)Hungarian-American aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization.*Wikipedia [another who died very close to his birthday (May 11), someday I must do statistics on this.]  He was director of the Institute for Aerodynamics at the Rheinisch-Westfälische Technische Hochschule (RWTH) in AACHEN, Nordrhein-Westfalen, in 1913-1934. The main lecture theatre complex is named the Kármán Auditorium and there is a photo and a bust of him in the foyer.  He is buried in a vault in the Hollywood Forever Cemetery in Los Angeles, Ca. USA

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*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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