## Monday, 20 March 2017

### On This Day in Math - March 20

 Newton Statue in Trinity Chapel, Cambridge UK *R.B.

The mathematical education of the young physicist [Albert Einstein] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
~Hermann Minkowski

The 79th day of the year, 78*79 = 6162 (note that the product of consecutive numbers produces a number that is the concatenation of two successive numbers 61 and 62 in ascending order (and 61 is prime).  (Can you find another number, not necessarily prime, so that n(n-1)= a concatenation of consecutive numbers?)

79 = 27 - 72

79 is the smallest number that can not be represented with less than 19 fourth-powers.

79 = 11 + 31 + 37. Curiously, the sum holds for the reversals: 97 = 11 + 13 + 73, and all are primes.

279 is the smallest power of 2 which is greater than Avogadro's number

1079 has been called the "Universe number" because it is considered a reasonable lower limit estimate for the number of atoms in the observable universe.  *Prime Curios

EVENTS

71 A.D.: A hybrid solar eclipse is noted by the scholar Plutarch from Greece where it was total.  *David Dickinson ‏ @Astroguyz

1664 (1665 NS) Robert Hooke becomes the Gresham Professor of Mathematics.  The failure of many of the professors to give their lectures had caused the College to go into decline. Hooke wrote in his diary that he frequently gave no lecture as “no one attended”.  The College is generally in decline for the next 100-200 years.  Hooke held the position until his death in 1703.

1732 Laura Maria Caterina Bassi first (and last for a long while) woman elected to Bologna Academy of Science:

The University of Bologna is the oldest university in Europe and at the beginning of the eighteenth century students were still examined by public disputation, i.e. the candidate was expected to orally defend a series of academic theses. At the beginning of 1732 Bassi took part in a private disputation in her home with members of the university faculty in the presence of many leading members of Bolognese intellectual society. As a result of her performance during this disputation she was elected a member of the prestigious Bologna Academy of Science on 20th March. Rumours of this extraordinary young lady quickly spread and on 17th April she defended forty-nine theses in a highly spectacular public disputation. On 12th May following a public outcry she was awarded a doctorate from the university in a grand ceremony in the city hall of Bologna.  Following a further public disputation the City Senate appointed her professor of philosophy at the university, making her the first ever female professor at a European university.

See more at *Thony Christie, The Renaissance Mathematicus

1774 Ben Franklin to Condorcet on capacity of African American Slaves
*Science and the Founding Fathers, I. Bernard Cohen

In 1800, Alessandro Volta dated a letter announcing his invention of the voltaic pile to Sir Joseph Banks, president of the Royal Society, London. “On the electricity excited by the mere contact of conducting substances of different kinds"” described his results of stacking sandwiches of copper and zinc metal discs between pads of moist material. The letter had to pass from Italy, through France, which was then at war with Britain, so Volta sent the message in two parts. When the first pages arrived, Banks showed them to Anthony Carlisle, a London surgeon, who with William Nicholson immediately began trying to repeat Volta's experiments. By 2 May 1800, they stumbled upon electrolysis of water.*TIS
It was an article by Nicholson about the way the Torpedo fish produced it's electric shock that had inspired Volta's latest experiments.  He had been sparring with Galvani about the possibility of mechanical energy for years. In the same letter mentioned above, he credits Nicholson, "The hypothesis of this learned and laborious philosopher …. is indeed very ingenious."
His image, and of the battery named for him, appear on the 10,000 Lira note before Italy converted to the Euro.

1816 John Dalton makes the last entry in his first meteorological notebook. Dalton came to his views on atomism through his interest in meteoroligy.  The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816.  He would begin a second volume the next day.

1916 Albert Einstein submitted his general theory of relativity to Annalen der Physik. *A. Hellemans and B. Bunch, The Timetables of Science
Einstein's Theory of General Relativity was titled “Die Grundlagen der allgemeinen Relativitästheorie.” This theory accounted for the slow rotation of the elliptical path of the planet Mercury, which Newtonian gravitational theory failed to do. Fame and recognition came suddenly in 1919, when the Royal Society of London photographed the solar eclipse and publicly verified Einstein's general theory of relativity. In 1921 he was awarded the Nobel Prize for Physics for his photoelectric law and work in the field of theoretical physics, but such was the controversy still aroused by this theories on relativity that these were not specified in the text of the award. *TIS

1997 Cellular Phone Encryption Is "Cracked," Highlighting Privacy Concerns:
Computer security experts announce that they have cracked the code designed to protect the privacy of calls made with digital cellular phones. The breakthrough showed that cellular phone transmissions remained insecure despite recent developments. The National Security Agency, however, cautioned against more advanced encryption that might allow terrorists to conspire by telephone.*chm

2016 Spring officially comes to Possum Trot, Ky. The equinox passed last night in the dark, daffodils are blooming and dogwoods are budding nicely. The word equinox is derived from the Latin words meaning “equal night.” The spring and fall equinoxes are the only dates with equal daylight and dark as the Sun crosses the celestial equator. At the equinoxes, the tilt of Earth relative to the Sun is zero, which means that Earth’s axis neither points toward nor away from the Sun. *Farmer's Almanac

2017 On this day the public schools of the city of Boston, Mass briefly put spherical and projective geometry in the news. On that date the schools began converting their classroom maps from the common Mercator Projection, to the little known Gall-Peters Projection. The Mercator projection makes some areas, Greenland and Alaska, for example, look much larger than other similar sized areas by comparison. The Gall–Peters projectionmaps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes.

BIRTHS

1546  Baha ad-din Muhammad ibn Husayn al-Amili (20 Mar 1546; 20 Aug 1622 at age 76)
Syrian-Iranian theologian, mathematician and astronomer, a.k.a. Shaykh Baha'i). He became a very learned Muslim whose genius touched every field of knowledge from mathematics and philosophy to architecture and landscape design. He revived the study of mathematics in Iran. His treatise on the subject, Khulasat al-hisab (“The Essentials of Arithmetic”), and translations from the original Arabic was in use as a textbook until the end of the 19th century. His treatise in astronomy, Tashrihu'l-aflak ("Anatomy of the Heavens") summarised the works of earlier masters. He was born within a year of William Gilbert in England and Tycho Brahe in Denmark, and was still a child when his family left Syria to escape religious persecution.*TIS

1664 Johann Baptist Homann (20 March 1664 – 1 July 1724) was a German geographer and cartographer, who made maps of the Americas.
Homann was born in Oberkammlach near Kammlach in the Electorate of Bavaria.
Homann acquired renown as a leading German cartographer, and in 1715 was appointed Imperial Geographer by Emperor Charles VI. Giving such privileges to individuals was an added right that the Holy Roman Emperor enjoyed. In the same year he was also named a member of the Prussian Academy of Sciences in Berlin. Of particular significance to cartography were the imperial printing privileges (Latin: privilegia impressoria). These protected for a time the authors in all scientific fields such as printers, copper engravers, map makers and publishers. They were also very important as recommendation for potential customers.
In 1716 Homann published his masterpiece Grosser Atlas ueber die ganze Welt (Grand Atlas of all the World). Numerous maps were drawn up in cooperation with the engraver Christoph Weigel the Elder, who also published Siebmachers Wappenbuch.
Homann died in Nuremberg. He was succeeded by the Homann heirs company, in business until 1848. *Wik A beautiful pocket globe he created can be seen at the Vault, Slate's History blog.

1840 Franz Carl Joseph Mertens (20 March 1840 in Schroda, Posen, Prussia (now Środa Wielkopolska, Poland) - 5 March 1927 in Vienna, Austria) Mertens worked on a number of different topics including potential theory, geometrical applications to determinants, algebra and analytic number theory, publishing 126 papers. Bruce C Berndt writes, "Mertens is perhaps best known for his determination of the sign of Gauss sums, his work on the irreducibility of the cyclotomic equation, and the hypothesis which bears his name. "
Many people are aware of Mertens contributions since his elementary proof of the Dirichlet theorem appears in most modern textbooks. However he made many deep contributions including Mertens' theorems, three results in number theory related to the density of the primes. He proved these results using Chebyshev's theorem, a weak version of the prime number theorem. *SAU
In his youth, Mertens moved to Berlin where he became a student at Berlin
University, and where he studied under Kronecker and Kummer.  Mertens first worked in Krakow, and then moved to Austria. Ernst Fischer and Schrodinger, for instance, were students of Mertens at the University of Vienna. *Julio Gonzalez Cabillon, Historia Matematica Discussions

1856 Frederick Winslow Taylor (20 Mar 1856, 21 Mar 1915 at age 58)  was an American engineer and inventor who is known as the father of scientific management. His system of industrial management has influenced the development of virtually every country enjoying the benefits of modern industry. He introduced a scientific approach (1881) to “time and motion study” while chief engineer at Midvale Steel Company, Philadelphia, Pa. Taylor and his associates used stop-watches to time the laborers as they performed various tasks, counted the number of shovel-loads they each moved, and the load per shovel. Thus he was able to determine an optimum shovel size and length. Such careful observations, aimed at recognizing wasted effort and minimizing time used, increased the efficiency of actions of factory workers.*TIS
The term "scientific management" was coined by US Supreme Court justice Louis Brandeis to describe Taylor's principles, and in 1911, Taylor published his life's work in the book The Principles of Scientific Management. Taylor was an accomplished tennis and golf player. He and Clarence Clark won the inaugural United States National tennis doubles championship at Newport Casino in 1881 Taylor was a lifelong member of the Philadelphia Country Club, and finished fourth in the 1900 Olympic individual golf event. *Wik *Sports Reference

1884  Philipp Frank (20 Mar 1884; 22 Jul 1966 at age 82)  Austrian-American physicist and mathematician whose theoretical work covered a broad range of mathematics, including variational calculus, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Frank had a deep and lasting interest in the philosophy of science. In a number of writings, he strove to reconcile science and philosophy and “bring about the closest rapprochement between” them. The 1907 paper he wrote analyzing the law of causality caught Einstein's attention, who in 1912 recommended Frank as his successor as professor of theoretical physics at the German University of Prague. He held that position until 1938, when he moved to Harvard University in the U.S., first as visiting lecturer, but remaining there until retirement in 1954. He wrote on misinterpretations of the Theory of Relativity.*TIS

1920 Douglas George Chapman (20 Mar 1920; 9 Jul 1996 at age 76) was a Canadian-born U.S. mathematical statistician  and an expert on wildlife statistics. He was one of the scientific advisors to the International Whaling Commission that warned in the 1960s that the number of whales being taken by the whaling industry was far in excess of what the population could stand, and proposed annual fin whale catch quotas that would permit the depleted populations of this species to recover. His later research on fish farming expanded to include mollusk aquaculture and he directed a program to develop quantitative methods to aid in the management of fisheries resources.*TIS

1938  Sergi Petrovich Novikov (20 Mar 1938,   ) Russian mathematician who was awarded the Fields Medal in 1970 for his work in algebraic topology. His parents were both mathematicians, and Novikov showed his own talent while a youth. In 1960, the year he obtained his first degree, he published a paper on some problems in the topology of manifolds connected with the theory of Thom spaces. In 1965, he proved his famous theorem on the invariance of Pontryagin classes. He was unable receive the Fields Medal in person because Soviet authorities would not permit his travel. Thereafter he pursued an interest in mathematical physics, including the theory of solitons, quantum field theory and string theory. *Tis

DEATHS

 Rubens illustration of projection
1617 François d'Aguilon (also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a Belgian Jesuit mathematician, physicist and architect.
D'Aguilon was born in Brussels. He became a Jesuit in 1586. In 1611, he started a special school of mathematics, in Antwerp, which was intended to perpetuate mathematical research and study in among the Jesuits. This school produced geometers like André Tacquet and Jean Charles della Faille.
His book, Opticorum Libri Sex philosophis juxta ac mathematicis utiles (Six Books of Optics, useful for philosophers and mathematicians alike), published in Antwerp in 1613, was illustrated by famous painter Peter Paul Rubens. It was notable for containing the principles of the stereographic and the orthographic projections, and it inspired the works of Desargues and Christiaan Huygens. *Wik

1726/7 Isaac Newton  (25 December 1642 – 20 March 1726 [NS: 4 January 1643 – 31 March 1727)  English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colors. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS
Newton died intestate. Immediately his relatives began to quarrel over the division of his estate, which amounted to a considerable fortune. Thomas Pellet examined Newton’s manuscript holdings in hopes of turning a quick proﬁt. His “thick clumsy annotations ‘Not ﬁt to be printed,’ now seem at once pitiful and ludicrous.” See Whiteside, Newton Works, I, xvii ﬀ for details. *VFR

1878 (Julius) Robert Mayer (25 Nov 1814; 20 Mar 1878) a German physicist. While a ship's doctor sailing to Java, he considered the physics of animal heat. In 1842, he measured the mechanical equivalent of heat. His experiment compared the work done by a horse powering a mechanism which stirred paper pulp in a caldron with the temperature rise in the pulp. He held that solar energy was the ultimate source of all energy on earth, both living and nonliving. Mayer had the idea of the conservation of energy before either Joule or Helmholtz. The prominence of these two scientists, however, diminished credit for Mayer's earlier insights. James Joule presented his own value for the mechanical equivalent of heat. Helmhotlz more systematically presented the law of conservation of energy. *TIS

1895 Ludwig Schläfli (15 Jan 1814 in Grasswil, Bern, Switzerland - 20 March 1895 in Berne, Switzerland) Schläfli is best known for the so-called Schläfli symbols which are used to classify polyhedra. In this work, Theorie der vielfachen Kontinuität (Theory of continuous manifolds), Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra. Schläfli introduced what is today aclled the Schläfli symbol. It is defined inductively. {n} is a regular n-gon, so {4} is a square. There {4, 3} is the cube, since it is a regular polyhedron with 3 squares {4} meeting at each vertex. Then the 4 dimensional hypercube is denoted as {4, 3, 3}, having three cubes {4, 3} meeting at each vertex. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions {3, 3, 3}, {4, 3, 3}, {3, 3, 4}, {3, 4, 3}, {5, 3, 3}, and {3, 3, 5}, but only three in dimension n where n ≥ 5, namely {3, 3, ..., 3}, {4, 3, 3, ....,3}, and {3, 3, ...,3, 4}.
Most of Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. His eight papers on Bessel functions played an important role in the preparation of G N Watson's major text Treatise on the theory of Bessel functions (1944). *SAU

1993  Polykarp Kusch (26 Jan 1911; 20 Mar 1993) German-American physicist who shared the Nobel Prize for Physics in 1955 for his accurate determination that the magnetic moment of the electron is greater than its theoretical value. This he deduced from researching the hyperfine structure of the energy levels in certain elements, and in 1947 found a discrepancy of about 0.1% between the observed value and that predicted by theory. Although minute, this anomaly was of great significance and led to revised theories about the interactions of electrons with electromagnetic radiation, now known as quantum electrodynamics. (He shared the prize with Willis E. Lamb, Jr. who performed independent but related experiments at Columbia University on the hyperfine structure of the hydrogen atom.)*TIS

1962 Andrew Ellicott Douglass (5 Jul 1867, 20 Mar 1962 at age 94) American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS

1983  Ivan Matveyevich Vinogradov (2 Sep 1891, 20 Mar 1983 at age 91) Soviet mathematician known for his contributions to the analytical theory of numbers, including a partial solution of the Goldbach conjecture proving that every sufficiently large odd integer can be expressed as the sum of three odd primes. He described his methods in his most celebrated piece of work Some Theorems Concerning the Theory of Prime Numbers (1937).*TIS

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