Tuesday 5 March 2024

On This Day in Math - March 5


Terrestrial globe by Mercator dating from 1541. It is now in the museum collection of the Palazzo Ducale in Urbania, Italy, and is one of about 22 existing Mercator globes.*Wik

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.
~Julian Lowell Coolidge

The 64th day of the year; 64 is the smallest power of two with no prime neighbor. (What is next value of 2n with no prime neighbor?)  Also the smallest even square number without a prime neighbor.

64 is also the smallest non-trivial positive integer that is both a perfect square and a perfect cube.

64 can be expressed as the sum of primes using the first four natural numbers once each, 41 + 23 = 64,  It can also be done with its reversal, 46 = 41 + 3 + 2.

There were 64 disks in Eduard Lucas' myth about the Towers of Hanoi.

 64 is also the number of hexagrams in the I Ching, and the number of sexual positions in the Kama Sutra. (I draw no conclusions about that information)

There are 64 ordered permutations of nonempty subsets of {1,..., 4}: Eighteenth-  and nineteenth-century combinatorialists call this the number of  (nonnull) "variations" of 4 distinct objects.

64 is a superperfect number—a number such that σ(σ(n)) = 2n. The sum of the divisors (including itself) of 64 is 127, and the sum of the divisors of 127, 1 and 127, add up to 128= 2*64. It is the last Year Day that is Super-Perfect.

And I was told that 64 is the maximum number of strokes used in a Kanji character.

Most mathematicians know the story of 1729, the taxicab number which Ramanujan recognized as a cube that was one more than the sum of two cubes, or the smallest number that could be expressed as the sum of two cubes in two different ways.  But not many know that 94 is part of the second such   \(64^3 + 94^3 = 103^3 + 1^3  \)   


In 1223 BC, the oldest recorded eclipse occurred, according to one plausible interpretation of a date inscribed on a clay tablet retrieved from the ancient city of Ugarit, Syria (as it is now). This date is favored by recent authors on the subject, although alternatively 3 May 1375 BC has also been proposed as plausible. Certainly by the 8th century BC, the Babylonians were keeping a systematic record of solar eclipses, and possibly by this time they may have been able to apply numerological rules to make fairly accurate predictions of the occurrence of solar eclipses. The first total solar eclipse reliably recorded by the Chinese occurred on 4 Jun 180 BC*TIS

 The Ugarit eclipse darkened the sky for 2 minutes and 7 seconds on May 3, 1375 B.C., according to an analysis of a clay tablet, discovered in 1948. Then, a report in the journal Nature in 1989 suggested, in fact, the eclipse actually occurred on March 5, 1223 B.C. That new date was based on an historical dating of the tablet as well as an analysis of the tablet’s text, which mentions the visibility of the planet Mars during the eclipse.

The Ugaritic texts are a corpus of ancient cuneiform texts discovered since 1928 in Ugarit (Ras Shamra) and Ras Ibn Hani in Syria, and written in Ugaritic, an otherwise unknown Northwest Semitic language. Approximately 1,500 texts and fragments have been found to date. The texts were written in the 13th and 12th centuries BC.

A tablet in the collection.

In 1590, Tycho Brahe discovered a comet in the constellation Pisces.*TIS    Prior to his death in 1601, he was assisted for a year by Johannes Kepler, who went on to use Tycho's data to develop his own three laws of planetary motion.

In 1616, Copernican theory was declared "false and erroneous" in a decree delivered by Cardinal Robert Bellarmine, and issued by the Catholic Church in Rome. Further, no person was to be permitted to hold or teach the theory that the earth revolves around the sun. When Galileo subsequently violated the decree, he was put on trial and held under house arrest for the final eight years of his life. *TIS Copernican theory was declared "false and erroneous" by the 11 theologians, appointed by the Pope to examine it, on 24 February 1616. Bellarmine, who was not one of these 11, was ordered by the Pope to convey this decision to Galileo, which he did verbally on 26 February 1616. The Decree of the Index was issued on 5 March 1616 in which "…the books by Nicolaus Copernicus and Diego Zúñiga be suspended until corrected…" This decree was signed by the Most Illustrious and Reverend Lord Cardinal of St. Cecilia, Bishop of Albano P. (Paolo Sfondrati) and Fra Francisco Magdelenus Capiferreus, O.P., Secretary. *Thony Christie, My thanks to Thony for the correction More detail about this event can be found on the Feb 26 Post about Galileo

Original 1543 Nuremberg edition of De revolutionibus orbium coelestium (English translation: On the Revolutions of the Heavenly Spheres)

1639 Debeaune to Mersenne: “I do not think that one could acquire any solid knowledge of nature in physics without geometry, and the best of geometry consists of analysis, of such kind that without the latter it is quite imperfect.” *VFR

1673 Hooke presents Arithmetic Engine to Royal Society. After a presentation of a calculating machine by Leibniz on January 22, (after which Leibniz complained to Oldgenburg that Hooke's examination of the machine had shown "almost indecent interest") Hooke became interested in creating a better machine and announced such intention to the Royal Society. Working with Richard Shortgrave, Harry Hunt and John Pell he produced a machine which would multiply to twenty places over the next six weeks. His diary entry seemed to indicate the demonstration went well, but within a few days he seemed to have dismissed such machines entirely. *Stephen Inwood, Forgotten Genius
Image of Leibniz calculator: 

1684 Halley's father mysteriously went missing and five weeks later was found murdered on the banks of the Medway. *Kate Morant, halleyslog.wordpress.com

On March 5, 1750, Euler read his own Recherches sur la Précession at the Berlin Academy. Two days later he wrote d'Alembert giving an extended account of his struggle to derive the precession and giving d'Alembert credit for re-inspiring his efforts to solve it. * Curtis Wilson, Historia Mathematica, Volume 35, Issue 4, November 2008, Pages 329–332


1831 Birth of "The Average Man". Adolphe Quetelet read a memoir to the Brussels Academy Royal. The newborn l'homme moyen would not be officially named by Quetelet until July. *Statistics on the Table: The History of Statistical Concepts and Methods By Stephen M. Stigler  

image: First edition of Quetelet's principal work in which he presented his conception of the homme moyen (“average man”) as the central value about which measurements of a human trait are grouped according to the normal distribution. Sur l’Homme et le Développement de ses Facultés, ou Essai de Physique Sociale. Lambert Adolphe Jacques Quetelet.

On this day in 1835 a ceremony to honor The Genius and Discoveries of Sir Isaac Newton was organized by the citizens of the Lincolnshire, his area of birth, a few years after the centennial of his death. By unanimous choice, the committee selected as the speaker, the 19 year-old George Boole.

All present were struck by the youthful age of the speaker and not a little amazed by both his knowledge of the subject and his confident lecturing style.  *SAU

1876 Sylvester, at age 61, appointed professor of mathematics at Johns Hopkins University. This was the real beginning of graduate mathematics education in the United States. *VFR

1960 Gao–Guenie (H5 ordinary chondrite) meteorites fell in Burkina Faso on March 5, 1960 at 17:00 (local time). After three separate detonations, several thousands of stones rained down over an area of about 70 square kilometres (27 sq mi). The sound of the fall was heard as far as Ouagadougou, which is 100 kilometers (62 mi) away. Eyewitnesses said that some trees were broken and henhouses destroyed. The largest stones recovered weigh up to 10 kilograms (22 lb)*Wik 

1963 On this day in 1963, the Hula-Hoop, a hip-swiveling toy that became a huge fad across America when it was first marketed by Wham-O in 1958, is patented by the company’s co-founder, Arthur “Spud” Melin. An estimated 25 million Hula-Hoops were sold in its first four months of production alone. *http://www.history.com

1981  Today in 1981  the ZX81, a pioneering British home computer, is launched by Sinclair Research and would go on to sell over 1 1⁄2 million units around the world.  The ZX81 is a home computer that was produced by Sinclair Research and manufactured in Dundee, Scotland, by Timex Corporation. It was launched in the United Kingdom in March 1981 as the successor to Sinclair's ZX80 and designed to be a low-cost introduction to home computing for the general public. It was hugely successful; more than 1.5 million units were sold. In the United States it was initially sold as the ZX-81 under licence by Timex. It had a smashing 1Kb of Ram.  

1993 Talking Laptop Helps Blind Student Earn B.S.:
In an early demonstration of the impact computers could have on people's lives, the Los Angeles Times reports that a blind student was taking advantage of a talking laptop computer to help him complete courses necessary to graduate from UCLA. After 15 years of going to college on and off, the computer provided Robert Antunez the independence and aid he needed to complete a bachelor's degree in political science. *CHM

1995 The Yahoo! search engine officially launches on the Internet. 13 months later, Yahoo! will hold its IPO at a price of $13 per share. Yahoo!’s stock will peak at $475 in January 2000, and fall to $8.02 in September 2001.



1512 Gerardus Mercator (5 Mar 1512- 2 Dec 1594) Flemish cartographer whose most important innovation was a map, embodying what was later known as the Mercator projection, on which parallels and meridians are rendered as straight lines spaced so as to produce at any point an accurate ratio of latitude to longitude. He also introduced the term atlas for a collection of maps. *TIS A nice blog about the Mercator projection, which he suggests should be called the Mercator Wright projection is at the Renaissance Mathematicus blogsite.
For those interested in a quick look at the math involved in the Mercator-Wright projection, this Endeavour blog by John D. Cook may help.

Mercator 1569 world map (Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata) showing latitudes 66°S to 80°N

1575 William Oughtred (5 Mar 1575; 30 Jun 1660 at age 85) English mathematician and Episcopal minister who invented the earliest form of the slide rule, two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner rule with tongue-in-groove linear construction came later. He also introduced the familiar multiplication sign x in a 1631 textbook, along with the first use of the abbreviations sin, cos and tan.*Tis There is an Oughtred Society dedicated to the history and preservation of slide rules.

William Oughtred's most important work was first published in 1631, in Latin, under the title Arithemeticæ in Numeris et Speciebus Institutio, quae tum Logisticæ, tum Analyticæ, atque adeus totius Mathematicæ quasi Clavis est (i.e. "The Foundation of Arithmetic in Numbers and Kinds, which is as it were the Key of the Logistic, then of the Analytic, and so of the whole Mathematic(s)"). It was dedicated to William Howard, son of Oughtred's patron Thomas Howard, 14th Earl of Arundel.

This is a textbook on elementary algebra. It begins with a discussion of the Hindu-Arabic notation of decimal fractions and later introduces multiplication and division sign abbreviations of decimal fractions. Oughtred also discussed two ways to perform long division and introduced the "~" symbol, in terms of mathematics, expressing the difference between two variables. Clavis Mathematicae became a classic, reprinted in several editions. It was used as a textbook by John Wallis and Isaac Newton among others. A concise work, it argued for a less verbose style in mathematics, and greater dependence on symbols. 

The first edition of John Wallis's foundational text on infinitesimal calculus, Arithmetica Infinitorum (1656), carries a long letter of dedication to William Oughtred.

1624/25 John Collins (5 March 1624 in Wood Eaton (4km north of Oxford), England - 10 Nov 1683 in London, England) was an accountant and publisher who corresponded extensively with the mathematicians of his day. Collins's importance is, as Barrow said, being "the English Mersenne" . He corresponded with Barrow, David Gregory, James Gregory, Newton, Wallis, Borelli, Huygens, Leibniz, Tschirnhaus and Sluze.
Collins published books by Barrow and Wallis and left a collection of 2000 books and an uncounted number of manuscripts.
He did publish works of his own, however. For instance he published works on sundials, trigonometry for navigation and the use of the quadrant. He had a paper on cartography published and also wrote on accounting, compound interest and annuities. His major works were An introduction to merchant's accounts (1652), The sector on a quadrant (1658), Geometrical dialling (1659), The mariner's plain scale new plained (1659) and, in 1664, he published Doctrine of Decimal Arithmetick. *SAU

About twenty-five years after Collins's death his books and papers came into the possession of William Jones, F.R.S. They included a voluminous correspondence with Newton, Leibniz, Gregory, Barrow, John Flamsteed, Wallis, Slusius, and others. From it was selected and published in 1712, by order of the Royal Society, the Commercium Epistolicum, of material relevant to Newton's priority over Leibniz in the discovery of the infinitesimal calculus; specimens of results from the use of the fluxional method were transmitted 20 July 1669 through Barrow to Collins, and by him made widely known. *Wik

1779 Benjamin Gompertz (March 5, 1779 – July 14, 1865), was a self educated mathematician, denied admission to university because he was Jewish.  Nevertheless he was made Fellow of the Royal Society in 1819. Gompertz is today mostly known for his Gompertz law (of mortality), a demographic model published in 1825. The model can be written in this way:

N(t) = N(0) e-c (e{at}-1),

where N(t) represents the number of individuals at time t, and c and a are constants.

This model is a refinement of the demographic model of Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.

1794 Jacques Babinet (5 March 1794 – 21 October 1872) was a French physicist, mathematician, and astronomer who is best known for his contributions to optics. A graduate of the École Polytechnique, which he left in 1812 for the Military School at Metz, he was later a professor at the Sorbonne and at the Collège de France. In 1840, he was elected as a member of the Académie Royale des Sciences. He was also an astronomer of the Bureau des Longitudes.
Among Babinet's accomplishments are the 1827 standardization of the Ångström unit for measuring light using the red Cadmium line's wavelength, and the principle (Babinet's principle) that similar diffraction patterns are produced by two complementary screens. He was the first to suggest using wavelengths of light to standardize measurements. His idea was first used between 1960 and 1983, when a meter was defined as a wavelength of light from krypton gas.
In addition to his brilliant lectures on meteorology and optics research, Babinet was also a great promoter of science, an amusing and clever lecturer, and a brilliant, entertaining and prolific author of popular scientific articles. Unlike the majority of his contemporaries, Babinet was beloved by many for his kindly and charitable nature. He is known for the invention of polariscope and an optical goniometer. *Wik

The polariscope is an optical inspection device used to detect internal stresses in glass and other transparent materials such as plastics.   A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (gōnía) 'angle' and μέτρον (métron) 'measure'. The protractor is a commonly used type in the fields of mechanics, engineering, and geometry.

The first known description of a goniometer, based on the astrolabe, was by Gemma Frisius in 1538.

1815 Angelo Genocchi (5 March 1817 – 7 March 1889) was an Italian mathematician who specialized in number theory. He worked with Giuseppe Peano. The Genocchi numbers are named after him. G(t)= 2t/(et+1)for integer values of t. The first few are 1, −1, 0, 1, 0, −3, 0, 17...(A001469 in OEIS)
Genocchi was President of the Academy of Sciences of Turin.*Wik  The unsigned coefficients of Genocchi numbers give expansion of x*tan(x/2). *PB

1943 Elizabeth Ruth Naomi Belville (5 March 1854 – 7 December 1943), also known as the Greenwich Time Lady, was a businesswoman from London. She, her mother Maria Elizabeth, and her father John Henry, sold people the time. This was done by setting a watch to Greenwich Mean Time, as shown by the Greenwich clock, and then selling people the time by letting them look at the watch. *Wik A nice blog about time, and the time lady by Greg Ross at Futility Closet. and a book by David Rooney.

Ruth Belville, the "Time Lady," died Dec. 7, 1943, at the age of 89. For almost 50 years, Ruth sold the time to a select clientele in London. She would travel to Greenwich Observatory every Tuesday, where she would synchronize the family chronometer, a large pocket watch, to the master clock at Greenwich. Then she would take the train to London, dropping in one by one on her subscribers, who for various reasons needed to know the exact time, so they could set their timepieces from hers. She inherited this odd profession, and the chronometer, from her father, John Henry, who began distributing time in 1836, and then her mother Maria, who continued the practice after her father's death, until she retired in 1892 and Ruth took over.

When the time-sharing business began in 1836, the only way to know the exact time, unless you were inside the Observatory looking at the master clock, was to wait for the time ball to drop to the Observatory roof at exactly 1:00 PM each day. That was fine if you were on a ship on the Thames, but hardly of use to a watchmaker in London. John Henry, who was in charge of the time ball, was instructed by the Astronomer Royal to carry the exact time to London once or twice a week, so that London clockmakers and railroad managers could ensure that their timepieces were accurate. It is usually said that John Henry carried the time himself, but that is hardly likely, as he was one of the busiest employees at the Observatory, so he probably just set the watch and had a carrier take it to London.

Linda Hall Org

1880 Sergei Natanovich Bernstein (March 5, 1880 – October 26, 1968) was a Russian and Soviet mathematician. His doctoral dissertation, submitted in 1904 to the Sorbonne, solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations. Later, he published numerous works on Probability theory, Constructive function theory, and mathematical foundations of genetics. From 1906 until 1933, Bernstein was a member of the Kharkov Mathematical Society. *Wik

He interrupted his studies in France to spend three terms at the University of Göttingen, beginning in the autumn of 1902, where his studies were supervised by David Hilbert.

Hilbert stated his nineteenth problem as a regularity problem for a class of elliptic partial differential equation with analytic coefficients. Therefore the first efforts of researchers who sought to solve it were aimed at studying the regularity of classical solutions for equations belonging to this class. For C 3  solutions, Hilbert's problem was answered positively by Sergei Bernstein (1904) in his thesis.  

.On the other hand, direct methods in the calculus of variations showed the existence of solutions with very weak differentiability properties. For many years there was a gap between these results. The solutions that could be constructed were known to have square integrable second derivatives, but this was not quite strong enough to feed into the machinery that could prove they were analytic, which needed continuity of first derivatives. This gap was filled independently by Ennio De Giorgi (1956, 1957), and John Forbes Nash (1957, 1958), who were able to show the solutions had first derivatives that were Hölder continuous. By previous results this implied that the solutions are analytic whenever the differential equation has analytic coefficients, thus completing the solution of Hilbert's nineteenth problem. Subsequently, Jürgen Moser gave an alternate proof of the results obtained by Ennio De Giorgi (1956, 1957), and John Forbes Nash (1957, 1958)

1885 Pauline Sperry born in Peabody, Massachusetts. After graduating Phi Beta Kappa from Smith College in 1906 she taught several years before doing graduate work at the University of Chicago under the projective differential geometer Ernest Julius Wilczynski (1876–1932). Her doctoral thesis, "Properties of a certain projectively defined two-parameter family of curves on a general surface", drew on his work as the founder of the American school of projective differential geometry. After receiving her Ph.D. in 1916 she taught at the University of California at Berkeley, becoming the first woman to be promoted to assistant professor in mathematics (in 1923). In 1950 she was fired for refusing to sign a loyalty oath.  

At the height of McCarthyism, the Board of Regents required university employees to sign a loyalty oath. Sperry, Hans Lewy, and others who refused were barred from teaching without pay in 1950. In the case Tolman v. Underhill, the California Supreme Court ruled in 1952 the loyalty oath unconstitutional and reinstated those who refused to sign. Sperry was reinstated with the title emeritus associate professor and later awarded back pay. *Wik

1915 Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work (developing the theory of distributions, a new notion of generalized functions motivated by the Dirac delta-function of theoretical physics). He was the first French mathematician to receive the Fields medal. For a long time he taught at the École polytechnique. *Wik

1931 Vera S. Pless (nee Stepen; March 5, 1931 – March 2, 2020)  is an American mathematician specializing in combinatorics and coding theory. She was professor emeritus at the University of Illinois at Chicago. She has co-authored several articles with John H. Conway, giving her an Erdős number of 2.

As a teenager, she was more interested in playing the cello than in mathematics, but she left high school two years early to go to the University of Chicago, and finished her studies there in three years.

Inspired by Irving Kaplansky to study abstract algebra, she stayed at the university for a master's degree, which she earned in 1952 not long after marrying her husband, a high-energy experimental physicist.

Two years later, bored with being a stay-at-home mother, Pless began teaching courses at Boston University, and a few years later began searching for a full-time job. Unable to obtain an academic position, she took a position at the Air Force Cambridge Research Laboratory in Massachusetts. where she began working on error-correcting codes.

She returned to Chicago in 1975 as a full professor of Mathematics, Statistics and Computer Science at the University of Illinois at Chicago. Her husband and youngest son had remained in the Boston area, and five years after the move, she and her husband divorced.

She retired in 2006 and died at her home in Oak Park, Illinois on March 2, 2020 at the age of 88.*Wik



1827 Pierre Simon, Marquis de Laplace (23 Mar 1749, 5 Mar 1827 at age 78) was a French mathematician, physicist, statistician and astronomer known for his mathematical analysis of the stability of the solar system (1773), alleviating Isaac Newton's concerns about perturbations between planets. He took an exact approach to science. He developed an explanation of surface tension of a liquid in terms of inter-molecular attractions, investigated capillary action and the speed of sound. He assisted Antoine Lavoisier (1783) investigating specific heat and heats of combustion, initiating the science of thermochemistry. He believed the solar system formed from a collapsing nebula. He contributed to the mathematics of probability and calculus, in which a differential equation is known by his name, and was involved in establishing the metric system.*TIS His last words were, “What we know is very slight; what we don’t know is immense.” *Eves, Revisited, 319◦

The first American translation of his classic Traité de mécanique céleste was done by Nathanial Bowditch. The work was twelve volumes long by the time it was completed by Laplace, the first four volumes  extended to 1508 quarto (small) pages.  By the time Bowditch completed his translation of the four volumes, explaining the work took 3832 large pages.  Perhaps we can now more clearly understand Bowditch's famous quote, "Whenever I meet in La Place with the words 'Thus it plainly appears,' I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears."



1827 Count Alessandro Giuseppe Antonio Anastasio Volta (18 Feb 1745; 5 Mar 1827 at age 82) Italian physicist who invented the electric battery (1800), which for the first time enabled the reliable, sustained supply of current. His voltaic pile used plates of two dissimilar metals and an electrolyte, a number of alternated zinc and silver disks, each separated with porous brine-soaked cardboard. Previously, only discharge of static electricity had been available, so his device opened a new door to new uses of electricity. Shortly thereafter, William Nicholson decomposed water by electrolysis. That same process later enabled Humphry Davy to isolate potassium and other metals. Volta also invented the electrophorus, the condenser and the electroscope. He made important contributions to meteorology. His study of gases included the discovery of methane. The volt, a unit of electrical measurement, is named after him.*TIS

1875 Claude-Louis Mathieu (25 Nov 1783; 5 Mar 1875) French astronomer and mathematician who worked particularly on the determination of the distances of the stars. He began his career as an engineer, but soon became a mathematician at the Bureau des Longitudes in 1817 and later professor of astronomy in Paris. For many years Claude Mathieu edited the work on population statistics L'Annuaire du Bureau des Longitudes produced by the Bureau des Longitudes. His work in astronomy focussed on determining the distances to stars. He published L'Histoire de l'astronomie au XVIII siècle in 1827. *TIS

1982  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. *Wikipedia

1925 Johan Ludwig William Valdemar Jensen (8 May 1859 in Nakskov, Denmark - 5 March 1925 in Copenhagen, Denmark)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 center and the value at the center. "
He also studied infinite series, the gamma function and inequalities for convex functions.*SAU


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

1885 John Radford Young (1799– March 5,1885; Peckam, England) was a mathematician, professor and author, who was almost entirely self-educated. At an early age he became acquainted with Olinthus Gilbert Gregory, who perceived his mathematical ability and assisted him in his studies.
In 1833, he was appointed Professor of Mathematics at Belfast College. When Queen's College, Belfast, opened in 1849, the Presbyterian party in control there prevented Young's reappointment as Professor in the new establishment. From that time he devoted himself more completely to the study of mathematical analysis, and made several original discoveries. He appears to have been the first to use the term "circular function" when he used it in 1831 in the an edition of Elements of the Differential Calculus "Thus, ax, a log x, sin x, &c., are transcendental functions: the first is an exponential function, the second a logarithmic function, and the third a circular function"
In 1847, he published in the Transactions of the Cambridge Philosophical Society a paper "On the Principle of Continuity in reference to certain Results of Analysis", and, in 1848, in the Transactions of the Royal Irish Academy a paper "On an Extension of a Theorem of Euler". As early as 1844, he had discovered and published a proof of Newton's rule for determining the number of imaginary roots in an equation. In 1866, he completed his proof, publishing in The Philosophical Magazine a demonstration of a principle which in his earlier paper he had assumed as axiomatic. In 1868, he contributed to the Proceedings of the Royal Irish Academy a memoir "On the Imaginary Roots of Numerical Equations".

1930 Christine Ladd-Franklin (1 Dec 1847; 5 Mar 1930) American scientist and logician known for contributions to the theory of colour vision accounting for the development of man's color sense which countered the established views of Helmholtz, Young, and Hering. Her position was that color-sense developed in stages. Ladd- Franklin's conclusions were particularly useful in accounting for color-blindness in some individuals. In logic, she published an original method for reducing all syllogisms to a single formula *TIS Ladd-Franklin was the first woman to have a published paper in the Analyst. She was also the first woman to receive a Ph.D. in mathematics and logic. The majority of her publications were based on visual processes and logic. Her views on logic influenced Charles S. Peirce’s logic and she was highly praised by Prior.

In 1878, Ladd was accepted into Johns Hopkins University with the help of James J. Sylvester, an English mathematician among the university's faculty who remembered some of Ladd's earlier works in the Educational Times. Ladd's application for a fellowship was signed "C. Ladd", and the university offered her the position without realizing she was a woman.[8] When they did realize her gender, the board tried to revoke the offer, but Sylvester insisted that Ladd should be his student, and so she was.[8] She held a fellowship at Johns Hopkins University for three years, but the trustees did not allow her name to be printed in circulars with those of other fellows, for fear of setting a precedent.[8] Furthermore, dissension over her continued presence forced one of the original trustees to resign. *Wik

Sylvester's letter in support of Ladd

1954 Julian Lowell Coolidge (28 Sep 1873, 5 Mar 1954 at age 80) American mathematician and educator who published numerous works on theoretical mathematics along the lines of the Study-Segre school. Coolidge received a B.A. at Harvard (1895), then in England he graduated (1897) with a B.Sc. from Balliol College Oxford. (It is interesting that this degree from Oxford was in natural science and it was the first natural science degree ever awarded by Oxford.) He taught at Groton School, Conn. (1897-9) where one of his pupils was Franklin D Roosevelt, the future U.S. president. From 1899 he taught at Harvard University. Between 1902 and 1904, he went to Turin to study under Corrado Segre and then to Bonn where he studied under Eduard Study. His Mathematics of the Great Amateurs is perhaps his best-known work. *TIS . This geometer wrote several noteworthy books on the history of geometry.*VFR

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

1 comment:

Patrick said...

I think your day of the year might be off by one because of the leap year. Continue to love your site and read it almost every day.