Thursday, 22 March 2018

On This Day in Math - March 22

1727 Eclipse Map *

We [he and Halmos] share a philosophy about linear algebra:
we think basis-free,
we write basis-free,
but when the chips are down
we close the office door and compute with matrices like fury.
~Irving Kaplansky

The 81st day of the year; 81 is the only integer (except 1) which is the square of the sum of its digits.

The smallest 10 digit pandigital number is 1023456789, 81 or  34 is a factor.  The other two factors are both four digit numbers. Can you find the smallest which is prime?    ;-}

81 is one of only three non-trivial numbers for which the sum of the digits * the reversal of the sum yields the original number (8+1 = 9; 9*9 = 81). The other two are the famous Hardy-Ramanujan taxicab # 1729, which is the smallest number which is the sum of two positive cubes in two ways.(1+7+2+9 = 19; 19*91 = 1729), and 1458 (1+4+5+8 = 18; 18*81=1458) which is also unique for being the maximum determinant possible for a 11x11 matrix with only ones and zeros. The Hardy-Ramanujan number's properties were first noted by Frénicle de Bessy in 1657(without mention of a taxicab).That is, he knew it was the sum of two cubes in two ways, not sure if he knew the sum of the digits property above... anyone?


1129 Chinese accounts state “there was a Black spot within the Sun” on March 22, 1129, which “died away” on April 14th. This may well have been one of the sunspots John of Worcester had observed 104 days earlier (8 December, 1128), on the other side of the world. Worcester's observation prompted the earliest known drawing of sunspots, which appear in his Chronicle recorded in 1128. *Joe Hanson,

1675. John Evelyn records in his diary a visit with William Petty and the story of the rejuvenation of Anne Greene after she was hanged until dead. "Supped at Sir William Petty's, with the Bishop of Salisbury, and divers honorable persons. ..grown famous...for his recovering a poor wench that had been hanged for felony; and her body having been begged (as the custom is) for the anatomy lecture, he bled her, put her to bed to a warm woman, and, with spirits and other means, restored her to life." *The Diary of John Evelyn

1727 The first detailed documentation and map of an eclipse in the New World came from Mexico in 1727. (At Top of page)
This map in the pamphlet Spherographia de la Obscuration de la Tierra en el Eclypse de Sol de 22. de Marzo de 1727 has several interesting features. It predates the earliest eclipse map from the United States by 104 years. Curiously, it also seems to predate any known eclipse map from Spain. Of special interest to historians of cartography, this map shows California as an island. *

1818 The last time that Easter fell on this date, the earliest possible. It will not happen again until the year 2285. By definition Easter is the first Sunday after the first full moon on or after the vernal equinox. Since the Roman Catholic Church defined the vernal equinox to be 21 March and uses a tabulated moon, not the real moon, this is a mathematical issue, not an astronomical event. *VFR

1880 The New York Times comments, somewhat tongue-in-cheek, on the Fifteen Puzzle that was sweeping the country, “No pestilence has ever visited this or any other country which has spread with the awful celerity of what is popularly called the ‘Fifteen Puzzle.’ now threatens our free institutions, inasmuch as from every town and hamlet there is coming up a cry for a ‘strong man’ who will stamp out this terrible puzzle at any cost of Constitution or freedom” *Jerry Slocum, Dic Sonneveld, The 15 Puzzle

1945 On 22 March 1945, the first female Fellows were elected to the Royal Society. This followed a statutory amendment in 1944 that read "Nothing herein contained shall render women ineligible as candidates", and was contained in Chapter 1 of Statute 1. Following approval by the Council, Marjory Stephenson (From Burwell in the Fens of East Anglia, and just west of my old school in Lakenheath) and Kathleen Lonsdale were elected as Fellows.

1960 The first laser was patented (U.S. No. 2,929,922) by Arthur Schawlow and Charles Hard Townes under the title “Masers and Maser Communications System.” What distinguished this invention as the first laser is that it was the first to operate in the visible light spectrum. The patent was assigned to the Bell Telephone Laboratories, where they had done the research. *TIS

1993 Intel Begins Shipping "Pentium" Chip":
Intel announces it is shipping its Pentium microprocessor. Engineers Federico Faggin, Ted Hoff, San Mazor, and Matsatoshi Sima, an engineer from the Japanese firm of Busicom, invented the world's first microprocessor at Intel in 1971 -- the Intel 4004. The new processor continued the exponential increase in speed and power for personal computers, also allowing for a smoother incorporation of speech, sound, handwriting, and photographs into documents.*CHM

1997 Comet Hale-Bopp makes its closest approach to the Earth at 1.315 AU. The comet was discovered independently on July 23, 1995 by two observers, Alan Hale and Thomas Bopp, both in the United States. *David Dickinson‏@Astroguyz, *Wik


1394 Ulugh Beg (22 Mar 1394- 27 Oct 1449) The only important Mongol scientist, mathematician, and the greatest astronomer of his time. His greatest interest was astronomy, and he built an observatory (begun in 1428) at Samarkand. In his observations he discovered a number of errors in the computations of the 2nd-century Alexandrian astronomer Ptolemy, whose figures were still being used. His star map of 994 stars was the first new one since Hipparchus. After Ulugh Beg was assassinated by his son, the observatory fell to ruins by 1500, rediscovered only in 1908. Written in Arabic, his work went unread by the world's next generation of astronomers. When his tables were translated into Latin in 1665, telescopic observations had surpassed them. *TIS

1644 Otto Mencke (22 March (OS) April 2, 1644 – 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1784 Samuel Hunter Christie (22 March 1784 – 24 January 1865) was a British scientist and mathematician.
He studied mathematics at Trinity College, Cambridge, where he won the Smith's Prize and was second wrangler. It may help to understand the difficulty of this exam by looking at some of the great achievers who did NOT win Senior Wrangler. A short list of Second Wranglers, include Alfred Marshall, James Clerk Maxwell, J. J. Thomson, and Lord Kelvin.
Those who have finished between third and 12th include Karl Pearson and William Henry Bragg (third), George Green and G. H. Hardy (fourth), Adam Sedgwick (fifth), John Venn (sixth), Bertrand Russell and Nevil Maskelyne (seventh), Thomas Malthus (ninth), and John Maynard Keynes (12th).

Christie was particularly interested in magnetism, studying the earth's magnetic field and designing improvements to the magnetic compass. Some of his magnetic research was done in collaboration with Peter Barlow. He became a Fellow of the Royal Society in 1826, delivered their Bakerian Lecture in 1833 and served as their Secretary from 1837 to 1853. In 1833 he published his 'diamond' method, the forerunner of the Wheatstone bridge, in a paper on the magnetic and electrical properties of metals, as a method for comparing the resistances of wires of different thicknesses. However, the method went unrecognized until 1843, when Charles Wheatstone proposed it, in another paper for the Royal Society, for measuring resistance in electrical circuits. Although Wheatstone presented it as Christie's invention, it is his name, rather than Christie's, that is now associated with the device.
Christie taught mathematics at the Royal Military Academy, Woolwich, from 1838 until his retirement in 1854. He died at Twickenham, on 24 January 1865. *Wik

1799 Friedrich Wilhelm August Argelander (22 Mar 1799, 17 Feb 1875 at age 75)
German astronomer who established the study of variable stars as an independent branch of astronomy and is renowned for his great catalog listing the positions and brightness of 324,188 stars of the northern hemisphere above the ninth magnitude. He studied at the University of Königsberg, Prussia, where he was a pupil and later the successor of Friedrich Wilhelm Bessel. In 1837, Argelander published the first major investigation of the Sun's motion through space. In 1844 he began studies of variable stars.*TIS

1868 Robert Andrews Millikan (22 Mar 1868, 19 Dec 1953) American physicist who was awarded the 1923 Nobel Prize for Physics for "his work on the elementary charge of electricity and on the photoelectric effect." Millikan's famous oil-drop experiment (1911) was far superior to previous determinations of the charge of an electron, and further showed that the electron was a fundamental, discrete particle. When its value was substituted in Niels Bohr's theoretical formula for the hydrogen spectrum, that theory was validated by the experimental results. Thus Millikan's work also convincingly provided the first proof of Bohr's quantum theory of the atom. In later work, Millikan coined the term "cosmic rays" in 1925 during his study of the radiation from outer space.*TIS

1868 Nathan Rosen (22 Mar 1909, 18 Dec 1995) U.S.-born Israeli theoretical physicist who in 1935 collaborated with Albert Einstein and Boris Podolsky on a much-debated refutation of the theory of quantum mechanics; he later came to accept the theory. The famous Einstein-Podolsky-Rosen critique of quantum mechanics was published in the 1935 Physical Review. (A New York Times obituary described The Physical Review as "one of the most impenetrable periodicals in the English language.") Rosen founded the Institute of Physics at Technion in Haifa.*TIS

1917 Irving "Kap" Kaplansky (22 March 1917 in Toronto, Ontario, Canada - 25 June 2006 in Sherman Oaks, Los Angeles, California) was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act. In this video she talks about her dad a few years after his death, and sings the song which is amazingly nice, but listen for it, she misses a digit in there I think...

He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

1931 Burton Richter (22 Mar 1931, ) American physicist who was jointly awarded the 1976 Nobel Prize for Physics with Samuel C.C. Ting for the discovery of a new subatomic particle, the J/psi particle. *TIS He led the Stanford Linear Accelerator Center (SLAC) team which co-discovered the J/ψ meson in 1974, alongside the Brookhaven National Laboratory (BNL) team led by Samuel Ting. This discovery was part of the so-called November Revolution of particle physics. He was the SLAC director from 1984 to 1999.*Wik


1772 John Canton (31 Jul 1718, 22 Mar 1772 at age 53) British physicist and teacher, who educated himself about science, and for developing a new method of preparing artificial magnets, won election to the Royal Society (1749). In July 1752, he was the first Englishman to repeat French experiments verifying Franklin's hypothesis that lightning was just a huge electric spark, (as seen from charged Leyden jars). Following this, he studied the polarity of the charge on a cloud. He invented a portable electroscope to detect charge present in a system, and he remains well-known for electrostatic induction experiments. Canton proved that water is slightly compressible (1762). Noting compass needle irregularities during a prominent aurora borealis he made the first observations of magnetic storms (1756-9). *TIS

1840 Étienne Bobillier (April 17, 1798 – March 22, 1840) was a French mathematician.
At the age of 19 he was accepted into the École Polytechnique and studied there for a year. However, due to a shortage of money, in 1818 he became an instructor in mathematics at the École des Arts et Métiers in Châlons-sur-Marne. In 1829, he was sent to Angers to be director of studies. The following year he served in the national guard during the 1830 revolution. In 1832 he returned to Châlons after his post was abolished, and was promoted to professor.
In 1836 he began suffering from health problems, but continued teaching; declining to take a leave to recuperate. As a result he died in Châlons at the relatively early age of 41.
He is noted for his work on geometry, particularly the algebraic treatment of geometric surfaces and the polars of curves. He also worked on statics and the catenary.
The crater Bobillier on the Moon is named after him.*Wik

1926 Joseph Jean Baptiste Neuberg (30 Oct 1840 in Luxembourg City, Luxembourg - 22 March 1926 in Liège, Belgium) Neuberg worked on the geometry of the triangle, discovering many interesting new details but no large new theory. Pelseneer writes, "The considerable body of his work is scattered among a large number of articles for journals; in it the influence of A. Möbius is clear." *SAU

1953 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.
Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik

1987 Andrew Paul Guinand (3 March 1912 in Renmark, South Australia, - 22 March 1987 in Peterborough, Ontario, Canada) Guinand worked on summation formulae and prime numbers, the Riemann zeta function, general Fourier type transformations, geometry and some papers on a variety of topics such as computing, air navigation, calculus of variations, the binomial theorem, determinants and special functions. In [1] W N Everitt writes,
"As a student of Titchmarsh in Oxford in the years immediately before the second world war it was natural that Guinand's research interests should be directed into the field of Fourier analysis and the Riemann zeta function. ... [In an important paper in 1948] the main application of the general result yields a deep-seated connection between the distribution of the prime numbers and the location of the zeros of the Riemann zeta function on (or near to it if the Riemann hypothesis is false) the critical line in the complex plane... Guinand was convinced that these results could lead to more information about the Riemann zeta function, and he was disappointed that he was not able to advance further in this area and that others did not take up the possibility themselves. "

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

Wednesday, 21 March 2018

On This Day in math - March 21

Fourier Series approximation of a square wave, *Mathworld

True greatness is when your name is like ampere, watt, and fourier—when it's spelled with a lower case letter.
~Richard Hamming (creator of the hamming code, with a lower case h)

The 80th day of the year; There are 80 four-digit primes which are concatenations of two-digit primes. (3137 is one example, can you find the rest?) *Prime Curios!
80 in Roman Numerals is not suitable for minors, LXXX,

The Pareto principle (sometimes called the 80-20 rule)says that, for many events, roughly 80% of the effects come from 20% of the causes, ie, \( \approx 80\% \) of the accidents are caused by 20% of the drivers.

\(n*2^{n-1} \) gives the number of edges (segments) in a n-dimensional cube, and in the 5th dimension, (went there once in a dream) there are 80 edges,  5*24
(It also has eighty two-dimensional square faces.)

And 80 is the smallest number diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, ...) *Tanya Khovanova 


---Commonly considered the first day of spring, a tradition dating from the Council of Nicaea in A.D. 325. The most recent year in which this was in fact true in the U.S. was 1979, when the vernal equinox occurred at 12:22 a.m. EST. The next time the vernal equinox will be on March 21 is in 2103 when it will occur at 1:09:04 a.m. EST. This computation uses a tropical year of 365 days, 5 hours, 48 minutes, and 46 seconds. [Mathematics Magazine, 55(1982), 46–47] *VFR

1522 Copernicus read the German version of his treatise, Modus cudendi monetam (The Way to Strike Coin), before the Royal Prussian Assembly attended by King Sigismund Is envoys at Grudziądz (Graudenz). Copernicus discusses general issues related to the theory of money and formulates inter alia a law of bad money driving out good. In the second he focused on the current monetary situation in Royal Prussia and in particular on the decline in the value of Prussian coinage, and concluded his presentation with a proposal to mint three Prussian szelągi as an equivalent of one Polish grosz (groshen) and thus to equalize the value of the new Prussian coinage with that issued by the Crown. *Leszek Zygner
Nicolaus Copernicus University (Students may not know that, in addition to being a respected astronomer, Copernicus was a respected economist.)

1543 Copernicus’ De Revolutionibus published, {{{This date seems incorrect, Thony Christie sent me a note that, "in his An Annotated Census of Copernicus' De Revolutionibus Owen Gingerich writes, 'The printing was finished on 20 April 1543 when Rheticus autographed a presentation copy of the completed work. (Copernicus himself did not receive the final pages until a month later, the day on which he died.)' However I have a note from a post by Teresa Borawska of Nicolaus Copernicus University that says, "There is no information whether a copy of the book printed shortly before 21 March 1543 ever reached Warmia before the astronomers death." and gives no other publication date.}}} The book was so technically complex that only true astronomers could read through it so the 400 copies didn't even sale out. In addition Osiander had written a disclaimer (without, it seems, the dying Copernicus' permission) that readers should view it as a useful mathematical fiction with no physical reality, thereby somewhat shielding it from accusations of blasphemy. But eventually it was banned. It was placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616 as part of the Galileo "incident". [while I was researching this note I came across a nice bit of information that I am not sure where else I could use. De revolutionibus was printed in Hans Petreiuss printing shop in Nuremberg. The building of Petreiuss former printing shop at 9, Öberg Street, (located near Albrecht Durers birthplace) luckily survived the ravages of WWII. You can see in the banner an image of the shop at The Renaissance Mathematicus blog.]

1599 Tycho sends a letter to Longomontanus, in which he reports his revised theory on the movement of the moon. On January 31, During an observation of the lunar eclipse, he had discovered that his predictive theory about the movement of the Moon was wrong since the eclipse started 24 minutes before his calculations predicted.*Wik

1665-6 Hooke writes to C. Huygens to send him a paper on Gravity he has written and presented to the Royal Society.

1684 Giovanni Domenico Cassini discovered two moons of Saturn: Tethys and Dione, using a refractor telescope with an aperture of 108mm. He had previously discovered two other satellites of Saturn: Iapetus (Sep 1671) and Rhea (1672). Christiaan Huygens was the first to discover a moon of Saturn, when he viewed Titan (the largest and easiest to see) on 25 Mar 1655.*TIS

1797 Gauss makes an entry in his diary that the perimeter of the lemniscate can be divided into five equal parts by ruler and compass. Abel would show in 1827 that the division of the lemniscate with classical tools is possible for the same numbers n as the circle. This is an important theorem in elliptic functions. *John Stillwell, Mathematics and Its History

1801 Thomas Jefferson to Joseph Priestly:

-- I learnt some time ago that you were in Philadelphia, but that it was only for a fortnight; supposed you were gone. It was not till yesterday I received information that you were still there, had been very ill, but were on the recovery. I sincerely rejoice that you are so. Yours is one of the few lives precious to mankind,  for the continuance of which every thinking man is solicitous.
*The Letters of Thomas Jefferson,

1816 John Dalton makes the first entry in the second volume of his meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816. Volume II would continue until 31 Aug, 1827

In 1925, Wolfgang Pauli published his “exclusion principle.” At the young age of 24, in an article in Zeitschrift für Physik, Pauli introduced the idea that two nearby electrons cannot be in exactly the same state at the same time. For this, now fundamental, contribution to quantum mechanics, he was awarded a Nobel Prize in 1945. *TIS

1925 The Butler Act is signed into law. A law in Tennessee prohibiting the teaching of Darwin’s theory of evolution passed the state senate on March 13, and was signed into law by Governor Austin Peay (for whom the university in Clarksville, Tennessee is named) on March 21. The Butler Act was a Tennessee law:
That it shall be unlawful for any teacher in any of the Universities, Normals and all other public schools of the State which are supported in whole or in part by the public school funds of the State, to teach any theory that denies the Story of the Divine Creation of man as taught in the Bible, and to teach instead that man has descended from a lower order of animals.
It would remain the law in Tennessee until repealed on September 1, 1967. *Wik Within a few months, John Scopes became a willing defendant in the “Scopes Monkey Trial,” which began 10 Jul 1925, and received world attention as the statute was tested. He was convicted and fined $100, which was overturned on appeal. *TIS

1943 Joseph Needham, 43, known at that point as a brilliant biologist, arrives in China for the first time. By the time he left, he would be well on his way to being the foremost student of China in the Western World. His "Science and Civilization in China", would alter the basis and direction of math/science history. *Simon Winchester, The Man Who Loved China

1963 When this date is written in the form 3/21/63, the product of the first two numbers is the third. This happens 212 times each century. *VFR (you have 211 left to find)

1989 NCTM released its Curriculum and Evaluation Standards for School Mathematics, a document intended to change fundamentally the way mathematics is taught. *VFR

2016 France issues stamp honoring Sophie Germain.

2016 Sphere packing for 24 dimensions is solved by Maryna Viazovska. In 1611, Kepler conjectured that there was no way to pack spheres more densly than the way we would normally stack oranges or cannonballs, with every triangle of three supporting another nestled above (and below) tangent to all of the first three. By 1831 Gauss had managed to prove the conjecture for 3d. In her paper on May 14th Viazovska proved no packing of unit balls in Euclidean space R8 has density greater than that of the E8-lattice packing. One week later, (March 21) building on her work, with collaboration of four others, they were able to prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions, and that it is the unique optimal periodic packing. *arxiv.


1768 Baron Jean-Baptiste-Joseph Fourier (21 Mar 1768; 16 May 1830 at age 62) French mathematician, Egyptologist and administrator who exerted strong influence on mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat). He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS His work on heat was termed by Maxwell, “a great mathematical poem.” He traveled to Egypt with Napoleon and became convinced that desert heat was ideal for good health. Consequently, he wore many layers of garments and lived in rooms of unbearably high heat. This hastened his death, by heart disease, so that he died, thoroughly cooked. [Eves, History of Mathematics, 362] *VFR

1866 Antonia Coetana de Paiva Pereira Maury (21 Mar 1866; 8 Jan 1952 at age 85) was an American astronomer and ornithologist whose painstaking classifications of stars by their spectra included elaborate work on 681 bright stars of the northern skies published in Annals of Harvard College Observatory (1896), a significant early catalog. Yet she was unappreciated by her observatory director, Edward C. Pickering. Her work was important in Ejnar Hertzsprung's verification of the distinction between dwarf stars and giant stars, as now seen in the Hertzsprung-Russell diagram. After Pickering discovered the first spectroscopic binary star, Mizar, she was first to measure its period, 104 days. In 1889, she identified the second such star, Beta Aurigae, with a period of about 4 days. Antonia was the niece of astronomer Henry Draper, and the granddaughter of John William Draper who pioneered in the use of photography in astronomy.*TIS
In 1897, having examined 4,800 photographs, she published her findings on 681 bright northern stars in the Annals of the Harvard College Observatory. It was the first Harvard observatory publication credited to a woman, which she had insisted on, writing to Pickering, “I worked out the theory at the cost of much thought and elaborate comparison and I think that I should have full credit for my theory of the relations of the star spectra.” *Time

1884 George David Birkhoff (21 Mar 1884, 12 Nov 1944) American mathematician, foremost of the early 20th century, who formulated the ergodic theorem. As the first American dynamicist, Birkhoff picked up where Poincaré left off, gaining distinction in 1913 with his proof of Poincaré's Last Geometric Theorem, a special case of the 3-body problem. Although primarily a geometer, he discovered new symbolic methods. He saw beyond the theory of oscillations, created a rigorous theory of ergodic behavior, and foresaw dynamical models for chaos. His ergodic theorem transformed the Maxwell- Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. He also produced a mathematical model of gravity. *TIS 

1909 Founder of ACM Edmund Berkeley Is Born:
Edmund Berkeley, founder of the Association of Computing Machinery, is born. A graduate of Harvard University, Berkeley participated in the development of Harvard's Mark II while enlisted in the Navy during World War II. In addition to co-founding the ACM in 1947, he wrote one of the first books on computers intended for a general audience, "Giant Brains, or Machines that Think." *CHM

1920 John Michael Hammersley (21 March 1920 in Helensburgh, Dunbartonshire, Scotland - 2 May 2004 in Oxford, England) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. (Wikipedia) when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)
During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, `On the enfeeblement of mathematical skills by `Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. *from his Independent obituary

1927 Halton Christian Arp (21 Mar 1927, ) American astronomer noted for challenging the theory that red shifts of quasars indicate their great distance. Arp is one of the key actors in the contemporary debate on the origin and evolution of galaxies in the universe. His landmark compilation of peculiar galaxies led him to challenge the fundamental assumption of modern cosmology, that redshift is a uniform indicator of distance. Astronomers have debated Arp's assertion that quasars are related to peculiar galaxies since the late 1960's. Most astronomers believe that quasars are unrelated to the peculiar galaxies. Yet, no one has been able to explain why the quasars seem to be more numerous around the peculiar galaxies. *TIS

1951 David Nualart (21 March 1951 - ) is a Spanish mathematician working in the field of probability theory, in particular on aspects of stochastic processes and stochastic analysis.
He obtained his PhD titled "Contribución al estudio de la integral estocástica" in 1975 at the University of Barcelona under the supervision of Francesc d'Assís Sales Vallès. After positions at the University of Barcelona and the Polytechnique University of Barcelona he took up a professorship at Kansas University and is currently the Black-Babcock Distinguished Professor in its Mathematics Department.
He published hundreds of scientific articles in his field, served on several scientific committees, has been an associate editor of many journals and from 2006 to 2008 was the Chief Editor of Electronic Communications in Probability.
He has been elected a Fellow of the Institute of Mathematical Statistics in 1997. He received a Doctor Honoris Causa by the University Blaise Pascal of Clermond-Ferrand in 1998. He received the Prize IBERDROLA de Ciencia y Tecnologia in 1999. He has been a Corresponding Member of the Real Academia de Ciencias Exactas Fisicas y Naturales of Madrid since 2003. He has been a member of the Reial Academia de Ciencies i Arts of Barcelona since 2003. He received the Research Prize of the Real Academia de Ciencias de Madrid in 1991.
In March 2011 the International Conference on Malliavin Calculus and Stochastic Analysis in honor of David Nualart took place at University of Kansas. *Wik


1699 Erhard Weigel (December 16, 1625 – March 21, 1699) was a German mathematician, astronomer and philosopher. He earned his Ph.D. from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. *Wik
A post at the Renaissance Mathematicus about Weigel and some of his lesser known students (most student's would be "lesser known" compared to Leibniz) also pointed out that "Another Weigel innovation in celestial cartography was his eclipse map from 1654. An eclipse map is a map that shows the path on the surface of the earth from which a solar eclipse will be visible. Weigel’s was the first such printed map ever produced. This honor is usually falsely accredited to Edmund Halley for his 1715 eclipse map."
For religious reasons, he wanted to rename all the constellations, and made several globes of the sky with his renamed constellations.

1762 Abbé Nicolas Louis de Lacaille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS

1822 D'Amondans Charles de Tinseau (19 April 1748 in Besançon, France - 21 March 1822 in Montpellier, France) wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes that Tinseau's works, "... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space."
Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites. He also wrote Solution de quelques questions d'astronomie on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics. *SAU

1864 Luke Howard, FRS (28 November 1772 – 21 March 1864) was a British manufacturing chemist and an amateur meteorologist with broad interests in science. His lasting contribution to science is a nomenclature system for clouds, which he proposed in an 1802 presentation to the Askesian Society.
He has been called "the father of meteorology" because of his comprehensive recordings of weather in the London area from 1801 to 1841 and his writings, which transformed the science of meteorology. *Wik

1915 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

1928 Edward Walter Maunder (12 Apr 1851, 21 Mar 1928 at age 76) English astronomer who was the first to take the British Civil Service Commission examination for the post of photographic and spectroscopic assistant at the Royal Observatory, Greenwich. For the next forty years that he worked there, he made extensive measurements of sunspots. Checking historical records, he found a period from 1645 to 1715 that had a remarkable lack of reports on sunspots. Although he might have questioned the accuracy of the reporting, he instead attributed the shortage of report to an actual dearth of sunspots during that period. Although his suggestion was not generally accepted at first, accumulating research has since indicated there are indeed decades-long times when the sun has notably few sunspots. These periods are now known as Maunder minima.*TIS

1933 Enrico D'Ovidio (11 Aug 1842 in Campobasso, Italy - 21 March 1933 in Turin, Italy) D'Ovidio was to work for 46 years in the University of Turin. He was chairman of the Faculty of Science in 1879-80 and rector of the University between 1880 and 1885. Another spell as chairman of the Faculty of Science between 1893 and 1907 ended when he was appointed Commissioner of the Polytechnic of Turin.
Euclidean and noneuclidean geometry were the areas of special interest to D'Ovidio. He built on the geometric ideas which had been introduced by Lobachevsky, Bolyai, Riemann and Cayley. D'Ovidio's most important work is probably his paper of 1877 The fundamental metric functions in spaces of arbitrarily many dimensions with constant curvature.
D'Ovidio also worked on binary forms, conics and quadrics. He had two famous assistants, Peano (1880-83) and Corrado Segre (1883-84). D'Ovidio and Corrado Segre built an important school of geometry at Turin. *SAU

1934 Thomas Muir (25 Aug 1844 in Stonebyres, Falls of Clyde, Lanarkshire, Scotland
- 21 March 1934 in Rondebosch, South Africa) He is noted for a four volume work on the history of determinants. *VFR He also proved an important lemma about determinants of skew symmetric matrices

1960 Sheila Scott Macintyre (née Sheila Scott, April 23, 1910 - March 21, 1960) was a Scottish mathematician well known for her work on the Whittaker constant. Macintyre is also well known for creating a multilingual scientific dictionary: written in English, German, and Russian; at the time of her death, she was working on Japanese.*Wik

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

Monday, 19 March 2018

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. (Before you read blythly on, there are three more year days that also require the sum of 19 fourth-powers... find one.)

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


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.


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


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

On This Day in Math - March 19

Pearls of Sluze, *Mathworld Wolfram

There is no reason why the history and philosophy of science should not be taught in such a way as to bring home to all pupils the grandeur of science and the scope of its discoveries.
~Prince Louis-Victor de Broglie

The 78th day of the year; 78 is the smallest number that can be written as the sum of 4 distinct squares in 3 ways.  *What's Special About This Number

78 is the sum of the first twelve integers, and thus a triangular number.

The cube of 78 is equal to the sum of three distinct cubes, 783 = 393 + 523 + 653
(Historically, it seems Ramanujan was inspired by a much smaller such triplet 63 = 33 + 43 + 53

77 and 78 form the fourth Ruth-Aaron pair, named for the number of home runs hit by Babe Ruth, 714, and the number when Aaron broke the record, 715 (he hit more afterward).  They are consecutive numbers that have the same sums of their prime factors (77 = 7*11, 78 = 2*3*13, and 7+11 = 2+3+13).


In 1474, the Venetian Patent Law, the first of its kind in the world, declared that “each person who will make in this city any new and ingenious contrivance, not made heretofore in our dominion, as soon as it is reduced to perfection... It being forbidden to any other in any territory and place of ours to make any other contrivance in the form and resemblance thereof, without the consent and licence of the author up to ten years.” The law was intended to attract inventors and investors to Venice and stimulate new economic activities. *TIS

*Mark Jardine,
1681 Last observation of C/1680 V1, also called the Great Comet of 1680, Kirch's Comet, and Newton's Comet. It has the distinction of being the first comet discovered by telescope. Discovered by Gottfried Kirch on 14 November 1680, New Style, it became one of the brightest comets of the 17th century--reputedly visible even in daytime--and was noted for its spectacularly long tail. Passing only 0.4 AUs from Earth on 30 November, it sped around an incredibly close perihelion of .006 AU (898,000 km) on 18 December 1680, reaching its peak brightness on 29 December as it rushed outward again. It was last observed on 19 March 1681. As of December 2010 the comet was about 252.1 A.U. from the Sun. While the Kirch Comet of 1680-1681 was discovered and subsequently named for Gottfried Kirch , credit must also be given to the Jesuit, Eusebio Kino, who charted the comet’s course. During his delayed departure for Mexico, Kino began his observations of the comet in Cadíz in late 1680. Upon his arrival in Mexico City, he published his Exposisión astronómica de el [sic] cometa (Mexico City, 1681) in which he presented his findings. Kino’s Exposisión astronómica is among one of the earliest scientific treatises published by a European in the New World. Aside from its brilliance, it is probably most noted for being used by Isaac Newton to test and verify Kepler's laws. *Wik

1706 Advertisement in English Tabloid for William Jones's Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics. This is the book in which Jones introduces the symbol pi for the ratio of the circumference to diameter of a circle.
*Review of the State of the English Nation (Cumulation) (London, England), Tuesday, March 19, 1706; Issue 34.

1752 Following the death of her father on March 19, 1752, a new phase of Maria Agnesi’s life began that lasted until her death. She restricted her study to theology and gave her time, effort, and money to devotional and charitable activities. Although continuing to live with her family, she kept a separate apartment, where she cared for a few poor, sick people. From 1759 she lived in a rented house with four of her poor people; and when money was needed for her charitable activity, she sold her gifts from the Empress Maria Theresa to a rich Englishman. Besides caring for the sick and indigent, she often taught catechism to working-class people. *Hubert Kennedy, Eight Mathematical Biographies, Pg 8

1791 Prior to 1784, when Jefferson arrived in France, most if not all of his drawings were made in ink. In Paris, Jefferson began to use pencil for drawing, and adopted the use of coordinate, or graph, paper. He treasured the coordinate paper that he brought back to the United States with him and used it sparingly over the course of many years. He gave a few sheets to his good friend David Rittenhouse, the astronomer and inventor:

"I send for your acceptance some sheets of drawing-paper, which being laid off in squares representing feet or what you please, saves the necessity of using the rule and dividers in all rectangular draughts and those whose angles have their sines and cosines in the proportion of any integral numbers. Using a black lead pencil the lines are very visible, and easily effaced with Indian rubber to be used for any other draught."
A few precious sheets of the paper survive today. *
Jefferson was widely interested in Science. For those who wish to know more about his scientific interest, I can recommend this book

1791 Report made to the Paris Academy of Sciences advocating the metric system, including the decimal subdivision of the circle. The committee consisted of J. C. Borda, J. Lagrange, P. S. Laplace, G. Monge, and de Condorcet. [Cajori, History of Mathematics 266] See April 14, 1790. *VFR
A metric system of angles was brought in, with 400 degrees in a full turn (100 degrees in a right angle). Now the earth would rotate 40 degrees in an hour and, since the metre had been designed so that one quarter meridian was 10 million metres, each degree of latitude would be 100 kilometres long. It was certainly a rational system but its introduction would require all watches, all clocks, all trigonometric tables, all charts etc. to be changed. Condorcet proposed that teams of out of work wig makers should be used to recalculate new mathematical tables with the new units. Why, one might ask, were the wig makers out of work? Well they had been employed by the aristocrats who, following the Revolution, no longer required their services! *SAU

1797 The date of the entry in Gauss’s scientific diary showing that he had already discovered the double periodicity of certain elliptic functions. *VFR Gauss was investigating the lemniscate.

1892 E. Hastings Moore, of Northwestern University, was elected professor of mathematics by the Board of Trustees of the new University of Chicago. *T. W. Goodspeed, The Story of the University of Chicago

1918 "An Act to preserve daylight and provide standard time for the United States" was enacted on March 19, 1918. It both established standard time zones and set summer DST to begin on March 31, 1918. *WebExhibits 

1937 John von Neumann gave a popular lecture at Princeton on the game of poker. Game Theory became one of his substantial contributions to mathematics. [A. Hodges, Alan Turing. The Enigma, p. 550]The Book that inspired the movie.

In 1958, Britain's first planetarium, the London Planetarium, opened in the west wing of Madame Tussaud's. It is one of the world's largest. The site used was that of the former Cinema and Restaurant added in 1929, that had been destroyed by a German bomb in 1940.*TIS

1953 Frances Crick writes a letter to his son. "Dear Michael, Jim Watson and I have probably made a most important discovery.” This was only two weeks after Crick solved the DNA puzzle and may well be the first written description of the code. The letter, to be auctioned at Christie’s on April 10, is expected to fetch at least $1 million at auction. *NY Times Science

2016 Spring Equinox. Spring officially comes to Possum Trot, Ky at 11:30 P.M. CDT, this evening. 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


1782 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids... current Andromedids are only weakly represented by displays of less than three meteors per hour around November 14. ) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS

1799 William Rutter Dawes (19 Mar 1799, 15 Feb 1868 at age 68) English amateur astronomer who set up a private observatory and made extensive measurements of binary stars and on 25 Nov 1850 discovered Saturn's inner Crepe Ring (independently of American William Bond). In 1864, he was the first to make an accurate map of Mars. He was called "Eagle-eyed Dawes" for the keenness of his sight with a telescope (though otherwise, he was very near-sighted). He devised a useful empirical formula by which the resolving power of a telescope - known as the Dawes limit - could be quickly determined. For a given telescope with an aperture of d cm, a double star of separation 11/d arcseconds or more can be resolved, that is, be visually recognized as two stars rather than one. *TIS

1862 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

1900 Frederic Joliot-Curie (19 Mar 1900; 14 Aug 1958 at age 58) French physicist and physical chemist who became personal assistant to Marie Curie at the Radium Institute, Paris, and the following year married her daughter Irène (who was also an assistant at the institute). Later they collaborated on research, and shared the 1935 Nobel Prize in Chemistry "in recognition of their synthesis of new radioactive elements." For example, they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. By 1939 he was investigating the fission of uranium atoms. After WW II he supervised the first atomic pile in France. He succeeded his wife as head of the Radium Institute upon her death in 1956. *TIS

1910 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.
While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. He died of a heart attack in Tampa, Florida, where he was a professor at the University of South Florida.
Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory.*Wik

1910 Jerome Namias (19 Mar 1910, 10 Feb 1997 at age 86) American meteorological researcher most noted for having pioneered the development of extended weather forecasts and who also studied the Dust Bowl of the 1930s and the El Niño phenomenon. *TIS In 1971 he joined the Scripps Institution and established the first Experimental Climate Research Center. His prognosis of warm weather during the Arab oil embargo of 1973 greatly aided domestic policy response.*Wik

1927 Allen Newell (March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *Wik

1951 Arthur T. Benjamin (March 19, 1961; ) is an American mathematician who specializes in combinatorics. Since 1989 he has been a Professor of Mathematics at Harvey Mudd College.
He is known for mental math capabilities and mathemagics performances. These have included shows at the Magic Castle and TED. He is also the first mathematician to have been featured on the Colbert Report.
The Mathematical Association of America gave him a regional award for distinguished teaching in 1999 and a national one in 2000. He was the Mathematical Association of America's George Pólya Lecturer for 2006-8. In 2012 he became a fellow of the American Mathematical Society.
Benjamin was one of the performers at the inaugural San Diego Science Festival on April 4, 2009. He also won the American Backgammon Tour in 1997. *Wik A video of his "mathmagic" is here 
And his new book, The Magic of Math: Solving for x and Figuring Out Why, is delightful,


1406 Ibn Khaldūn or Ibn Khaldoun  Al-Ḥaḍrami, May 27, 1332 AD/732 AH – March 19, 1406 AD/808 AH) was a Muslim historiographer and historian who is often viewed as one of the fathers of modern historiography,sociology and economics.
He is best known for his Muqaddimah (known as Prolegomenon in English), which was discovered, evaluated and fully appreciated first by 19th century European scholarship, although it has also had considerable influence on 17th-century Ottoman historians like Ḥajjī Khalīfa and Mustafa Naima who relied on his theories to analyze the growth and decline of the Ottoman Empire. Later in the 19th century, Western scholars recognized him as one of the greatest philosophers to come out of the Muslim world. *Wik

1862 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU His 1903 book, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, popularized the ideas of Sophus Lie among British mathematicians.
He was elected a Fellow of the Royal Society in 1905, and served as President of the London Mathematical Society from 1918 to 1920. *Wik

1685 René François Walter de Sluse (2 July 1622 in Visé, Principality of Liège (now Belgium) - 19 March 1685 in Liège, Principality of Liège (now Belgium)) a French mathematician, intellectual and clergyman who wrote many books about mathematics and contributed to the development of mathematics.
Plague in Église Saint-Martin

He studied at a university in Rome, and later moved to Liège. His position in the church prevented him from visiting other mathematicians, but he corresponded with the mathematicians and intellectuals of the day.
He studied calculus and his work discusses spirals, tangents, turning points and points of inflection.
There is a family of curves named after him called the Pearls of Sluze: the curves represented by the following equation with positive integer values of m, n and p:
yn = k(a - x)pxm *Wik
This group of curves was studied by de Sluze between 1657 and 1698. It was Blaise Pascal who named the curves after de Sluze.

1922 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory.
After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU

1930 Henry Faulds (1 Jun 1843, 19 Mar 1930 at age 86) Scottish physician who, from 1873, became a missionary in Japan, where he worked as a surgeon superintendent at a Tokyo hospital, taught at the local univeristy, and founded the Tokyo Institute for the Blind. In the late 1870s, his attention was drawn to fingerprints of ancient potters remaining on their work that he helped unearth at an archaeological dig site in Japan. He commenced a study of fingerprints, and became convinced that each individual had a unique pattern. He corresponded on the subject with Charles Darwin, and published a paper about his ideas in Nature (28 Oct 1880). When he returned to Britain in 1886, he unsuccessfully offered his fingerprinting identification scheme for forensic uses to Scotland Yard. Undeserved confusion on priority for the discovery with Francis Galton and Sir William J. Herschel lasted until 1917. *TIS

1978 Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.*Wik A report of his bravery during WWI during which he lost his nose:
January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.
When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU

1984 Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics. A Bellman equation, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. The "Curse of dimensionality", is a term coined by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.*Wik

1987 Louis Victor Pierre Raymond duc de Broglie (15 Aug 1892,19 Mar 1987 at age 94) was a French physicist best known for his research on quantum theory and for his discovery of the wave nature of electrons. De Broglie was of the French aristocracy - hence the title "duc" (Prince). In 1923, as part of his Ph.D. thesis, he argued that since light could be seen to behave under some conditions as particles (photoelectric effect) and other times as waves (diffraction), we should consider that matter has the same ambiguity of possessing both particle and wave properties. For this, he was awarded the 1929 Nobel Prize for Physics. *TIS
He is buried in the Cimetière de Neuilly-sur-Seine (Ancien),Hauts-de-Seine, Ile-de-France Region, France. (Just outside Paris)

2011 J(ames) Laurie Snell, (January 15th, 1925, Wheaton, Illinois; March 19, 2011, Hanover, New Hampshire) was an American mathematician.
A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*Wik

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