Friday, 18 August 2017

On This Day in Math - August 18

The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.
~Karl F. Gauss

The 230th day of the year; 230 is the smallest number such that it and the next number are both sphenic numbers, the product of three distinct primes (230 = 2*5*23 and 231 = 3*7*11). *Prime Curios (can there be three consecutive numbers that are the product of three (or n) distinct primes

Their are 230 possible crystal shapes that can tile space (this counts the chiral reflections as separate). This is the analogy of the better known 17 "wallpaper groups" which tile the plane. Interestingly, both were proved by the same man, Evgraf Fedorov, in 1891. He did the plane problem the hard way, he proved the case for space first, then worked backwards to the plane.


1709 Cotes writes to Newton in hopes of prompting the revision of the Principia which Newton had promised to deliver in "a fortnights time.". The revised papers (through Prop XXXIII) would be delivered by Cotes neighbor Whiston in September when he returned from London. *Correspondence of Sir Isaac Newton and Professor Cotes, pg 3

1783 The 1783 Great Meteor was an unusually bright Bolide observed on August 18, 1783, from the British Isles at a time when such phenomena were not well understood. The meteor was the subject of much discussion in the Philosophical Transactions of the Royal Society and was the subject of a detailed study by Charles Blagden. *Wik Christopher Goulding reproduced this Paul Sandby watercolor of the meteor as seen from the terrace of Windsor Castle on 18 August 1783. Goulding lists the observers as James Lind, the Italian physicist Dr Tiberio Cavallo (1749-1809), Dr. Lockman (the Canon of St George's, Windsor), Thomas Sandby (the brother of the artist), and two unknown women.*GeoCosmo History

1813 On August 18, 1913, at the famous Monte Carlo casino, black came up 26 times in a row. Supposedly the house made a fortune against people betting that the long overdue red HAD to show up. *PB Personal notes

In 1868, Pierre Janssan discovered helium in the solar spectrum during eclipse, but did not recognize it as a new element. The first evidence of helium was observed on August 18, 1868 as a bright yellow line with a wavelength of 587.49 nanometers in the spectrum of the chromosphere of the Sun. The line was detected by French astronomer Janssen during a total solar eclipse in Guntur, India. This line was initially assumed to be sodium. English astronomer Norman Lockyer observed a yellow line in the solar spectrum during the same eclipse, which he named the D3 Fraunhofer line because it was near the known D1 and D2 lines of sodium. He concluded that it was caused by an element in the Sun unknown on Earth. Lockyer and English chemist Edward Frankland named the element with the Greek word for the Sun, Helios. Terrestrial helium was found about 10 years later by William Ramsay. *Wik

1877 Asaph Hall discovered Phobos, a satellite of Mars. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars.”

1881 “The matter is so perfectly clear that we cannot be amazed enough how the mathematicians so stubbornly insist on mystifying it.” Comment of Friedrich Engels on a manuscript of Karl Marx on the differential calculus. *VFR

1913 On August 18, 1913, at the famous Monte Carlo casino, black came up 26 times in a row. Supposedly the house made a fortune against people betting that the long overdue red HAD to show up. *PB Personal notes

1978 Henri Cohen gives lecture to confirm Roger Apery's proof that Apéry's constant ζ(3) is irrational. In June 1978 Roger Apéry gave a talk entitled "Sur l'irrationalité de ζ(3)." During the course of the talk he outlined proofs that ζ(3) and ζ(2) were irrational, the latter using methods simplified from those used to tackle the former rather than relying on the expression in terms of π. Due to the wholly unexpected nature of the result and Apéry's blasé and very sketchy approach to the subject many of the mathematicians in the audience dismissed the proof as flawed. Three of the audience members suspected Apéry was onto something, though, and set out to confirm his proof.
Two months later these three—Henri Cohen, Hendrik Lenstra, and Alfred van der Poorten—finished their work, and on August 18 Cohen delivered a lecture giving full details of Apéry's proof. Following the talk Apéry himself took to the podium to explain the source of some of his ideas. *Wik


1685 Brook Taylor born (18 August 1685 – 29 December 1731). Remembered in introductory Calculus classes for Taylor's Theorem and Taylor series. His 1713 "Methodus.." was the first book published on the calculus of finite differences and also the first use of Taylor's Theorem.
In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings, and needed the elucidation bestowed on it in the treatises of John Joshua Kirby (1754) and Daniel Fournier. *Wik

1832 Eugène Rouché (18 August 1832 at Sommières, Hérault, France, -19 August 1910 at Lunel, Hérault) French Geometer who edited Laguerre's "Collected Works". He also is known for Rouche's Theorem on Complex functions. *SAU

1861 William J Greenstreet (18 Aug 1861 in Milton, Kent, England
- 28 June 1930 in Burghfield Common, Reading, England) graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette. *SAU

1897 Bern Dibner (18 Aug 1897; 6 Jan 1988 ) Ukrainian-American engineer and science historian. Dibner worked as an engineer during the electrification of Cuba. Realizing the need for improved methods of connecting electrical conductors, in 1924, he founded the Burndy Engineering Company. A few years later, he became interested in the history of Renaissance science. Subsequently, he began collecting books and everything he could find that was related to the history of science. This became a second career as a scholar that would run parallel with his life as a businessman. He wrote many books and pamphlets, on topics from the transport of ancient obelisks, to authorative biographies of many scientific pioneers, including Volta, inventor of the electric battery, and Roentgen, discoverer of the X ray. *TIS

1910 Paul Turán (18 Aug 1910,26 Sept 1976) Paul Erdos, who co-authored many papers with Turan wrote:
Probably the most important, most enduring and most original of Turán's results are in his power sum method and its applications. I was there when it originated in 1938. Turán mentioned these problems and told me that they were not only interesting in themselves but their positive solution would have many applications. Their importance first of all is that they lead to interesting deep problems of a completely new type; they have quite unexpectedly surprising consequences in many branches of mathematics - differential equations, numerical algebra, and various branches of function theory.
In fact Turán invented the power sum method while investigating the zeta function and he first used the method to prove results about the zeros of the zeta function.*SAU


1652 Florimond DeBeaune died (7 October 1601, Blois – 18 August 1652, Blois). His name is attached to one of the first problems ever posed in differential equations. *VFR DeBeaune was a friend of Descartes, and helped van Schooten write the Latin Translation of Descartes "Geometrie". De Beaune asked to find a curve for which the subtangent had a fixed length. De Beaune did not give this curve a name, but it has come to be called by his name. Leibniz solve De Beaune's question in his first paper on calculus in 1684. *Ed Sandifer, How Euler Did It. (Oct 2008)
In a 1638 letter to Descartes, de Beaune posed the problem of solving the differential equation

\( \frac{\operatorname{d}y}{\operatorname{d}x}=\frac{\alpha}{y-x} \)

now seen as the first example of the inverse tangent method of deducing properties of a curve from its tangents.
His Tractatus de limitibus aequationum was reprinted in England in 1807; in it, he finds upper and lower bounds for the solutions to quadratic equations and cubic equations, as simple functions of the coefficients of these equations. His Doctrine de l'angle solide and Inventaire de sa bibliothèque were also reprinted, in Paris in 1975. Another of his writings was Notae breves, the introduction to a 1649 edition of Descartes' La Géométrie. *Wik

1823 André-Jacques Garnerin (31 Jan 1769, 18 Aug 1823) French aeronaut, the first person to use a parachute regularly and successfully. He perfected the parachute and made jumps from greater altitudes than had been possible before. On 22 October 1797, at age 28, Garnerin made his first jump above the Parc Monceau in Paris. He dropped from a hot-air balloon at 3000 feet. His parachute, with 36 ribs and lines, was semi-rigid, somewhat resembling an umbrella. The descent was a success, except that he shook back and forth violently while falling. The physicist Lalande, who attended the event, suggested improving air flow with a small opening at the top of the canopy. Garnerin died aged 41. While preparing balloon equipment, a beam struck his head inflicting a mortal wound. *TIS

1960 Carlo Emilio Bonferroni (28 Jan 1892 in Bergamo, Italy - 18 Aug 1960 in Florence, Italy) His articles are more of a contribution to probability theory than to simultaneous statistical inference. He also had interests in the foundations of probability. He developed a strongly frequentist view of probability denying that subjectivist views can even be the subject of mathematical probability. *SAU He is best known for the Bonferroni inequalities, and gives his name to (but did not devise) the Bonferroni correction in statistics. *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

Thursday, 17 August 2017

On This Day in Math - August 17

Base eight is just like base ten, really… if you're missing two fingers!
~Tom Lehrer, "New Math"

The 229th day of the year; 229 is a prime, and is the smallest prime that added up to the reversal of its digits yields another prime, (229 + 922) = 1151 (can you find the next one?)

The sum of the digits of 229 is prime (13) and the sum of squares of the digits is also prime (89).

extra: 229 is the difference between 3³ and 4⁴ *jim wilder ‏@wilderlab


1585 The Roanoak Colony in Virginia (to later become known as the "lost" colony) was founded on this day by Sir Walter Raleigh's agents, led by Ralph Lane. If you don't know why that is on a math page, read more here.

1655 William Oughtred writes to John Wallis to praise his methods in "Arithmetica Infinitorum" . It was received too late to be included in the first edition, but was included in the 1695 second edition.  *The Arithmetics of Infinitesimals, J. Stedall, pg 11

1762 The Board of Longitude Grants £500 to Christopher Irwin for his marine chair. Marine chairs, despite often having been ignored by modern scholars in favor of the chronometer and lunar-distance approaches to estimating longitude, reappeared throughout the history of the British Commissioners of the Longitude. Christopher Irwin of Ireland generated a lot of national and international interest in the late 1750s and early 1760s with his design. The Board funded the finishing and sea trial of it, granting him £500 on 17 August 1762. Nevil Maskelyne considered the chair alongside the lunar-distance method and one of John Harrison's longitude timekeepers on his 1763 trip to Barbados. (Maskelyne, who in 1765 would become Astronomer Royal and a Commissioner of Longitude, reported that the invention was useless. *Cambridge Digital Library

1771 Joseph Priestley sets out to test the rejuvenating effect of mint growing in a sealed container. He placed a candle in the covered glass and let it burn out in the presence of the mint. Ten days later he would return to the experiment and relight the candle and found, "it burned perfectly well in it." *Steven Johnson, The Invention of Air

1811 “Having to conduct my grandson through his course of mathematics, I have resumed the study with great avidity. It was ever my favorite one. We have no theories there, no uncertainties remain on the mind; all is demonstration and satisfaction.” So wrote Thomas Jefferson (1743– 1826) to Benjamin Rush. Taken from The Writings of Thomas Jefferson, edited by A. A. Lipscomb, vol. 13 (1903), p. 75, as quoted from Cajori, Mathematics in Liberal Education, p. 109, which is a collection of interesting quotations on the value of mathematics.  The following year, his 70th, Jefferson describes his early affection for mathematics in a letter to William Duane "When I was young, mathematics was the passion of my life." *John Fauval, lecture at Univ of Va.

1825 A royal decree granted Niels Henrik Abel, then 23, sufficient funds for a year’s travel in France and Germany. *VFR

1877 Asaph Hall discovered Phobos, inner satellite of Mars. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik
In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars. "

1896 Mrs. Bridget Driscoll of Croydon, Surrey, became the 1st pedestrian in Britain to die after being hit by a car. Mrs Driscoll, a 44 year old housewife, who was traveling from Old Town, Croydon to a folk-dancing display in Crystal Palace, was hit by a demonstration car traveling at 4mph (according to the driver, Arthur Edsel) . She died within minutes of receiving a head injury.
At her inquest, Coroner William Percy Morrison said he hoped that "such a thing would never happen again" and was the first to apply the term ‘accident’ to violence caused by speed. Coroners across the country have followed his example ever since. *Road Safety Center Cardiff.

1934 Dunham Jackson personalizes a book. Harold Bacon recalls that Jackson was an inspired writer of limericks. When Bacon purchased Jackson's "The Theory of Approximations" he took it to Jackson's office and requested he sign it, suggesting a limerick. Without any visible prethought Jackson wrote on the flyleaf:
There was a young fellow named Bacon
Whose judgement of books was mistaken
In a moment too rash
He relinquished some cash
And his faith in the Author was shaken
August 17, 1934
*Steven Krantz, Mathematical Apocrypha Redux
Harold M Bacon was a long-serving calculus professor at Stanford where a teaching award in his name has been created since his death in 1992. 

1941 When Herbert Robbins saw the proof sheet of the title page of What is Mathematics? with only the name Richard Courant on it, his first reaction was “My god, the man’s a crook.” Realizing that a quiet meeting on their co-authorship of the book would be impossible, Robbins wrote Courant on this date that, while the custom might be different in Europe, in this country the junior author did receive credit. Courant backed down, and so today we know this lovely book as one by Courant and Robbins. For the two sides of this story see Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician (Springer 1976), 223– 226 and 230–232 as well as “An interview with Herbert Robbins,” The College Mathematics Journal, 15(1984), 4–6. *VFR

1966 Launch of Pioneer 7, American solar satellite. Studied prominences and solar atmosphere. *NSEC

1601 Pierre de Fermat (17 Aug 1601; 12 Jan 1665) French mathematician, often called the founder of the modern theory of numbers. Together with Rene Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. He anticipated differential calculus with his method of finding the greatest and least ordinates of curved lines. He proposed the famous Fermat's Last Theorem while studying the work of the ancient Greek mathematician Diophantus. He wrote in pencil in the margin, "I have discovered a truly remarkable proof which this margin is too small to contain," that when the Pythagorean theorem is altered to read an + bn = cn, the new equation cannot be solved in integers for any value of n > 2 . *TIS

1936 Margaret Heafield Hamilton (August 17, 1936 - ) is a computer scientist, systems engineer and business owner. She was Director of the Software Engineering Division of the MIT Instrumentation Laboratory, which developed on-board flight software for the Apollo space program. In 1986, she became the founder and CEO of Hamilton Technologies, Inc. in Cambridge, Massachusetts. The company was developed around the Universal Systems Language based on her paradigm of Development Before the Fact (DBTF) for systems and software design.
In one of the critical moments of the Apollo 11 mission, Hamilton's team's work prevented an abort of the landing on the Moon. Among other things, Hamilton credits the Apollo Guidance Computer (AGC) together with its asynchronous executive as a foundation that provided the means for her to design systems software that included AGC error detection and recovery mechanisms such as the Display Interface Routines, the purpose of which was to warn the astronauts in case of an emergency, by interrupting the astronaut's normal mission sequence displays and replacing them with priority displays (e.g., the priority displays of the 1201 and 1202 alarms that took place during the Apollo 11 landing). Three minutes before the Lunar lander reached the Moon's surface, several computer alarms were triggered. The computer was overloaded with incoming data, because the rendezvous radar system (not necessary for landing) updated an involuntary counter in the computer, which stole cycles from the computer. Due to its robust architecture, the computer was able to keep running; the Apollo onboard flight software was developed using an asynchronous executive so that higher priority jobs (important for landing) could interrupt lower priority jobs.

Hamilton has published over 130 papers, proceedings, and reports concerned with the 60 projects and six major programs in which she has been involved. *Wik

1954 Ingrid Daubechies ( born 17 August 1954- ) is a Belgian physicist and mathematician. She is currently Professor in the mathematics and applied mathematics departments at Princeton University. In January 2011 she moved to Duke University as a Professor in mathematics. She is the first woman president of the International Mathematical Union (2011–2014). She is best known for her work with wavelets in image compression. In 2000 Daubechies became the first woman to receive the National Academy of Sciences Award in Mathematics, presented every 4 years for excellence in published mathematical research. The award honored her "for fundamental discoveries on wavelets and wavelet expansions and for her role in making wavelets methods a practical basic tool of applied mathematics."
In January 2005, Daubechies became just the third woman since 1924 to give the Josiah Willard Gibbs Lecture sponsored by the American Mathematical Society. Her talk was on "The Interplay Between Analysis and Algorithm."*Wik


1786 Death of Frederick the Great. Euler's interest in lotteries began at the latest in 1749 when he was commissioned by Frederick the Great to render an opinion on a proposed lottery. The first of two letters began 15 September 1749. A second series began on 17 August 1763.

1924 Pavel Samuilovich Urysohn, Pavel Uryson (February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer) is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology. His name is also commemorated in the term Menger-Urysohn dimension and in the term Urysohn integral equation. The modern definition of compactness was given by him and Pavel Alexandrov in 1923.*Wik

1927 (Erik) Ivar Fredholm (7 Apr 1866,17 Aug 1927) Swedish mathematician who founded modern integral equation theory. *TIS

1969 Otto Stern (17 Feb 1888; 17 Aug 1969 at age 81) German-American scientist and winner of the Nobel Prize for Physics in 1943 for his development of the molecular beam as a tool for studying the characteristics of molecules and for his measurement of the magnetic moment of the proton. *TIS

2004 Shizuo Kakutani August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem.
The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory.
Kakutani's other mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems). They also include his solution of the Poisson equation using the methods of stochastic analysis.
The Collatz (or 3n+1) conjecture is also known as the Kakutani conjecture. *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

Wednesday, 16 August 2017

On This Day in Math - August 16

Projective geometry is all geometry.
~Arthur Cayley

The 228th day of the year; 228 is the number of ways, up to rotation and reflection, of dissecting a regular 11-gon into 9 triangles.

228 + 1,  822 + 1, and (228 + 822) + 1 are all primes. Is there another such year day?

228 in binary is written 11100100 notice that this is all four possible two digit binary combinations in descending order, 11, 10, 01, 00.


1878 Hermite writes to Sylvester at Johns Hopkins concerned about his accepting a Math Chair in America to questioned the ability of the American people to contribute to research-level mathematics. Only three years later he would be reading the paper of Fabian Franklin, a young assistant mathematics instructor at Johns Hopkins, before the French Academy. The paper was on a short, purely graphic, proof of Euler's theorem on pentagonal numbers. *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900

In 1898, the loop-de-loop Roller Coaster was patented by Edwin Prescott.*TIS The vertical loop is not a recent roller coaster innovation. Its origins can be traced back to the 1850s when centrifugal railways were built in France and Great Britain. In 1901 Prescott built the Loop-the-Loop at Coney Island. This ride used the modern teardrop-shaped loop and a steel structure, however more people wanted to watch the attraction, rather than ride. No more looping roller coasters were built until 1976 when Revolution opened at Six Flags Magic Mountain.*Wik

1966 Stephen Smale, University of California, Berkeley, received the Fields Medal at the International Congress of Mathematicians in Moscow for his work on dynamical systems. Ten days later on the steps of Moscow University he will make a speech condemning American
military activity in Vietnam and Soviet military involvement in Hungary. *VFR

1983 Poland issued a stamp celebrating the 50th anniversary of the Enigma Decoding Machine. VFR  


1744 Pierre (-François-André) Méchain (16 Aug 1744; 20 Sep 1804). a French astronomer and hydrographer at the naval map archives in Paris recruited by Jean Delambre. He was a mathematical progidy. In 1790, they were chosen by the National Assembly to establish a decimal system of measurement based on the meter. Since this was defined to be one ten-millionth of the distance between the Earth's pole and the equator, Mechain led a survey of the meridian arc from Dunkirk, France, to Barcelona, Spain. Through his astronomical observations, Mechain discovered 11 comets and provided 26 additions to Messier's catalog. He calculated the orbits of the two comets he found in 1781. Mechain died of yellow fever while making further surveys for the meridian measurement. *TIS

1821 Arthur Cayley, (16 August 1821 – 26 January 1895) English mathematician who played a leading role in founding the modern British school of pure mathematics. He trained first as a lawyer, and from 1849, spent 14 years at the bar, during which time he maintained an interest in mathematics and published about 250 mathematical papers. In 1863, Cayley followed his passion and commenced a new career as professor of Pure Mathematics at Cambridge and during his tenure published 900 papers and notes covering nearly every aspect of modern mathematics. The legacy of his work in n-dimensional geometry was later applied in physics to the study of the space-time continuum. His work on matrices served as a foundation for quantum mechanics developed by Werner Heisenberg in 1925. *TIS

1836 Marc-Antoine Parseval des Chênes (April 27, 1755 – August 16, 1836) was a French mathematician, most famous for what is now known as Parseval's theorem, which presaged the unitarity of the Fourier transform.
He was nominated to the French Academy of Sciences five times, from 1796 to 1828, but was never elected. His only mathematical publications were, apparently, five papers, published in 1806 as Mémoires présentés à l'Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences mathématiques et physiques. (Savants étrangers.) This combined the following earlier monographs:
  1. "Mémoire sur la résolution des équations aux différences partielles linéaires du second ordre," (May 5, 1798).
  2. "Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaires du second ordre, à coefficients constants," (April 5, 1799).
  3. "Intégration générale et complète des équations de la propagation du son, l'air étant considéré avec ses trois dimensions," (July 5, 1801).
  4. "Intégration générale et complète de deux équations importantes dans la mécanique des fluides," (August 16, 1803).
  5. "Méthode générale pour sommer, par le moyen des intégrales définies, la suite donnée par le théorème de M. Lagrange, au moyen de laquelle il trouve une valeur qui satisfait à une équation algébrique ou transcendante," (May 7, 1804).
It was in the second, 1799, memoir in which he stated, but did not prove (claiming it to be self-evident), the theorem that now bears his name. He further expanded upon it in his 1801 memoir, and used it to solve various differential equations. The theorem was first printed in 1800 as a part (p. 377) of Traité des différences et des séries by Lacroix.

1837 Joseph-Marie de Tilly,(16 Aug 1837 in Ypres, Belgium - 4 Aug 1906 in Munich, Germany) Belgian mathematician, born. In 1899 he was dismissed from his teaching post at the Ecole Militaire for unduly emphasizing the scientific education of future officers and using the notions of the infinitely small and the differential. *VFR

1845 Gabriel Lippman (16 Aug 1845; 13 Jul 1921).French physicist, born Hollerich, Luxembourg, who received the Nobel Prize for Physics in 1908 for producing the first colour photographic plate. Lippmann was a giant of his day in classical physics research, especially in optics and electricity. He worked in Berlin with the famed Hermann von Helmholtz before settling in Paris to head (in 1886) the Sorbonne's Laboratories of Physical Research until his death. His inventions include an instrument for precisely measuring minute differences in electrical power and the "coleostat" for steady, long-exposure sky photography.*TIS

1884 Hugo Gernsback (August 16, 1884 – August 19, 1967), born Hugo Gernsbacher, was a Luxembourgish-American inventor, writer, editor, and magazine publisher, best known for publications including the first science fiction magazine. His contributions to the genre as publisher were so significant that, along with the novelists H. G. Wells and Jules Verne, he is sometimes called "The Father of Science Fiction". In his honour, annual awards presented at the World Science Fiction Convention are named the "Hugos" *Wik

1904 Wendell Meredith Stanley (16 August 1904 – 15 June 1971) was an American biochemist, virologist and Nobel laureate. Stanley was born in Ridgeville, Indiana, and earned a BS in Chemistry at Earlham College in Richmond, Indiana. He then studied at the University of Illinois, gaining an MS in science in 1927 followed by a Ph.D. in chemistry two years later. His later accomplishments include writing the book "Chemistry: A Beautiful Thing" and achieving his high stature as a Pulitzer Prize nominee.
Stanley was awarded the Nobel Prize in Chemistry for 1946. His other notable awards included the Rosenburger Medal, Alder Prize, Scott Award, and the AMA Scientific Achievement Award. He was also awarded honorary degrees by many universities both American and foreign, including Harvard, Yale, Princeton and the University of Paris. Most of the conclusions Stanley had presented in his Nobel-winning research were soon shown to be incorrect (in particular, that the crystals of mosaic virus he had isolated were pure protein, and assembled by autocatalysis)
Stanley married Marian Staples (1905-1984) in 1929 and had three daughters (Marjorie, Dorothy and Janet), and a son, (Wendell M. Junior). Stanley Hall at UC Berkeley (now Stanley Biosciences and Bioengineering Facility) and Stanley Hall at Earlham College are named in his honor. *Win

1905 Marian Adam Rejewski (16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in 1932 solved the plugboard-equipped Enigma machine, the main cipher device used by Germany. The success of Rejewski and his colleagues Jerzy Różycki and Henryk Zygalski jump-started British reading of Enigma in World War II; the intelligence so gained, code-named "Ultra", contributed, perhaps decisively, to the defeat of Nazi Germany.
While studying mathematics at Poznań University, Rejewski had attended a secret cryptology course conducted by the Polish General Staff's Biuro Szyfrów (Cipher Bureau), which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptologic "card catalog," derived using his "cyclometer," and the "cryptologic bomb."
Five weeks before the German invasion of Poland in 1939, Rejewski and his colleagues presented their results on Enigma decryption to French and British intelligence representatives. Shortly after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued their work in collaboration with the British and French. They were again compelled to evacuate after the fall of France in June 1940, but within months returned to work undercover in Vichy France. After the country was fully occupied by Germany in November 1942, Rejewski and fellow mathematician Henryk Zygalski fled, via Spain, Portugal and Gibraltar, to Britain. There they worked at a Polish Army unit, solving low-level German ciphers. In 1946 Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptologic work until 1967. *Wik

1907 Dura Kurep (16 Aug 1907, 2 Nov 1993)The topics which Kurepa investigated are very varied but lie mostly within topology, set theory and number theory. He published over 200 papers but this number rises to over 700 items if we include books, articles and reviews. He was fascinated by the continuum hypothesis and the axiom of choice. Perhaps best known is his work on trees and partitions, especially Aronszajn and Suslin trees. His book The Theory of Sets written in Serbo-Croatian and published in 1951 illustrates his interests in that particular area. After introducing the fundamental concepts and elementary operations in Chapter 1, he looks at cardinal numbers in the second chapter, then partially ordered sets and ordinal numbers in the third. Chapter 4 is on topological and metric spaces, with the fifth and final chapter on limiting processes in analysis, measure theory, Borel and Souslin sets.
In number theory he made many contributions, but perhaps his most famous is his open problem on the left factorial function. In 1971 he published his definition of !n, the left factorial function, defined by
!n = 0! + 1! + 2! + 3! + ... + (n-1)!.
Kurepa conjectured that the greatest common divisor of !n and n! was 2 for all n > 1. There are many equivalent forms of the conjecture, but one of the most natural was given by Kurepa in the same 1971 paper, namely that !n is not divisible by n for any n > 2. If the left factorial conjecture is false we certainly know that it will fail for n > 1000000.*SAU
The same left factorial notation is more commonly used for the subfactorial used in derangements. Many mathematicians simply use "factorial sum" for Kurepa's !n. It is interesting that no one seems to have picked up on the use of an inverted exclamation point as suggested by G. Chrystal in his "Algebra, an Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges", (1889 (pg 25))

1920 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


1705 Jakob Bernoulli . (27 December 1654 – 16 August 1705) He was so fascinated with the way the logarithmic spiral reproduces itself in its involute, its evolute, and its caustics of reflection and refraction, that he requested it be engraved on his tombstone, together with the inscription Eadem mutata resurgo (Though changed, I will arise the same). *VFR (the spiral on his tombstone is not logarithmic, but Archimedian... perhaps he is spinning in his grave even yet.)
 He was one of the first to fully utilize differential calculus and introduced the term "integral" in integral calculus. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra (1685), work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any
triangle into four equal parts with two perpendicular lines.(a nice exercise to try) By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. He published five treatises on infinite series (1682 - 1704). He was the first of the Bernoulli family of mathematicians. *TIS
Jacob Bernoulli’s Ars Conjectandi from 1713 is the first major book on the theory of probability and statistics. It is because of its 300 years anniversary that 2013 was named the international year of Statistics. The exhibited copy is in fact a first edition! It is showing the proof of the law of large numbers, one of the results for which it is famous. * University of Copenhagen Dept of Math Sciences

1920 Sir Joseph Norman Lockyer (17 May 1836, 16 Aug 1920) British astronomer who in 1868 discovered and named the element helium that he found in the Sun's atmosphere before it had been detected on Earth. He also applied the name chromosphere for the sun's outer layer. Lockyer discovered, together with Pierre J. Janssen, the prominences (red flames) that surround the solar disk. He was also interested in the classification of stellar spectra and developed the meteoric hypothesis of stellar evolution. His works include the books Contributions to Solar Physics (1873), The Sun's Place in Nature (1897) and Inorganic Evolution (1900). *TIS

1995 Thomas Brooke Benjamin​, FRS (15 April 1929 – 16 August 1995) was an English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations. *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

Tuesday, 15 August 2017

On This Day in Math - August 15

voyager exits solar system 1990, see Events(2006)

The 227th day of the year; 227 is a prime number, but it can also be written as the sum of the sum and the product of the first four primes: (2 + 3 + 5 + 7)+(2 x 3 x 5 x 7) = 227. In a similar way, the first two primes work (2+3)+(2x3)=11 is prime. Can you find another? (Ben Vitale has found all the cases under 1000 for which p = (a + b + c + … ) + (a * b * c …) He even found another way to express 227. His blog also has lots of other number curiosities, so give it a look. Much fun.

227 is also the largest day number of the year which can NOT be expressed as a prime added to twice a square.  There are three others you might find, and three others larger than 366 (and that seems to be ALL of them that exist)


310 BC "Agathocles, who was already at the point of being overtaken and surrounded, gained unhoped for safety as night closed in. On the next day there occurred such an eclipse of the Sun that utter darkness set in and the stars were seen everywhere; wherefore Agathocles' men, believing that the prodigy portended misfortune for them, fell into even greater anxiety about the future. After they had sailed for six days and the same number of nights, just as day was breaking, the fleet of the Carthaginians was unexpectedly seen far away." From: Diodorus Siculus (Greek historian, 1st century BC), Library of History. Agathocles was a tyrant who had made his escape, with a fleet of sixty ships, from a blockade at Syracuse harbor by the Carthaginians. Quoted in Historical Eclipses and Earth's Rotation, by F Richard Stephenson, Cambridge University Press, 1997,

1665 Robert Hooke writes to Boyle in Oxford about his newly devised reflecting quadrant, "My quadrant does to admiration for taking angles, so that thereby we are able from hence to tell the true distance between (St.) Paul's and any other church steeple in the city.... within the quantity of twelve foot." *Lisa Jardine, Ingenious Pursuits, pg 152

1768 Lagrange, in a letter to D’Alembert, expressed his difficulty in solving the problem: Given a nonsquare positive integer n, to find a square integer x2 such that nx2 +1 shall also be a square. *VFR
In the same letter, he showed that x2/3 could be expanded in a trigonometric series. D'Alembert had often used the function as an example that could not be so expanded. *Mathematical thought from ancient to modern times, Volume 2 , Morris Kline

1771 Benjamin Franklin writes to John Canton to share the news of Priestley's discovery that, unlike animals, a plant seemed to survive after months. He would later be inspired to place a life animal under the glass with the plant and realize that the animal survived longer. *Steven Johnson, The Invention of Air

1951 The Soviet Union issued a postage stamp with a portrait of Sonya Kovalevskaya. *VFR

2006 Voyager 1, the most distant man-made object, reached 100 astronomical units from the sun - meaning 100 times more distant from the sun than is Earth - about 15,000 million km (9,300 million miles) from the sun. At such great distance, the sun is a mere point of light, so solar energy is not an option, but having a nuclear power source, Voyager 1 continues to beam back information. The spacecraft, launched nearly 30 years earlier, on 5 Sep 1977, had flown beyond the outer planets and reached the heliosheath, the outer edge of our solar system, where the sun's influence wanes. Voyager 1 continues traveling at a speed of about one million miles per day and could cross into interstellar space before 10 years later.


1720 Jean-Baptiste Le Roy (15 August 1720;Paris, France - 21 January 1800, Paris) Son of the renowned clockmaker Julien Le Roy, Jean-Baptiste Le Roy was one of four brothers to achieve scientific prominence in Enlightenment France; the others were Charles Le Roy (medicine and chemistry), Julien-David Le Roy (architecture), and Pierre Le Roy(chronometry). Elected to the Académie Royale des Sciences in 1751 as adjoint géomètre, Le Roy played an active role in technical as well as administrative aspects of French science for the next half-century. He was elected pensionnaire mécanicies in 1770 and director of the Academy for 1773 and 1778, and became both a fellow of the Royal Society and a member of the American Philosophical Society in 1773.
Le Roy’s major field of enquiry was electricity, a subject on which European opinion was much divided at mid-century. The most prominent controversy engaged the proponents of the Abbé Nollet’s doctrine of two distinct streams of electric fluids (outflowing and inflowing) and the partisans of Benjamin Franklin’s concept of a single electric fluid. This debate intensified in France in 1753 with an attack on Franklin’s views by Nollet. Le Roy, later a friend and correspondent of Franklin, defended his single-fluid theory and offered considerable experimental evidence in support thereof. He played an important role in the dissemination of Franklin’s ideas, stressing particularly their practical applications, and published many memoirs on electrical machines and theory in the annual Histoires and Mémoires of the Academy and in the Journal de Physique.
A regular contributor to the Encyclopédie, Le Roy wrote articles dealing with scientific instruments. The most important of these included comprehensive treatments of “Horlogerie,” “Télescope,” and “Électrométre” (in which Le Roy claimed priority for the invention of the electrometer). He also promoted the use of lightning rods in France, urged that the Academy support technical education, and was active in hospital and prison reform. After the Revolutionary suppression of royal academies, Le Roy was appointed to the first class of the Institut National (section de mécanique) at its formation in 1795. *

1795 Émile Léger (Born: 15 Aug 1795 in Lagrange-aux-Bois, France; Died: 15 Dec 1838 in Paris, France)Léger only published four mathematical papers but one contains possibly the first mention of what today is a well known fact about the Euclidean algorithm,
Émile Léger appears to have been the first (or second, if the work of de Lagny ... is counted) to recognise that the worst case of the Euclidean algorithm occurs when the inputs are consecutive Fibonacci numbers.  *SAU

1863 Aleksei N. Krylov, (15 Aug 1863 in Visyaga, Simbirskoy [now Ulyanovskaya], Russia - 26 Oct 1945 in Leningrad, USSR [now St Petersburg, Russia]) noted for mathematics, mechanics and engineering. *VFR Krylov made many mathematical advances in his applications of mathematics to shipbuilding. In hydrodynamics, among many advances, he made significant contributions to the theory of ships moving in shallow water. In 1904 he constructed a mechanical integrator to solve ordinary differential equations, being the first in Russia to make such an instrument. He improved Fourier's method for solving boundary value problems in a 1905 paper and gave many applications. *SAU

1865 Hantaro Nagaoka (15 Aug 1865; 11 Dec 1950)Japanese physicist who was influential in advancing physics in Japan in the early twentieth century. In 1904, he published his Saturnian model of the atom, inspired by the rings around the planet Saturn. He placed discrete, negatively charged electrons of the same tiny mass, spaced in a ring revolving around a central huge positive spherical mass at its centre. Considering the electrostatic forces, hee made a mathematical analogy to Maxwell's model of the stability of the motion of Saturn's rings in a huge central gravitational field. However, Nagaoka's theory failed in other ways, and he sidelined it in 1908. *TIS

1892 Louis Victor Pierre Raymond duc de Broglie (15 Aug 1892 -19 Mar 1987) 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

1893 Leslie (John) Comrie (15 Aug 1893-11 Dec 1950) was a New Zealand astronomer and pioneer in the application of punched-card machinery to astronomical calculations. He joined HM Nautical Almanac Office (1926-36), where he replaced the use of logarithm tables with desk calculators and punched card machines for the production of astronomical and mathematical tables. This made scientific use of these machines, made originally for only business uses. In 1938, he founded the Scientific Computing Service Ltd., the first commercial calculating service in Great Britain, to further his ideas of mechanical computation for the preparation of mathematical tables. His use of card processing systems prepared the way for electronic computers.*TIS

1905 Hermann Alexander Brück (15 August 1905 in Berlin, Germany – 4 March 2000 in Edinburgh, Scotland) was a German-born astronomer who spent the great portion of his career in the United Kingdom.
Upon graduation from Munich, Brück followed his friend Albrecht Unsöld to the Potsdam Astrophysical Observatory; Unsöld had earned his doctorate the year before, also under Sommerfeld. While there, he participated in the physics colloquium at the Humboldt University of Berlin with the physicists Max von Laue and Albert Einstein and the astronomer Walter Grotrian. With growing difficulties under National Socialism, Brück left Germany in 1936 to take a temporary research assistantship at the Vatican Observatory. In 1937 he moved to the University of Cambridge to join the circle of the modern astrophysicists around Arthur Eddington. In time, Brück became Assistant Director of the Observatories and John Couch Adams, specializing in solar spectroscopy. He taught a course in classical astronomy and started the student astronomical society, which fostered the careers of many astronomers.
In 1947, at the invitation of Éamon de Valera, Brück moved to Dublin to direct the Dunsink Observatory, which was part of the Dublin Institute for Advanced Studies, where he associated with Erwin Schrödinger. In 1950, the Observatory, along with the Royal Irish Academy, hosted the first meeting of the Royal Astronomical Society. In 1955, the International Astronomical Union held their triennial Assembly in Dublin. At this gathering, the Observatory demonstrated photoelectric equipment for photometry, which had been developed by M. J. Smyth, who had been Brück’s student in Cambridge. Also displayed was the UV solar spectroscopy which extended the Utrecht Atlas and formed part of the revised Rowland tables of the Solar spectrum; Brück’s wife, Dr. Mary Brück (née Conway), was a leading figure in this work.
In 1957, Brück moved to the University of Edinburgh. With his vision and drive, he transformed the Royal Observatory into an internationally-ranked center of research. He put together a team of astronomers and engineers headed initially by P. B. Fellgett and later by V. C. Reddish *Wik

1918 Jean Brossel ( 15 August 1918 in Périgueux , France - 4 February 2003 in France)developed with Alfred Kastler the technique of optical pumping at origin of lasers. *Arjen Dijksman ‏@materion


1758 Pierre Bouguer died (16 February 1698, Croisic – 15 August 1758, Paris). In 1727 he won the prize competition of the Acad´emie Royal des Sciences on the masting of ships. In this competition Euler only received the “accessit.” *vfr
Two days before (Aug 13)Charles-Etienne-Louis Camas was elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. (did Bouguer get the other half? Did Euler get any? is one, or more of these three pieces of information incorrect?)
French physicist whose work founded photometry, the measurement of light intensity. He was a child prodigy, a professor at age 15, following his father, Jean Bouguer, in hydrography - the study of bodies of water, both salt and fresh. He participated on the expedition to Peru (1735-44) to measure an arc of the meridian near the equator. In 1729, he invented a photometer to compare the intensity of two light sources illuminating separate halves of translucent paper. The eye itself, he determined, could not be used as a meter, but could establish the equality of brightness of adjacent surfaces. He determined the sun was 300 times brighter the moon. Bouguer's law gives the attenuation of a beam of light by an optically homogeneous (transparent) medium.*TIS

1789 Jakob II Bernoulli, There seems to be confusion about his date of death, although it is well known that he drowned while swimming in the Neva River at the age of 29 and that he was married to one of Euler's granddaughters. Part of the confusion may be due to the fact that Russia did not switch to the modern Gregorian calendar until after the 1918 revolution. Alternate date given is July 2. Should be Aug 5 if converting the same day from Julian to Gregorian. Anyone?

1798 Edward Waring (ca. 1736 – 15 August 1798) was an English mathematician who gave many results about decomposing numbers into sums of powers and sums of primes.*SAU He entered Magdalene College, Cambridge as a sizar and became Senior wrangler in 1757. He was elected a Fellow of Magdalene and in 1760 Lucasian Professor of Mathematics, holding the chair until his death. He made the assertion known as Waring's Problem without proof in his writings Meditationes Algebraicae. Waring was elected a Fellow of the Royal Society in 1763 and awarded the Copley Medal in 1784.
In number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers (for example, every number is the sum of at most 4 squares, or 9 cubes, or 19 fourth powers, etc.). The affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. *Wik

1927 Bertram Borden Boltwood (27 Jul 1870, 15 Aug 1927). was an American chemist and physicist whose work on the radioactive decay of uranium and thorium was important in the development of the theory of isotopes. Boltwood studied the "radioactive series" whereby radioactive elements sequentially decay into other isotopes or elements. Since lead was always present in such ores, he concluded (1905) that lead must be the stable end product from their radioactive decay. Each decay proceeds at a characteristic rate. In 1907, he proposed that the ratio of original radioactive material to its decay products measured how long the process had been taking place. Thus the ore in the earth's crust could be dated, and give the age of the earth as 2.2 billion years.*TIS

1953 Ludwig Prandtl (4 Feb 1875, 15 Aug 1953) German physicist who is remembered for his studies of both aerodynamics and hydrodynamics. He established the existence of the boundary layer adjoining the surface of a solid over which a fluid flows. The design of an efficient shape, weight, and mass for ships and aircraft owes much to his work, for which he is considered to be the father of aerodynamics. His made major studies on the effects of streamlining and the properties of aircraft wings. He made improvements to such constructions as wind tunnels. The Prandtl number is a dimensionless group used in the study of convection. The von Karman-Prandtl equation describes the logarithmic variation of water velocity within a channel from zero flow at the stream bed to a maximum velocity at the water surface.*TIS

1978 Viggo Brun (13 October 1885, Lier – 15 August 1978, Drøbak) was a Norwegian mathematician.
He studied at the University of Oslo and began research at the University of Göttingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors (9-almost primes); and that all large even integers are the sum of two 9 (or smaller)-almost primes.
In 1919 Brun proved that the sum of the reciprocals of the twin primes converges to Brun’s constant:
1⁄3 + 1 ⁄5 + 1⁄ 5 + 1⁄7 + 1 ⁄11 + 1⁄ 13 + 1⁄17 + 1 ⁄19 + . . . = 1.9021605 . . .by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919/20 and applied this to problems in musical theory.
He also served as praeses of the Royal Norwegian Society of Sciences and Letters in 1946.
It was in 1994, while he was trying to calculate Brun’s constant,
that Thomas R. Nicely discovered a famous flaw in the Intel Pentium
microprocessor. The Pentium chip occasionally gave wrong answers
to a floating-point (decimal) division calculations due to errors in five
entries in a lookup table on the chip. Intel spent millions of dollars
replacing the faulty chips.
More recently, Nicely has calculated that the value of Brun’s constant
1s 1.902160582582 _ 0.000000001620.

2002 Heinz Bauer (31 January 1928 – 15 August 2002) was a German mathematician.
Bauer studied at the University of Erlangen-Nuremberg and received his PhD there in 1953 under the supervision of Otto Haupt and finished his habilitation in 1956, both for work with Otto Haupt. After a short time from 1961 to 1965 as professor at the University of Hamburg he stayed his whole career at the University of Erlangen-Nuremberg. His research focus was the Potential theory, Probability theory and Functional analysis
Bauer received the Chauvenet Prize in 1980 and became a member of the German Academy of Sciences Leopoldina in 1986. Bauer died in Erlangen. *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, 14 August 2017

On This Day in Math - August 14

Nothing is difficult to him who would be learned.
~Giovanni Battista Benedetti

The 226th day of the year; The iteration of the sum of the squares of the digits leads to one (a happy number). What percentage of numbers have this property?

226 = 3!3+2!3+1!3 + 0!3 *Derek Orr

The binary expression for 226 has the same number of ones and zeros.


733 "In this year Aethelbald captured Somerton; and the Sun was eclipsed, and all the Sun's disc was like a black shield; and Acca was driven from his bishopric." The Anglo Saxon Chronicle Refers to the annular solar eclipse of 14 August AD 733.*NSEC

1612 Galileo explains his new method of observing the sun in his second letter to Marc Welser:
… I shall now describe the method of drawing the spots with complete accuracy. This was discovered, as I hinted in my other letter, by a pupil of mine, a monk of Cassino named Benedetto Castelli. …
The method is this: Direct the telescope upon the sun as if you were going to observe that body. Having focused and steadied it, expose a flat white sheet of paper about a foot from the concave lens; upon this will fall a circular image of the sun's disk, with all the spots that are on it arranged and disposed with exactly the same symmetry as in the sun. The more the paper is moved away from the tube, the larger this image will become, and the better the spots will be depicted. Thus they will be seen without damage to the eye, even the smallest of them — which, when observed through the telescope, can scarcely be perceived, and only with fatigue and injury to the eyes.”
Previously he had only observed the sun directly near sunrise or sunset. *Galileo's Sunspot Letters at

1659 In a letter from Fermat to Carcavi - Fermat claimed to be able to prove the following five theorems by the method of infinite descent:

(1) The area of a right-angled triangle whose sides are integers cannot be a square number.

(2) The equation x3 + y3 = z3 has no solutions in integers.

(3) The equation y2 + 2 = x3 admits no solutions in integers except x = 3, y = 5.

(4) The equation y2 + 4 = x3 admits no solutions in integers except x = 2, y = 2 and x = 5, y = 11.

(5) Each prime number of the form p = 4n + 1 is uniquely expressible as the sum of two squares.

He ends his letter to Carcavi as follows:-

Here you have a summary account of my dreams on the subject of numbers. I have only written it because I fear I will lack the leisure to fully express myself and to lay out the entirety of my demonstrations and methods; in any case, this outline will serve the savants to be able to prove for themselves that which I have not filled out, especially if MM de Carcavi and Frenicle give them some demonstrations by descent that I have sent them on the subject of some negative propositions. And perhaps posterity will be thankful for my having let them know that which the Ancients did not ... *SAU

1797 Caroline Herschel, having observed her eighth comet, took the extra measure of riding from Slough to Greenwich to notify Astronomer Royal Maskelyne. A nice article about this event is at The Guardian Web page.

1894 “The first summer meeting of the American Mathematical Society was held in one of the lecture-rooms of the Polytechnic Institute in Brooklyn, N.Y.” Only ten papers were presented! The meeting lasted two days; August 15 was the second. *VFR
This was on a Tuesday and Wednesday of the week to immediately precede the dates of the meeting of The American Association for the Advancement of Science. Thomas Friske's papers indicate this was not only the first summer meeting, it was the first meeting ever under the AMS name. The New York Association had dissolved and reformed itself into the AMS.
The following papers were presented :
1. Theorems in the calculus of enlargement. Dr. Emory
McOlintock, New York, N. Y.
2. A method for calculating simultaneously all the roots of
an equation. Dr. Emory McOlintock, New York, N. Y.
3. Elliptic functions and the Cartesian curve. Professor
Frank Morley, Haver ford, Pa.
4. Concerning the definition by a system of functional
properties of the function f\z) = sin 7tz . Professor E. Hastings
Moore, Chicago, 111.
5. Bertrand's paradox and the non-euclidean geometry»
Professor George Bruce Halsted, Austin, Texas.
6. Analytical theory of the errors of interpolated values
from numerical tables. Professor R. S. Woodward, New
York, N. Y.
7. Upon the problem of the minimum sum of the distances
of a point from given points. Professor V. Schlegel, Hagen,
8. On the fundamental laws of algebra. Professor Alexander
Macfarlane, Austin, Texas.
9. About cube numbers whose sum is a cube number. Dr.
Artemas Martin, Washington, D.O.
10. Reduction of the resultant of a binary quadric and w-ic
by virtue of its semicombinant property. Professor Henry S.
White, Evanston, 111.
In the absence of their authors, paper No. 7 was presented
by Professor Hyde, paper No. 9 by the Secretary, and No. 10
by Professor Ziwet.
*Bulletin of the American Mathematical Society

In 1894, the first wireless transmission of information using Morse code was demonstrated by Oliver Lodge during a meeting of the British Association at Oxford. A message was transmitted about 150 yards (50-m) from the old Clarendon Laboratory to the University Museum. However, as he later wrote in his Work of Hertz and Some of his Successors, the idea did not occur to Lodge at the time that this might be developed into long-distance telegraphy. "Stupidly enough, no attempt was made to apply any but the feeblest power, so as to test how far the disturbance could really be detected." Nevertheless this demonstration predated the work of Guglielmo Marconi, who began his experiments in 1896.*TIS

1940 John Atanasoff finishes a paper describing the Atanasoff Berry Computer, or ABC, the computer he designed with Clifford Berry to solve simultaneous linear equations. Atanasoff was only able to claim credit for this paper and title of inventor of the electronic digital computer after a long court battle that ended in 1972. The case - initiated on a charge by Honeywell Inc. that Sperry Rand​. Corp. had enforced a fraudulent patent - involved lengthy testimony by Atanasoff and ENIAC inventors Presper Eckert​ and John Mauchly​, who held the patent under review. A judge's ruling that Atanasoff was the true inventor led to invalidation of the ENIAC patent.
A working replica of the original ABC was completed in 1997 by staff and volunteers at Iowa State University at Ames. *CHM

2004 The US Postal Service announced the issue of a stamp honoring 1965 Nobel Laureate Richard Feynman. The day of the announcement was the independence day of Tannu Tuva, and it wasn’t a coincidence. Feynman and his friend and drumming partner Ralph Leighton had spent years trying to visit this small central Asian country near Mongolia. (see story here)

2012 A bit after 2:29 pm EDT, the U. S. Census Bureau said that the United States reached 314,159,265 residents.
Notice this is approximately pi * 100,000,000 .
*Hat tip to Tyler Clark, AMS Graduate Student Blog


1530 Giovanni Battista Benedetti (14 August, 1530 - 20 June 1598) He was taught only by his father, by Tartaglia, and as he says in his writing, "N Tartaglia taught me only the first four books of Euclid, all the rest I learned by myself with great care and study. Nothing is difficult to him who would be learned." (A poster for every teachers wall). He demonstrated the classic constructions using only a "broken compass"; a compass of a fixed opening. Interestingly this was a challenge problem from Tartaglia to Cardan and Ferrari. Benedetti had a very low opinion of Tartaglia, perhaps because he had been his student during the loss of face duel with Ferrarri in which he left before the problems were finished. He also wrote before Galileo on the mechanics of free-fall.

1645 Siguenza y Gongora (August 14, 1645 – August 22, 1700) was a Mexican astronomer and philosopher.*SAU was one of the first great intellectuals born in the Spanish viceroyalty of New Spain. A polymath and writer, he held many colonial government and academic positions. In 1691, he prepared the first-ever map of all of New Spain. He also drew hydrologic maps of the Valley of Mexico. In 1692 King Charles II named him official geographer for the colony. As royal geographer, he participated in the 1692 expedition to Pensacola Bay, Florida under command of Andrés de Pez, to seek out defensible frontiers against French encroachment. He mapped Pensacola Bay and the mouth of the Mississippi: in 1693*Wik

1737 Charles Hutton (14 August 1737 – 27 January 1823) was an English mathematician who wrote arithmetic textbooks. A textbook he wrote while at the Royal Military Academy, Woolwich was later adopted as the first math text by the USMA in West Point, NY and served as the principal math text for two decades.

1777 Hans Christian Oersted (14 Aug 1777, 9 Mar 1851 at age 73) Danish physicist and chemist whose discovery (1820) that an electric current in a wire causes a nearby magnetized compass needle to deflect, indicating the electric current in a wire induces a magnetic field around it, marks the starting point for the development of electromagnetic theory. For this, he can be called “the father of electromagnetism,” for which his name was adopted for the magnetic field strength in the CGS system of units (for which the SI system now uses the henry unit). Philosophically, he had believed nature's forces had a common origin. Oersted was the first to isolate aluminum as a metal (1825). He also made the first accurate determination of the compressibility of water (1822). Late in his career, he researched diamagnetism. In his final years, he turned back to philosophy, and started writing The Soul in Nature. *TIS

1842 Jean-Gaston Darboux, born (August 14, 1842, Nîmes – February 23, 1917, Paris) . French mathematician whose work on partial differential equations introduced a new method of integration (the Darboux integral) and contributed to infinitesimal geometry. He wrote a paper in 1870 on differential equations of the second order in which he presented the Darboux integral. In 1873, Darboux wrote a paper on cyclides and between 1887-96 he produced four volumes on infinitesimal geometry, including a discussion of one surface rolling on another surface. In particular he studied the geometrical configuration generated by points and lines which are fixed on the rolling surface. He also studied the problem of finding the shortest path between two points on a surface. *TIS

1850 Walter William Rouse Ball born in London. (14 August 1850 – 4 April 1925) a British mathematician, lawyer and a fellow at Trinity College, Cambridge from 1878 to 1905. He was also a keen amateur magician, and the founding president of the Cambridge Pentacle Club in 1919, one of the world's oldest such societies.*Wik Rouse Ball wrote A short account of the history of mathematics (1888) which provided a very readable and popular account of the subject. The fourth edition of 1908 was reprinted in 1960. He was also the author of the very popular Mathematical Recreations and Essays first published in 1892 which has run to fourteen editions (the last four being revised by H S M Coxeter).*SAU

1865 Guido Castelnuovo, (14 August 1865 – 27 April 1952) Italian algebraic geometer born. When Jewish students were barred from the state universities in the 1930’s, Castelnuovo organized courses for them. *VFR His father, Enrico Castelnuovo, was a novelist and campaigner for the unification of Italy. Castelnuovo is best known for his contributions to the field of algebraic geometry, though his contributions to the study of statistics and probability are also significant.*Wik He studied under Veronese and followed Cremona as the Advanced Geometry teacher in Rome.

1866 Charles-Jean Étienne Gustave Nicolas de la Vallée Poussin (14 August 1866 - 2 March 1962) was a Belgian mathematician. He is most well known for proving the Prime number theorem. This states that π(x), the number of primes ≤ x, tends to x/Ln(x) as x tends to infinity. (actually by this time the method of attack involved the use of Li(n), the logarithmic integral as described by Gauss).
The prime number theorem had been conjectured in the 18th century, but in 1896 two mathematicians independently proved the result, namely Hadamard (whose proof was much simpler) and Vallée Poussin. The first major contribution to proving the result was made by Chebyshev in 1848, then the proof was outlined by Riemann in 1851. The clue to two independent proofs being produced at the same time is that the necessary tools in complex analysis had not been developed until that time. In fact the solution of this major open problem was one of the major motivations for the development of complex analysis during the period from 1851 to 1896.
The king of Belgium ennobled him with the title of baron. *SAU

1886 Arthur Jeffrey Dempster (14 August, 1886 -11 Mar 1950)Canadian-American physicist who in 1918 built the first mass spectrometer (based on the invention of Francis W. Aston) and discovered isotope uranium-235 (1935). The mass spectrometer is an instrument that uses electric and magnetic fields to separate and measure a sample's atoms according to their mass and relative quantity. In 1935, he discovered that naturally occurring uranium, though mostly uranium-238, contained 0.7% U-235 (later used as the primary fuel in atomic bombs and reactors after Niels Bohr predicted it could be used to produce a chain reaction releasing huge amounts of nuclear fission energy). During WW II, Dempster worked with the secret Manhattan Project that developed the world's first nuclear weapons.*TIS

1888 Julio Rey Pastor (14 August 1888 – 21 February 1962) was a Spanish mathematician and historian of science. Rey proposed the creation of a "seminar in mathematics to arouse the research spirit of our school children.” His proposal was accepted and in 1915 the JAE created the Mathematics Laboratory and Seminar, an important institution for the development of research on this field in Spain.
In 1951, he was appointed director of the Instituto Jorge Juan de Matemáticas in the CSIC. His plans in Spain included two projects: the creation, within the CSIC, of an Institute of Applied Mathematics, and the foundation of a Seminar on the History of Science at the university. *Wik

1904 Léon Rosenfeld (14 August 1904 – 23 March 1974) was a Belgian physicist. He obtained a PhD at the University of Liège in 1926, and he was a collaborator of the physicist Niels Bohr. He did early work in quantum electrodynamics that predates by two decades the work by Dirac and Bergmann. He coined the name lepton. In 1949 Léon Rosenfeld was awarded the Francqui Prize for Exact Sciences. *Wik "The mind is able to build any constellation of concepts"

1906 Eugene Lukacs (14 August 1906 – 21 December 1987) was a Hungarian statistician born in Szombathely, notable for his work in characterization of distributions, stability theory, and being the author of Characteristic Functions, a classic textbook in the field.*Wik

1959 Peter Williston Shor (August 14, 1959; New York, NY - ) is an American professor of applied mathematics at MIT, most famous for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer.
While attending Tamalpais High School, in Mill Valley, California, he placed third in the 1977 USA Mathematical Olympiad. After graduating that year, he won a silver medal at the International Math Olympiad in Yugoslavia (the U.S. team achieved the most points per country that year). He received his B.S. in Mathematics in 1981 for undergraduate work at Caltech,[9] and was a Fellow of William Lowell Putnam Mathematical Competition in 1978. He earned his Ph.D. in Applied Mathematics from MIT in 1985. His doctoral advisor was Tom Leighton, and his thesis was on probabilistic analysis of bin-packing algorithms.
After graduating, he spent one year in a post-doctoral position at the University of California at Berkeley, and then accepted a position at Bell Laboratories. It was there he developed Shor's algorithm, for which he was awarded the Rolf Nevanlinna Prize at the 23rd International Congress of Mathematicians in 1998. Shor always refers to Shor's Algorithm as "the Factoring Algorithm."
Shor began his MIT position in 2003. Currently the Henry Adams Morss and Henry Adams Morss, Jr. Professor of Applied Mathematics in the Department of Mathematics at MIT, he also is affiliated with CSAIL and the Center for Theoretical Physics (CTP).
He received a Distinguished Alumni Award from Caltech in 2007*Wik


1795 George Adams Jr. (1750– August 14, 1795), continued his father's work with his younger brother Dudley, publishing an Essay on Vision (1789) and Astronomical and Geometrical Essays (1789) and succeeding his father as Instrument Maker to King George II and the British East India Company. Born in Southampton he was later appointed Optician to the Prince of Wales. His instruments included barometers, microscopes, orreries, sectors, telescopes, and a variety of electrical appliances. He also made geographical globes.  Wik

1834 Edmond Nicolas Laguerre, (April 9, 1834, Bar-le-Duc – August 14, 1886, Bar-le-Duc) studied approximation methods and is best remembered for the special functions: the Laguerre polynomials.*SAU

1858 George Combe (21 Oct 1788- 14 Aug 1858) Scottish lawyer who turned to the promotion of phrenology and published several works on the subject. He followed Johann Spurzheim who coined the word "phrenology" and promoted it in Europe and Britain, elaborating on "cranioscopy" he learned from Franz Josef Gall in Paris. Gall was a French physician who identified a number of areas on the surface of the head that he linked with specific localizations of cerebral functions and the underlying attributes of the human personality. Combe established the first infant school in Edinburgh and gave evening
lectures. He studied the criminal classes and lunatic asylums wishing to reform them. Andrew Combe, physiologist, was his younger brother. *TIS phrenology was commonly accepted in the 19th and early 20th century. The device pictured here was used to measure the characteristics of the skull for phrenology. *CabinetOfCuriosities ‏@wunderkamercast

1930 Florian Cajori (28 Feb 1859 - 14 Aug 1930)Swiss-born U.S. educator and mathematician whose works on the history of mathematics were among the most eminent of his time.*TIS at times Cajori's work lacked the scholarship which one would expect of such an eminent scientist, we must not give too negative an impression of this important figure. He almost single-handedly created the history of mathematics as an academic subject in the United States and, particularly with his book on the history of mathematical notation, he is still one of the most quoted historians of mathematics today. *SAU

1958 Frederic Joliot-Curie (19 Mar 1900 - 14 August, 1958) French physical chemist, husband of Irène Joliot-Curie, who were jointly awarded the 1935 Nobel Prize for Chemistry for their discovery of artificially prepared, radioactive isotopes of new elements. They were the son-in-law and daughter of Nobel Prize winners Pierre and Marie Curie.*TIS

1967 Jovan Karamata (February 1, 1902–August 14, 1967) was one of the greatest Serbian mathematicians of the 20th century. He is remembered for contributions to analysis, in particular, the Tauberian theory and the theory of slowly varying functions. Karamata was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts in 1946. *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

Sunday, 13 August 2017

On This Day in Math - August 13

It is clear that Economics, if it is to be a science at all,
must be a mathematical science.
~William Jevons

The 225th day of the year; 225 is the ONLY three digit square with all prime digits. Can you find a four digit square with all prime digits?

225 = 01+23+45+67+89

225 = (3!)3+(2!)3+ (1!)3

\(225 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 \) (which means, of course, that \( 225 = (1+2+3+4+5)^2 \)

*Derek Orr @Derektionary


3114 BC The first day of the previous Mayan “long count” calendar (adjusted for the Gregorian Calendar). The long count calendar lasts 22,507,528 days and the previous calendar ended on December 21 of 2012. Many predicted the end of the world at that time (my current theory is that it did NOT end on that day). If the world did NOT end, we went back to year zero of the Mayan calendar.

1661 , Sir Robert Moray, senior courtier to Charles II, advises Wren that since he did not have time to construct microscope-based drawings that the king had requested, the task was passed to Hooke.  This assignment from the king would lead to Hooke's publication of Micrographia in 1665.  *Lisa Jardine, Ingenious Pursuits, pg 62

1672, Christiaan Huygens discovered the Martian south polar cap.*TIS He created the drawing at right, *Dept of History, Un Cal Irvine

1727 Charles-Etienne-Louis Camas elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. Did Euler get the other half? *VFR

1849 Gauss writes to his former student, Mobius, to thank him for sending a copy of Mobius' paper on third order curves and advises him to investigate the form of analytic curves from Gauss' 1799 dissertation. *Carl Friedrich Gauss: Titan of Science
By Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse

1849 George Boole writes to De Morgan to tell him he has received the math professorship at Queen's College Cork. In spite of stating clearly in his application, "I am not a member of any university and have never studied at a college." He had written numerous papers in the mathematical journals including one that won a Gold Medal from the Royal Society, and he included recommendations from some heavyweights of the period, Cayley, De Morgan, Kelland (professor at Edinburgh) and Charles Graves(professor of math at Trinity College Dublin).

1894 Sir William Ramsay and Lord Rayleigh announced the discovery of the first noble gas argon, named after the Greek word ‘argos’ (meaning ‘lazy’) because it was completely unreactive. For this work, Sir William Ramsey was awarded the Nobel Prize in Chemistry and Lord Rayleigh the Nobel Prize in Physics in 1904. *

1898 The first Near Earth Asteroid, 433 Eros was discovered by Carl Gustav Witt *David Dickinson @Astroguyz It was discovered on the same night by Witt in Berlin and Auguste Charlois at Nice. Eros was one of the first asteroids to be visited by a spacecraft, and the first to be orbited and soft-landed on. NASA spacecraft NEAR Shoemaker entered orbit around Eros in 2000, and came to rest on its surface in 2001. On January 31, 2012, Eros passed the Earth at 0.17867 AU (26,729,000 km; 16,608,000 mi), or about 70 times the distance to the Moon. *Wik

1903 the journal Nature reported that helium gas is produced by the radioactive decay of the radium. This key discovery by William Ramsay and Frederick Soddy helped to reveal the structure of atoms. In 1908, Rutherford confirmed that alpha rays and these radium emanations were one and the same: the nuclei of helium atoms, bearing a positive electrical charge. Each were future Nobel laureates in Chemistry. Ramsey won the Nobel Prize in 1904 for his discovery of the noble gases. Rutherford was recognized in 1908 for his investigations into the disintegration of the elements. Soddy was honoured in 1921 for his pioneering contributions to understanding the chemical properties of radioactive elements such as radium and uranium.*TIS

2014 At the opening ceremony of the International Congress of Mathematicians 2014 on August 13, 2014, the Fields Medals (started in 1936) were presented. Among the winners was Maryam Mirzakhani, the first female (and mother) ever to receive the award. (Sadly, she would die within three years of cancer.)
The three other winners were Artur Avila, Martin Hairer, and Manjul Bhargava.
You can read about them here . *Springer


1625 Erasmus Bartholin (13 August 1625, Roskilde – 4 November 1698, Kopenhagen)..Bartholin was the editor of van Schooten's "Introduction to the geometry of Descartes", He also discovered double refraction of light using Icelandic Spar crystals. He worked with Ole Roamer in publishing some of Tycho Brahe's observations. His maternal grandfather was Thomas Fincke, the geometer who invented the terms tangent and secant. (*pb)

1704 Alexis Fontaine des Bertins, (13 August 1704 – 21 August 1771) in 1734 he gave a solution of the tautochrone problem which was more general than that given by Huygens, Newton, Euler or Jacob Bernoulli, and in 1737 he gave a solution to an orthogonal trajectories problem. The methods which he developed to solve these problems led to the calculus of variations. He used what he called the "fluxio-differential" method, so called because it used two independent first-order Leibniz type differential operators. This technique was praised by Johann Bernoulli, Euler and d'Alembert. Fontaine then used differential coefficients instead of differentials and Greenberg shows how Fontaine progressed from a calculus of variations to a calculus of several variables. *SAU

1814 Anders Jonas Ångström (13 August 1814, Lögdö, – 21 June 1874) was a Swedish physicist whose pioneering use of spectroscopy is recognised in the name of the angstrom, a unit of length equal to 10-10 meters. In 1853, he studied the spectrum of hydrogen for which Balmer derived a formula. He announced in 1862 that analysis of the solar spectrum showed that hydrogen is present in the Sun's atmosphere. In 1867 he was the first to examine the spectrum of aurora borealis (northern lights). He published his extensive research on the solar spectrum in Recherches sur le spectre solaire (1868), with detailed measurements of more than 1000 spectral lines. He also published works on thermal theory and carried out geomagnetical measurements in different places around Sweden.*TIS

1819 George Gabriel Stokes born. (13 August 1819 – 1 February 1903) (1st Baronet) British mathematical physicist who studied viscous fluids and formulated his law of viscosity for the speed of a solid sphere falling in a fluid. Other laws and mathematical work for which he is known includes Stokes's theorem, in the field of vector analysis. Stokes also worked in optics, the wave theory of light, diffraction (1849), the ultraviolet spectrum and other spectrum analysis. He investigated the nature of fluorescence and was a founder of the field of geodesy with his study of variations in gravity (1849). From 1849 until his death in 1903, he held the Lucasian Chair of Mathematics at Cambridge (held earlier by Isaac Newton, and more recently by Stephen Hawking). He came from a family with generations of scientists, mathematicians and engineers.*TIS

1861 Cesare Burali-Forti, born(13 August 1861 – 21 January 1931). He discovered the antinomy(paradox) of the class of all ordinals in 1897. He never held a permanent university position for he failed his libera docenze, or license to teach, because of the antagonism to the new methods of vector analysis on the part of some members of the examining committee. *VFR He was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered what came to be called the Burali-Forti paradox of Cantorian set theory. He died in Turin.

1861 Herbert Hall Turner (13 August 1861, Leeds – 20 August 1930, Stockholm) was a British astronomer and seismologist.
He was educated at Clifton College and Trinity College, Cambridge. In 1884 he accepted the post of Chief Assistant at Greenwich Observatory and stayed there for nine years. In 1893 he became Savilian Professor of Astronomy and Director of the Observatory at Oxford University, a post he held for 37 years until his sudden death in 1930.
He was one of the observers in the Eclipse Expeditions of 1886 and 1887. In seismology, he is credited with the discovery of deep focus earthquakes. He is also credited with coining the word parsec.
A few months before Turner's death in 1930, the Lowell Observatory announced the discovery of a new minor planet, and an eleven-year-old Oxford schoolgirl, Venetia Burney, proposed the name Pluto for it to her grandfather Falconer Madan, who was retired from the Bodleian Library Madan passed the name to Turner, who cabled it to colleagues at the Lowell Observatory in the United States. The new minor planet was officially named "Pluto" on 24 March 1930*Wik

1959 Steven Henry Strogatz (August 13, 1959, Torrington, Connecticut - ) is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He is known for his contributions to the study of synchronization in dynamical systems, and for his work in a variety of areas of applied mathematics, including mathematical biology and complex network theory.
In particular, his 1998 Nature paper with Duncan Watts, entitled "Collective dynamics of small-world networks", is widely regarded as a seminal contribution to the interdisciplinary field of complex networks, whose applications reach from graph theory and statistical physics to sociology, business, epidemiology, and neuroscience. As one measure of its importance, it was the most highly cited article about networks between 1998 and 2008, and the sixth most highly cited paper in all of physics.
Strogatz's writing includes the 1994 textbook Nonlinear Dynamics and Chaos, two popular books, and frequent newspaper articles. His most recent book, published in 2009, was The Calculus of Friendship, called "a genuine tearjerker" and "part biography, part autobiography and part off-the-beaten-path guide to calculus". His trade book Sync was chosen as a Best Book of 2003 by Discover Magazine. Strogatz also filmed a series of lectures on chaos theory for the Teaching Company, released in 2008, and, in late January 2010, Strogatz began writing a weekly column on mathematics in The New York Times. These columns, along with many others penned by Strogatz, will appear in a book slated for release in 2012. The New York Times columns have been described as "must reads for entrepreneurs and executives who grasp that mathematics is now the lingua franca of serious business analysis. *Wik


1822 Jean Robert Argand, (July 18, 1768 – August 13, 1822) Argand Diagrams, the method of drawing complex numbers as vectors on a coordinate plane, are named for him, as an amateur mathematician he described them in a paper in 1806. A similar method, although less complete, had been suggested as early as 120 years before by John Wallis, and developed extensively by Casper Wessel(1745-1818), a Norwegian surveyor. (Actually, at the time Wessel lived, the area where he was born was a part of Denmark. Norway became an independent government in 1905 after years of domination by Denmark and Sweden.) It may be that even after these multiple discoveries, the method was unknown to Gauss and he had to rediscover it for himself in 1831 although it has been suggested that Gauss may have discovered the idea as early as Wessel. Some parts of his Demonstratio Nova would seem almost miraculously derived without a knowledge of the ideas of the geometry of complex numbers.
Wessel's paper was published in Danish, and was not circulated in the languages more common to mathematics at that time. It was not until 1895 that his paper came to the attention of the mathematical community, long after the name Argand Diagram had stuck. Incredibly, there were at least three more individuals who may have independently discovered and written on the same idea; Abbe Bruee, C. V. Mourney, and John Warren.
Argand's Book, Essai sur une maniere de representer les quantities imaginaires dans les constructions geometriques, might have suffered the same fate as Wessel except for an unusual chain of events. I give here the version as presented by Michael Crowe in his A History of Vector Analysis
In 1813 J. F. Francais published a short memoir in volume IV of Gergonne's Annales de mathematiques in which Francais presented the geometrical representation of complex numbers. At the conclusion of his paper Francais stated that the fundamental ideas in his paper were not his own, he had found them in a letter written by Legendre to his (Francis') brother who had died. In this letter Legendre discussed the ideas of an unnamed mathematician. Francis added that he hoped this mathematician would make himself known and publish his results.
The unnamed mathematician had in fact already published his ideas, for Legendre's friend was Jean Robert Argand. Hearing of Francais' paper, Argand immediately sent a communication to Gergonne in which he identified himself as the mathematician in Legendre's letter, called attention to his book, summarized its contents, and finally presented an (unsuccessful) attempt to extend his system to three dimensions.
Even with so much interest and attention to the geometry of complex numbers, it was not until Gauss published a short work on the ideas that they became popular.
Translations of both Wallis' and Wessel's papers on the imaginaries can be found in A Sourcebook of Mathematics by David Eugene Smith. (*pb)

1882 Logician William Stanley Jevons died (1 September 1835 – 13 August 1882) . He was a British economist and logician.
Irving Fisher described his book The Theory of Political Economy (1871) as beginning the mathematical method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons' contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. *Wik

1907 Hermann Karl Vogel (April 3, 1841 – August 13, 1907) German astronomer who discovered spectroscopic binaries (double-star systems that are too close for the individual stars to be discerned by any telescope but, through the analysis of their light, have been found to be two individual stars rapidly revolving around one another). He pioneered the study of light from distant stars, and introduced the use of photography in this field.*TIS

1910 Florence Nightingale​ died; (May 12, 1820 – August 13, 1910) She is best remembered for her work as a nurse during the Crimean War​ and her contribution towards the reform of the sanitary conditions in military field hospitals. However, what is less well known about this amazing woman is her love of mathematics, especially statistics, and how this love played an important part in her life's work. *SAU Florence Nightingale had exhibited a gift for mathematics from an early age and excelled in the subject under the tutorship of her father. Later, Nightingale became a pioneer in the visual presentation of information and statistical graphics. Among other things she used the pie chart, which had first been developed by William Playfair in 1801. While taken for granted now, it was at the time a relatively novel method of presenting data.
Indeed, Nightingale is described as "a true pioneer in the graphical representation of statistics", and is credited with developing a form of the pie chart now known as the polar area diagram, or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram, in order to illustrate seasonal sources of patient mortality in the military field hospital she managed. Nightingale called a compilation of such diagrams a "coxcomb", but later that term has frequently been used for the individual diagrams. She made extensive use of coxcombs to present reports on the nature and magnitude of the conditions of medical care in the Crimean War to Members of Parliament and civil servants who would have been unlikely to read or understand traditional statistical reports.*Wik

1968 Oystein Ore, (7 October 1899 in Oslo, Norway – 13 August 1968 in Oslo) Ore is known for his work in ring theory, Galois connections, and most of all, graph theory. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then worked on noncommutative rings, proving his celebrated theorem on embedding a domain into a division ring. He then examined polynomial rings over skew fields, and attempted to extend his work on factorisation to non-commutative rings.
In 1930 the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject. Ore's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life. Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel.*Wik

2008 Henri Cartan (July 8, 1904 – August 13, 2008)is known for work in algebraic topology, in particular on cohomology operations, the method of "killing homotopy groups", and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Cartan also was a founding member of the Bourbaki group and one of its most active participants. His book with Samuel Eilenberg Homological Algebra (1956)[3] was an important text, treating the subject with a moderate level of abstraction and category theory.*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