Monday, 15 August 2022



On Aug 16, 1878 Charles Hermite wrote to J J Sylvester at Johns Hopkins concerned about his accepting a Math Chair in America and questioning 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. Hans Rademacher called this proof “the first major achievement of American mathematics.”

Some background for students: Pentagonal numbers are named for the ways of arranging dots into pentagons, much like the square numbers or triangular numbers. The true or pure pentagonal numbers are 1, 5, 12, 22, 35, 51, 70, 92,...

You can get them by using the formula \(  \frac{3n^2-n}{2} \) with n a positive integer.
But for what we are doing today, we need to also include the generalized pentagonal numbers. They are obtained from the formula given above, but with n taking values in the sequence 0, 1, −1, 2, −2, 3, −3, 4..., producing the sequence 0, 1, 2, 5, 7, 12, 15, 22, 26, 35,...

One of the amazing things about this sequence is that it shows up in relation to finding the sum of the divisors of n, and finding the number of partitions of n. As Euler used it for the Pentagonal Number theorem, it was written out as \( 1 − n − n^2 + n^5 + n^7 − n^{12} − n^{15} + n^{22} + n^{26} − n^{35} − etc\) Notice all these numbers are the same as the ones in the generalized pentagonal numbers, hence, the pentagonal number theorem.

All that is beautiful math, but today I focus on a detail of the theorem that led to the graphic proof. What the terms of the Pentagonal Number theorem really say, and a question about them. If we look, for instance, in the partitions of five, they are {5},{4,1}, {3,2}, {3,1,1}, {2,2,1}, {2,1,1,1,1}, and {1,1,1,1,1} These can be divided into two sets, can you figure out how some are different than the others? Look at the first three. Now look at the last four. Each of the last four have repeats of one or more numbers. The first three are all distinct. Of the three with distinct digits, two of them have an even number of integers in their composition, {4,1} and {3,2}. The other, {5}, has an odd number of integers. And if you look at the exponent of X5 in the theorem, you see that it is positive, and that's what the theorem really says. If you look at all the partitions of any number, this polynomial gives you the the number of even distinct partitions (an even number of integers in it) minus the number of odd distinct partitions. So 5 has one more even than odd, and 7 does as well, but 12 has one more odd than even. but what first aroused Franklin's curiosity, was why there were so many missing exponents, why there were so many like X3 and X4 and X6. These would all have an equal number of odd and even partitions, hence the terms with zero for a coefficient which simply did not appear. what would explain this?

Franklin's insight was that for numbers like 6, the numbers could be matched up into odd and even pairs that offset each other in the count. For example, the distinct partitions of 6 are {6}, {5,1}, {4,2}, {3,2,1} the other seven partitions of 6 all have a repeated value. In his plan, the first two were matched together, and the last two were converted to each other, and he even had a graphic plan to show it always would work.

Here are two partitions of the number 33. The first is a partition into {9,8,7,5,4} The right diagonal which has 3 dots in it, and the bottom row which has 4 dots in it are the key. Since 3 is less than four (and four then, is the smallest number in the partition, we can move the 3 dots in the diagonal to make a new row in the bottom, and reduce the top three rows by one. So the matching partition is {8,7,6,5,4,3} at right. Note that we have changed the odd permutation into an even one. And we can go back by moving the three on the bottom row in the right partition to return to the left. These two always match. But he realized that there might be a situation in which this didn't work. For instance if the number of dots in the diagonal and the number of dots in the bottom row are the same (they share a corner dot) then you couldn't move either one. This can only happen if the bottom row is equal to the diagonal, or if the diagonal is one more than the bottom row. Here are examples of numbers that can't be matched to another. The top row is made up of numbers that have them equal. If you try to shift either one to make and odd partition even, or vice versa it just won't work. And the bottom sets show numbers that can be arranged with a partition that has the lowest row one more than the diagonal. They won't work either.

Now look at these numbers, count the dots, what do you notice. These are all the numbers in the Pentagonal Theorem Polynomial. And try as you may, you can't find another partition of any of these numbers that can't be transformed from odd to even or even to odd. If this partition has an odd number of rows, then the coefficient of that power in the polynomial is positive (5 in top row and 7 in bottom row are both positive coefficients since there is one odd partition that can't be matched to this even partition. The distinct partitions of 7 are {7}, {6,1}. {5,2}, {4,3} and {4,2,1} . Draw the diagrams, 7 can be transformed to {6,1} by dropping the last dot (a diagonal of one) to be a second row. {5,2} and be transformed in the same way to make {4,2,1} but the {4,3} has no match, so 3 evens, 2 odds makes the coefficient one.

I had never seen this before until I read a paper "The Pentagonal Number Theorem and All That" by Dick Koch from 2016. I no longer have the link to it,  sorry!

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)

The harmonic sequence, or sum of the reciprocals of the integers grows to infinity, but slowly. It takes the 227th term (1/227) to finally push it over the value 6.(And don't even think about trying to get to seven!)
A beauty about six primes, 227 + 251 + 257 = 233 + 239 + 263, and if you square each one, 227^2 + 251^2 + 257^2 = 233^2 + 239^2 + 263^2 *Prime Curios.


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 than 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

Sunday, 14 August 2022

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

226 is one more than a square, and one less than a prime.  (Numbers one more than a power, 226=15^2+1 for example, are called Cunningham numbers after English mathematician A. J. C. Cunningham (1842 - 1928).

The binary expression for 226 has the same number of ones and zeros. There are only 49 such year days, 

See More Math Facts for every Year Day here.


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

1003 al-Biruni observed two lunar eclipses from Gurgān,(Azerbaijan)  one on 19 February and the other on 14 August. On 4 June of the following year, 1004, he observed a third lunar eclipse.  *Encylopedia . com

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. **see below

(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
 ** The right triangle theorem in number three is the only known complete proof of any of Fermat's "theorems". During his lifetime, Fermat challenged several other mathematicians to prove the non-existence of a Pythagorean triangle with square area, but did not publish the proof himself. However, he wrote a proof in his copy of Bachet's Diophantus, which his son discovered and published posthumously.

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, Haverford, 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

1912  Why didn't someone warn us sooner??? A newspaper clipping from 1912 that anticipates the global warming potential of burning coal is authentic and consistent with the history of climate science.  


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

Saturday, 13 August 2022

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

225 is also the largest year day which is a square number that is the sum of three distinct positive cubes.  \(15^2= 1^3 + 2^3 + 6^3\)

See Math Facts for every Year Day here.


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. *

 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

1927 Frances Sarnat Hugle (August 13, 1927 – May 24, 1968) was an American scientist, engineer, and inventor who contributed to the understanding of semiconductors, integrated circuitry, and the unique electrical principles of microscopic materials. She also invented techniques, processes, and equipment for practical (high volume) fabrication of microscopic circuitry, integrated circuits, and microprocessors which are still in use today.

In 1962, Hugle co-founded Siliconix, one of Silicon Valley's first semiconductor houses. She is the only woman included in the "Semiconductor Family Tree *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