The Rule(s) of Three and the Probability of Nothing, and of a single success

 

A Re-edit and Posting of a 2008 Blog with additional material (See, I do learn something over time.)

From 1827 Pike's Arithmetic

In my youth, back when dinosaurs roamed the earth, there was “the rule of three”… singular, one, and even then the name was often described as “archaic”. More modern books tended to develop “properties of proportions” or similar terms for the problems of proportionalities. Now there seem to be an abundance of them; including one for witches, and one about businesses. There is not space enough to talk about all of them so I will mention three, of course.
The first rule of three is as old as math, and shows up at least as early as the Hindu mathematician Brahmagupta, and in Fibonacci’s famous Liber Abaci(1202). It was once so common that it was introduced into common language. Abraham Lincoln is quoted in his biography as stating that he learned to "read, write, and cipher to the rule of 3."   So common that student's often wrote verse like the following, in their copy (practice) books.

Multiplication is vexation;

Division is as bad;

The Rule of Three doth puzzle me,

And Practice drives me mad

The most common and longest living form was the direct rule (although there was an inverse rule as well), in which case three numbers would be given and a fourth sought so that the ratio between the third and fourth would match the ratio between the first and second; a:b = c:d. Today students use the ideas in elementary school to complete fraction equivalences, “2/3 is the same as 10/?” Some of the ancient examples grew incredibly complicated.

I suppose the reason I chose to address three of the many “rules of three” is because of the rule of three from language and literature. Three just seems to be the right number for lots of things, there were Three Musketeers, Three Stooges, and Three Coins in the Fountain. It was Goldilocks and the Three Bears, and “bah bah black sheep” had “three bags full.” Comics in the newspaper usually have three panels and many jokes involve a three part ritual where the punch line is the third element, such as the t-shirt with “Great Cities of the World” on the top, and below, one after another, “Paris, Rome, Fargo”. The first two make the last funnier. In language the examples range from “Blood, sweat, and tears, to vidi, vidi, vici. If you don’t think there really is a mental tendency to have three terms, consider that in Churchill’s speech, he actually used four; “I say to the House as I said to ministers who have joined this government, I have nothing to offer but blood, toil, tears, and sweat. “

The final rule of three I would mention is from statistics, and is of more recent origin. It is also, I think, a really clever solution to what is a really difficult problem. Suppose something never happens; how can you assign a probability to it? It is not that it might not happen some day, just not so far. It is just such a problem the statistical rule of there was created to handle. Suppose you stopped at the same gum ball machine every day, but unlike the normal gumball machine, this one did not have a glass you could see into the gumballs inside. You buy a gum ball every day and get red ones, and green ones, but never a blue one. After a while you begin to wonder if they even put a blue one in the machine. So one day, after 20 days of getting all the other colors, over lunch you ask your local statistician (doesn’t everyone have lunch with a statistician?) how to figure out if there really is a blue one in there. He pauses, fork poised in mid-air, and informs you that you can be 95% sure (a common statistical benchmark) that the proportion of blue gum balls is no greater than 14.3%. He had mentally taken three, and divided by one more than the number of failed efforts, to get 3/21 or 1/7 as the upper limit of the possible fraction.
The idea is base on a simple extension of the binomial probability. If you knew that P % of the gum balls were blue, then you could calculate the probability that None showed up in 20 days. The probability would be (1-p)²⁰. Working back through this calculation many times you might notice that the number followed a pattern, a rule of thumb to calculate without tables and calculators, and that turns out to be 3/(n+1), the statistical rule of three. If you wanted greater certainty, you can use the rule of seven, which says that 7/(n+1) will give the 99% interval boundary. So in the case of your gumballs, you can be 99% sure the percentage of blue gumballs is less than 1/3.

But what if after a long string of failures, you have a success.  How does this change your confidence interval?   Thanks to a recent post from John D Cook I now can tell you that as well.  

So suppose you had worked your way as before with twenty failures to get the blue gumball, and then after the aforementioned lunch with a statistician,  you get a blue gumball on the 21st try.  Now what can you say about the expected percentage of blue gumballs.  

After the first success according to the Beta distribution would give a 95% confidence interval of appx. [.1/n, 4.7/n]  .  For our imagined 21 tries, this would be about [.0047, .224]  So our confidence interval has opened up considerably.  

It appears, if I understand correctly, that the blue gumball could have occurred anytime among the first 21 tries and thus would still be the CI.  So if we went another nine tries without success, we would adjust our CI to {.1/30, 4.7/30] ... [ .00333, .157], back much closer to our expectations before we ever had a success.

Comparing this interval to the binomial confidence interval you learned in high school math, p +/- 2 sqrt(p*(1-p)/n).  The customary warning on the normal expectation is beware of p being too high or too low.  Using one success in 30 tries we get a 95% CI of [-.03, .099]... perhaps the negative lower bound is a sign that we have strayed to close to zero with our p-hat.  A nice topic to spring on your AP stats teacher when you get to confidence intervals, but please be kind. 

On This Day in Math - September 13

 

Proof is the idol before whom the pure mathematician tortures himself.

~Sir Arthur Eddington


The 256th day of the year; 256 is the smallest composite to composite power,4⁴.

Paul Erdos conjectured that no power of 2 is the sum of distinct powers of three.

from jim wilder @ wilderlab √256 = 2 • 5 + 6

The sum of the cubes of the first 256 odd numbers is a perfect number. \( \sum\limits_{i=0}^{255} (2i+1)^3 = 8589869056\) the 6th perfect number. (all perfect numbers (except 6) are the sum of the cubes of first 2ⁿ odd cubes for some (but not all) n) (so \( 28 = 1^3 + 3^3\) and \( 496=1^3 + 3^3 + 5^3 + 7^3\)  ). 256 = ?

256 is the middle number in a run of three successive numbers which are all constructible regular n-gons. 255= 3*5*17, is the product of distinct Fermat Primes, 256=2⁸ and is a power of two, and 257 is a Fermat Prime. *HT to Don S. McDonald ‏@McDONewt

See More Math Facts for every Year Date here

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EVENTS

1763 Christopher Irwin’s marine chairs were loaded onto the Princess Louisa to head off to Barbados. Irwin’s chair was being tested alongside Tobias Mayer’s lunar tables and John Harrison’s sea watch.
On 13 September 1763, the log of Lieutenant Patrick Fotheringham records how the ship “Came alongside a Hoy with two Marine Chairs and apparatus for observing the Planet Jupiter in order to finding ye Longde. at Sea the Commissioners for ye Discovery to examine these Machines under ye Direction of Adml. Tyrrell in ye course of his Voyage; Do. came on Bd Mr. Christopher Erwin the Inventor of ye Marine Machine”. *Board of Longitude project, Greenwich

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1789 Wm. Herschel writes to Wollaston, "I have found that Saturn has a satellite which has hitherto escaped our observation...".

In 1789, shortly after this 40 ft instrument was operational, Herschel discovered a new moon of Saturn: Enceladus, . Discovery of a second moon (Mimas) followed, within the first month of observation. As he told Sir Joseph Banks—he directed it to the heavens (August 28th, 1789) before it had half come to its proper lustre. The stars came out well, and no sooner had he got hold of Saturn than a sixth satellite stood revealed to view! Its “younger brother” was detected September 17th.  (I have no way of explaining the date of the letter being four days earlier than the stated date of the actual discovery.  

* buffalolib.org 

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Francis Wollaston (23 November 1731, London – 31 October 1815) was an English priest and astronomer.He achieved some distinction as an astronomer, becoming a member of the Royal Society in 1769 and later serving on its council. He also produced a catalog of stars and nebulae in 1789, which was used by many including his friend, William Herschel, about which he comments near the bottom of the letter.

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1844 The term ABELIAN INTEGRAL is found in a letter of Sept. 8, 1844, from William Henry Fox Talbot: "What is the definition of an Abelian Integral? for it appears to me that most integrals possess the Abelian property." The letter was addressed to John Frederick William Herschel, who, in his reply of Sept. 13, 1844, wrote: "I suppose the most general definition of an Abelian Integral might be taken to be this that between ∫(x) and ∫(φ(x)) there shall subsist an algebraical relation between several such functions."  As a postscript, he adds that "a very curious photographic novelty occurred to me a day or 2 ago" in which he describes how to use a negative to create a positive image.(Talbot's original contributions included the concept of a negative from which many positive prints can be made (although the terms negative and positive were coined by Herschel), and the use of gallic acid for developing the latent image. [The Talbot letters are available here. ] *Jeff Miller Web site & Wik

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1883 Opening of the University of Texas at Austin and Galveston. *VFR

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1890 Scientific American carried an article featuring the latest writing technology for the classroom, a slate pen-tip eraser. The device, invented by Mrs Emma Hudson, nestled a piece of sponge inside a rubber casing which could be wetted to remove some, or all, of the marks on a student slate. (The first pencil tip eraser for a lead pencil had been invented in 1858.)

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1955 Minor Planet (3167) Babcock 1955 RS. Discovered 1955 September 13 at the Goethe Link Observatory at Brooklyn, Indiana. Named in memory of Harold D. Babcock (1882-1968) and in honor of his son Horace W. Babcock, (on whose birthday it was discovered, see BIRTHS below) astronomers at Mount Wilson Observatory, the latter also serving as director of Palomar Observatory. The elder Babcock's precise laboratory studies of atomic spectra allowed others to identify the first "forbidden" lines in the laboratory and to discover the rare isotopes of oxygen. With C. E. St. John and others, he extended Rowland's tables of the solar spectrum into the ultraviolet and infrared. The Babcocks ruled excellent large gratings, including those used in the coudé spectrographs of the 2.5-m and 5-m telescopes, and they measured the distribution of magnetic fields over the solar surface to unprecedented precision. The younger Babcock invented and built many astronomical instruments, including the solar magnetograph, microphotometers and automatic guiders. By combining his polarization analyzer with the spectrograph he discovered magnetic fields in other stars, and he developed important models of sunspots and their magnetism. (M 15089) Name proposed by F. K. Edmondson. *NSEC

Harold Delos Babcock

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1959 Lunik II hit the moon, being the first man-made object to do so.In 1959, the first space probe to strike the moon was the Soviet Luna 2, which crashed east of the Sea of Serenity. Thirty-six hours after its launch, it was the first man-made object to reach a celestial body. *TIS On September 15, 1959, the premier of the USSR, Nikita Khrushchev, presented to the American president Dwight D. Eisenhower a copy of the spherical pennant (used onboard the Luna 2) as a gift. That sphere is located at the Eisenhower Presidential Library and Museum in Abilene, Kansas.*Wik The actual time of collision was September 13, 1959, 21:02:24 UTC

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1983 Osborne Computer declares bankruptcy, two years after producing the first portable computer, the 24-pound Osborne I. Designed by company founder Adam Osborne, the \($1,795\) machine included software worth about \($1,500\). The machine featured a 5-inch display, 64 kilobytes of memory, a modem, and two 5 1/4-inch floppy disk drives.
In April 1981, Byte Magazine Editor-in-Chief Chris Morgan mentioned the Osborne I in an article on Future Trends in Personal Computing. He wrote: I recently had an opportunity to see the Osborne I in action. I was impressed with it's compactness: it will fit under an airplane seat. (Adam Osborne is currently seeking approval from the FAA to operate the unit on board a plane.) One quibble: the screen may be too small for some people's taste.*CHM

*CHM

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2007 Closing date for a prize for a solution to Fermat’s last theorem. Due to inflation the prize of one hundred thousand marks has long been worthless.*VFR (perhaps not completely worthless.) In 1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat’s great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth $50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik

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2013  On this day in 2013, Timothy Gowers and Persi Diaconis were awarded honorary degrees during a special graduation ceremony which formed part of the University of St Andrews' 600th Anniversary celebrations.  They were two of seventeen "international scholars and thinkers", "some of the best minds of our generation", who were honored in this way.  *MacTutor SAU

Gowers

BIRTHS

1755  Oliver Evans, an American mechanic and inventor, was born in Delaware on Sep. 13, 1755.  Evans first came to prominence when he designed and constructed a fully automatic flour mill. Using bucket conveyor belts, Archimedean screws, rotating stirrers, and a variety of hoppers, his mill was able to receive grain, raise it to the top of the mill, distribute it to the milling machinery, grind it to different degrees of fineness, spread and dry the grain, and then package and distribute it, all without human intervention, except to turn the machinery off and on and make repairs when necessary.  The entire mill was driven by a waterwheel.  He received a patent for his automated mill (the third U.S. patent ever granted, signed by Thomas Jefferson, but lost in the patent office fire of 1836), and his brothers implemented his design in their mills on Red Clay Creek in Delaware.

Evans’ best known effort in the realm of steam power was his Oruktor Amphibolis (amphibious digger), a steam-powered dredge that he built for the city of Philadelphia and launched in 1805.  It is described as an amphibious vehicle, but as far as I can tell, the only reason it had wheels on it was to get it to the water, since it weighed in at 17 tons.  It was only marginally successful as a steam dredge, paddling around Philadelphia on the Schuylkill River, before being dismantled in 1808, but it became better known as the years went on, especially after Evans' death in 1819.  Wood engravings of the Oruktor were included in nearly every history of steam power from 1830 on.  *Linda Hall org

*Linda Hall org

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1873 Constantin Caratheodory born. (13 Sep 1873; 2 Feb 1950) He worked on the calculus of variations and the theory of real functions. He is the only modern Greek mathematician “who does not suffer by comparison with the famous names of Greek antiquity.” *VFR.
German mathematician of Greek origin who made important contributions to the theory of real functions and to the theory of point-set measure. He demonstrated that the calculus of variations (the theory of maxima and minima in curves) could be applied not just to smooth curves, but also those with corners. He also contributed to thermodynamics and helped develop Einstein's special theory of relativity. *TIS

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1885 Wilhelm Blaschke  (13 Sep 1885; 17 Mar 1962) German mathematician whose major contributions to geometry concerned kinematics and differential geometry. Kinetic mapping (important later in the axiomatic foundations of various geometries) he both discovered and established it as a tool in kinematics. He also initiated topological differential geometry (the study of invariant differentiable mappings)*TIS

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1912 Horace Welcome Babcock (13 Sep 1912; 29 Aug 2003) was a American astronomer, son of Harold Babcock. Working together, they were the first to measure the distribution of magnetic fields over the surface of the Sun. Horace invented and built many astronomical instruments, including a ruling engine which produced excellent diffraction gratings, the solar magnetograph, and microphotometers, automatic guiders, and exposure meters for the 100 and 200-inch telescopes. By combining his polarizing analyzer with the spectrograph he discovered magnetic fields in other stars. He developed important models of sunspots and their magnetism, and was the first to propose adaptive optics.*TIS

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1913 Herman Heine Goldstine (September 13, 1913 – June 16, 2004), mathematician, computer scientist and scientific administrator, was one of the original developers of ENIAC, the first of the modern electronic digital computers.*Wik

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1920 William Bowen Bonnor ( 9 September 1920 – 17 August 2015) is a mathematician and gravitation physicist best known for his research into astrophysics, cosmology and general relativity. For most of his academic career he has been a professor of mathematics at the University of London.

Bonnor's research was published in about 150 papers in various scientific journals. The most cited paper described the effect of gravitation on Boyle's law; this has been extensively used in the theory of star formation. Another well-cited paper applies Newtonian dynamics to the formation of galaxies in cosmology. However, most of Bonnor's research was on the theory of general relativity.*Wik

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1923 Peter K Henrici (13 Sept 1923 , 13 March 1987) He made "major contributions to preserving and enriching our mathematical heritage. His books and papers have helped greatly in maintaining numerical analysis as a subject with beauty, order, and structure, in the spirit of the great pioneers of the past. He keeps reminding us to ask what Gauss would have done with a parallel computer - or with a pocket calculator."
"Henrici was truly an internationally recognized numerical analyst, having written 11 books and over 80 research papers. A very cultured person who was also a gifted pianist, he was an outstanding teacher particularly interested in helping younger mathematicians. His lectures showed great polish and inspired many. His guidance and unselfish contributions as an editor have helped make Numerische Mathematik the respected journal it is. For this alone, we owe him a great debt of gratitude." *SAU

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1926 Sidney David Drell (September 13, 1926 – December 21, 2016) was an American theoretical physicist and arms control expert. He is a professor emeritus at the Stanford Linear Accelerator Center (SLAC) and a senior fellow at Stanford University's Hoover Institution. Drell is a noted contributor in the field of quantum electrodynamics and particle physics. The Drell–Yan process is partially named after him. He was one of the winners of the 2000 Enrico Fermi Award.*Wik

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DEATHS

1296 Johannes Campanus (1220 in Novara, Italy - 13 Sept 1296 in Viterbo, Italy) also known as Campanus of Novara, was an Italian mathematician who published a Latin edition of Euclid's Elements. He also wrote on astronomy.*SAU

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1940 Myron Mathisson (15 Dec 1897 , 13 Sept 1940) was a Polish Jew known for his work on the equations of motion of bodies in general relativity and for developing a new method to analyze the properties of fundamental solutions of linear hyperbolic differential equations. In particular, he derived the equations for a spinning body moving in a gravitational field and proved, in a special case, the Hadamard conjecture on the class of equations that satisfy the Huygens principle. His work still exerts influence on current research.*Cornell Univ Library

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1924 Antony Hewish FRS FInstP (11 May 1924 – 13 September 2021) was a British radio astronomer who won the Nobel Prize for Physics in 1974 (together with fellow radio-astronomer Martin Ryle) for his role in the discovery of pulsars. ( Several prominent scientists protested the omission of Bell Burnell, though she maintained that the prize was presented appropriately given her student status at the time of the discovery) He  was also awarded the Eddington Medal of the Royal Astronomical Society in 1969

In late Nov 1967, using a radio telescope, Hewish and Ph.D. student Jocelyn Bell  observed an unusual signal corresponding to a sharp burst of radio energy at a regular interval of approximately one second. It is believed that rapidly rotating neutron stars with intense electromagnetic fields emit radio waves from their north and south poles. From a great distance, these radio emissions are perceived in pulses, similar to the way one sees the light from a lighthouse's rotating lantern. Hewish and Bell's discovery served as the first evidence of this phenomenon.

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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

Charles the Obscure, The one you never heard of, but should have.

  

JAC Charles

My good and generous friend, Dave Renfro, sometimes finds time in his busy writing and research schedule to send me copies of some of the old documents he's working through.  Recently a collection from him included a 1979 Isis article by J. B. Gough.

One in particular, which I opened only weeks after the anniversary of the death of the unfortunate Jacques Charles, called the Geometer in his lifetime to avoid confusing him with Charles the Balloonist, and sometimes Charles the inventor, who is J. A. C Charles, and the namesake for the chemistry law that is sometimes, probably without merit, called Charles' Law.  Unfortunately, the point of Gough's article is that they did become confused, often due to lack of effort or interest on the part of historical writers, to the point that now you can find little or nothing about the "geometer" and much of what you find about the more famous Charles is, in fact, a mis-credit for the work of Charles the Geometer. 
I would have assumed that articles like the one by Gough in 1979, and another by the famous science historian Roger Hahn a few years later would have set the record straight, but in fact as I scanned a couple of biographies on the internet they still contain the residue of the confusion.
One of the first points of confusion is that you may see the date for the induction of the famous Charles into the Academy of Sciences as 1785.  This is off by almost a full decade, and is the actual date of the induction of Charles the Geometer.   The famous Charles would be inducted into the  Académie des Science in 1795, almost four years after the other Charles had gone to an early grave.

The image is an illustration of JAC Charles first Balloon flight on 1 Dec, 1783

*Wik

A second, and even more common error is that you will often still see biographies of the famous J A C Charles that list him as a mathematician, and sometimes add something like, "most of his papers were in mathematics."  

Wikipedia currently lists JAC Charles as " French inventor, scientist, mathematician, and balloonist.,"and then follow up with, "Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences, entering on 12 May 1785." 

Searching for Jacque, the Geometer may be a long search, and unless you stumble across a copy of this blog, or the document I started from, you may find nothing at all.

 JAC Charles, the famous, it seems, was NOT a mathematician, and wrote almost nothing, including nothing about mathematics, and only the sketchiest outline of the law which, due to the graciousness of more capable scientists (you can read the name Joseph Louis Gay-Lussac here) would eventually bear his name.  J. B. Gough goes so far in his article in Isis to declare that this Charles was "nearly a mathematical illiterate."  He points out that of the eight articles credited to J. A. C Charles by Poggendorf, seven were actually by the more obscure (and more mathematical) Charles.

Here is how Wikipedia credits his axquiring credit for the law.

Charles's law (also known as the law of volumes), describing how gases tend to expand when heated, was first published by natural philosopher Joseph Louis Gay-Lussac in 1802,[2] but he credited it to unpublished work by JAC Charles, and named the law in his honour.

Around 1787 Charles did an experiment where he filled five balloons to the same volume with different gases. He then raised the temperature of the balloons to 80 °C (not at constant temperature) and noticed that they all increased in volume by the same amount. This experiment was referenced by Gay-Lussac in 1802 when he published a paper on the precise relationship between the volume and temperature of a gas. Charles' law states that under constant pressure, an ideal gas' volume is proportional to its absolute temperature. The volume of a gas at constant pressure increases linearly with the absolute temperature of the gas. The formula he created was V1/T1 = V2/T2.

Today many sources use the expression Gay-Lussac's Law. This law was independently and nearly simultaneously stated by John Dalton.

Gau-Lussac

In 1804, Gay Lussac and Jean-Baptiste Biot made a hydrogen-balloon ascent; a second ascent the same year by Gay-Lussac alone attained a height of 7,016 metres (23,018 ft) in an early investigation of the Earth's atmosphere. He wanted to collect air samples at different heights to record differences in temperature and moisture.

In 1752, when the obscure Jacque Charles was only 20 years old, Minutes of the French Academy of Science kept by Lavoisier of the meeting at which the report was read identify Charles as "professeur de mathematiques 'a l'ecole de Nanterre, a suburb of France.  His work was so advanced that, in the words of Roger Hahn in his 1981 Isis article, "More Light on Charles the Obscure", : 

{The committee of academicians examining it inferred that Charles was familiar with Euler's text on differential calculus, and that he showed promise. They said, "les solutions de ces deux problemes nous paraissent meriter les encouragements de l'Academie, mais elles ont pour objet des questions trop elementaires pour que nous les jugeions dignes d'etre impri-mees."}

Gay-Lussac, in his published paper about the law credits Charles with this statement (English translation) "Before going further, I must jump ahead. Although I had recognized on many occasions that the gases oxygen, nitrogen, hydrogen, carbonic acid, and atmospheric air all expand identically from 0° to 80°, citizen Charles had noticed the same property in these gases 15 years ago; however, since he never published his results, it is only by great luck that I knew it. He had also sought to determine the expansion of water-soluble gas, and he had found for each a particular dilation different from that of other gases. In this respect, my experiments differ strongly from his".
Gough points as far back as 1870 with evidence to the ongoing confusion.  A donation of the physics lectures of the more famous Charles to the Institute de France prompted a notice in Comptes Rendes with a brief description of Charles life and career on February 7 of 1870.  Shortly after the publication a letter to the Perpetual Secretary questioned if the article had not confused Charles the balloonist with the geometer.  A followup with a brief description of the lives of both men was given in Comptes Rendes on March 7 of the same year.

I first wrote about this in 2013, and today, nine years later, there is no biography of Charles the geometer in St Andrews MacTutor.  Encyclopedia dot com also has no article about Charles the geometer, but writes about J A C Charles, "Charles published almost nothing of significance." 

"Assertions to the contrary notwithstanding, there is no evidence that Charles knew anything but the rudiments of mathematics. Through an unfortunate confusion of names, biographers and bibliographers have completely confounded J. A. C. Charles with another contemporary known only as Charles le Géomètre.

 Wikipedia also has no page for Jacque Charles the geometer, but says, "(J A C )Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences,... He was sometimes called Charles the Geometer."

So what of the mathematical Charles, who has so sadly been overlooked for several hundred years?  It seems that he was born around 1752 in Cluny, France in the Burgendy region of France.  He seems to have attempted to gain entry to the Paris Academy of Science, to which both Charleses would eventually belong, at the ripe age of about 18 while still living in Cluny.  His article, on a problem in Algebra, probably reflecting his youth, was rejected by the academy as being too elementary.  Two years later, he  submit a second paper two years later, "sur le dynamique" impressed the judges who inferred that the author must be aware of Euler's differential calculus.  When it was read to the full meeting of the  academy, Lavoisier's minutes of the meeting list Charles as a Professor of Mathematics at the school at Nanterre, most probably referring to a popular academy in that suburb of Paris that trained young Nobles who were intending to proceed to Engineering colleges.
 Over the period from 1779 to 1785, Charles continued to submit articles to the Academy.  In all he submitted seven articles all of which were deemed appropriate for publication.  After the seventh, Condercet, who had reviewed the paper for the Academy, pointed out that this, and any of the previous six, certainly merited his admission to the Academy.  His major obstacle seems to have been the opposition to his appointment by Laplace, who was motivated more by his rivalry with Charles' sponsor, Charles Bossut(famed for his textbooks in France).  Finally a vote on May 11, 1785 (this date is often given as May 12, I use Hahn's date as few have better records to the history of the Paris Academy) secured Charles his membership.

Charles, through his association with Bossut, had already obtained the position as the Chair of Hydrolics, which brought with it, admission to the Paris Academy of Architecture, which made Charles a duel academician.

Somewhere around 1789 Charles was onset with a paralysis which greatly affected his ability to write.  It is said that he had, for a short while,  to request another member to sign him in at meetings.  He did manage to learn to write with his other hand, but never with full control.  A few years later, in 1791, he died apparently from the same paralytic problem.  Only sketchy records exist of his death and burial due to the confusion created by events related to the revolution.  It appears he died on (or near) August 20, 1791 and it is reported that he was buried at Saint-Germain-l'Auxilles on the 22nd of the same month.  A memorial service was held at the Oratoire on Dec 29,1971.  Due to the events of the revolution, no M'emoires of the Paris Academy were produced that year, and hence no obituary for members who died.

I am still trying to learn more about the actual writings of Jacques Charles, the Geometer and would love to hear from those who have greater knowledge on this subject, and the man himself, to share.

Here is the post I have about the lesser known Charles at On This Day in Math:

1791 Jacques Charles, (probably 1752, August 20, 1791) Mathematician, born in Cluny, France. He is often confused with the Jacques A. C. Charles who is credited (or mis-credited) with Charles' Law and much of the work of this Jacques Charles. During the Late 18th Century both were active in Paris scientific circles and both were members of the Paris Scientific Academy. They were often distinguished by calling this one Charles the Geometer, and the other Charles the Balloonist since JAC Charles was active in promoting the use of hydrogen balloons and had designed the first balloon that is known to have been used.
This Jacques Charles is also frequently referred to by the historians who are aware of the confusion between them as Charles the Obscure.
Jacques Charles first contact with the Paris Acad of Sci was in a 1770 letter in which he submitted an article on a problem in Algebra at about the age of 18. It was turned down by the academy due to it's elementary level. The address shows that he was living in Cluny at the time. But two years later a second correspondence to the academy is read to the Academy, and Lavosier's minutes list his position as a professor of Mathematics as the school at Nanterre, on the outskirts of Paris. It is suspected that this was a preparatory school for young nobles who were training to become engineers that had been located there since the 1760's.
Between 1779 and 1785 Jacques Charles submitted seven articles to the Paris Academy, all of which were deemed worthy of publication, but only the last seemed to merit his admittance to this esteemed group. Condorcet, who was then perpetual secretary of the Academy said that this, as well as his prior papers certainly warranted his admission. It seems that Laplace, who had a conflict with Charles' mentor/sponsor, Bossut, and had been blocking his entry. With some behind the scenes effort by Lavosier had created a new geometry section, he was voted into the Academy on May 11 (often given as May 12).
By 1792 due to the confusion of their names, much of the mathematical work of Charles the Geometer would be credited to Charles the Balloonist and the "Geometer" would become the "obscure". Even the energetic J. C. Poggendorf would miscredit eight papers by the geometer to the other, and in biographies of J. A. C. Charles written even in the 20th century, you will see him credited as a "mathematician" and statements that suggest that "most of his writings were in mathematics." J. B. Gough, writing in an article in Isis in 1979 describes the ballooning Charles as, "nearly a mathematical illiterate."
The confusion between the two men of common names was exacerbated by the timing of this Charles' death. The year 1791 and the problems related to the Revolution made this the Academy of Sciences did not publish a Memoires, and as a result, no eloge's for the members who died in that year. Strangely, this was still four years before the better remembered Charles was admitted to the Academy.
He was buried (according to an old note to Cvomptes Rendes) at St. Germain l'auxerrois, but this seems hard to confirm in the church records. (*J. B. Gough)
Charles was also the Royal Professor of Hydrodynamics, and as such was also inducted into The Academy of Architecture. *Roger Hahn, More Light on Charles the Obscure, Isis, Vol. 72, No. 1 (Mar., 1981), pp. 83-86

On This Day in Math - September 12

   

One began to hear it said that World War I was the chemists' war, World War II was the physicists' war, World War III (may it never come) will be the mathematicians' war.
~Davis, Philip J. and Hersh, Reuben, The Mathematical Experience, Boston: Birkhäuser, 1981.


The 255th day of the year; 255= 2⁸-1 and is the fourth Mersenne number that is not a prime. However it is the product of three distinct Fermat Primes, 3*5*17, and therefore the regular 255-gon is constructible with straightedge and compass. *HT to Don S. McDonald ‏@McDONewt who also pointed out that the next two numbers, 256 and 257 are also constructible since one is a power of two, and the other is a Fermat Prime.

255 is a also a repdigit in base 2 (11111111) in base 4 (3333), and in base 16 (FF). (What is the next number that is a repdigit in base two and base 4?) John D Cook has a nice overview of Mersene Numbers and Mersene Primes

255 is the number of levels on the Pac-Man arcade machine prior to the "kill screen" rendering game over... why 255? (Computer people know )*Jim Wilder@wilderlab

In the 3n+1 or Collatz problem, the sequence for n = 255 reaches higher than any other year day, to the value of 19,682. The previous high value was at 27, when the sequence reached 9232.
See More Math Facts for every Year Date here

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EVENTS1662: 1st Astronomer Royal's 1st recorded observation: John Flamsteed (aged 16) observes (partial) solar eclipse *Thony Christie ‏@rmathematicus  

He extended this experience by accurately calculating the solar eclipses of 1666 and 1668. He was responsible for several of the earliest recorded sightings of the planet Uranus, which he mistook for a star and catalogued as '34 Tauri'. The first of these was in December 1690, which remains the earliest known sighting of Uranus by an astronomer.

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1740 In a letter to Euler dated August 29th, 1740, Philippe Naudé (the Younger) asked Euler in how many ways a number n can be written as a sum of positive integers. In his answer written on September 12th (23rd), Euler explained that if we denote
this “partition number” by p(n), then

*Correspondence of Leonhard Euler with Christian Goldbach, Springer

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1859, Urbain Le Verrier presented a paper to the Academy of Sciences in which he attributed the advance of the perihelion of Mercury to an undiscovered planet, which he called Vulcan, closer to the Sun than Mercury or to a second asteroid belt so close to the Sun as to be invisible.

Speculation about, and even purported observations of, intermercurial bodies or planets date back to the beginning of the 17th century. The case for their probable existence was bolstered by the French mathematician Urbain Le Verrier who, by 1859, had confirmed unexplained peculiarities in Mercury's orbit and predicted they had to be the result of gravitational influences of another unknown nearby planet or series of asteroids. A French amateur astronomer's report that he had observed an object passing in front of the Sun that same year led Le Verrier to announce that the long sought after planet, which he gave the name Vulcan, had been discovered at last.  

Many searches were conducted for Vulcan over the following decades, but despite several claimed observations, its existence could not be confirmed. The need for the planet as an explanation for Mercury's orbital peculiarities was later rendered unnecessary when Einstein's 1915 theory of general relativity showed that Mercury's departure from an orbit predicted by Newtonian physics was explained by effects arising from the curvature of spacetime caused by the Sun's mass.  *Wik 

Vulcan in a lithographic map from 1846 *Wik

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1876 Johns Hopkins University, the first true graduate school in the U.S., formally opened its doors with an address—and without the benefit of a prayer—by the evolutionist T. H. Huxley. A Presbyterian minister wrote “It is bad enough to invite Huxley. It were better to have asked God to be present. It would have been absurd to ask them both.” *VFR

Huxley had little formal schooling and was virtually self-taught. He became perhaps the finest comparative anatomist of the later 19th century. He worked on invertebrates, clarifying relationships between groups previously little understood. Later, he worked on vertebrates, especially on the relationship between apes and humans. After comparing Archaeopteryx with Compsognathus, he concluded that birds evolved from small carnivorous dinosaurs, a view now held by modern biologists.

The tendency has been for this fine anatomical work to be overshadowed by his energetic and controversial activity in favour of evolution, and by his extensive public work on scientific education, both of which had significant effects on society in Britain and elsewhere. *Wik

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1883 Sylvester writes to Johns Hopkins President Gilman of his intent to resign his chair effective January 1 of the following year. He had grown lonely for his homeland and was hoping for a position at Oxford.

 He returned to England to take up the Savilian Professor of Geometry at Oxford University. He was the first Jew to hold an Oxbridge chair, and held this chair until his death, although in 1892 the University appointed a deputy professor to the same chair. 

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1933 Leo Szilard formulates an idea for a sustained nuclear chain reaction.
On a miserable, wet, quintessentially English autumn day, at the intersection where Russell Square meets Southampton Row, Leó Szilárd waited irritably at a traffic light waiting for it to change from red to green. He had just attended a lecture by the great English physicist Ernest Rutherford. Rutherford, known to many as the father of nuclear physics, was discussing the newly prophesied release of energy from atoms, most notably by science-fiction pioneer H G Wells in his book The World Set Free (inspired by Sir Fred Soddy's book, The Interpretation of Radium, When Well's wrote The World Set Free in 1914, he dedicated the novel to Soddy). In his baritone voice, Rutherford, the acknowledged master of the atomic domain, dismissed this fanciful idea as nonsense. Any thought of releasing the energy locked in atoms, he said, was “moonshine”. {I love this story, but many accounts say he had only read the article which appeared in The Times Newspaper that morning and not attended Rutherford's talk.}(Some historians believe Rutherford may have dismissed the idea because he felt that his opinion might cause some other countries from pursuing the idea.)
Szilard realized as he stepped off that curb was that if we found an element that when bombarded by one neutron would release two neutrons, it could lead to a chain reaction that could possibly release vast amounts of energy.

Ironically, when the first atomic bomb test was conducted in the New Mexico desert in the deathly stillness of the morning, in the midst of war and hope, the flash was so bright that it would have been seen reflected off the moon. It was, literally, “moonshine”. The rest was history. *Ashutosh (Ash) Jogalekar, Scientific American Blogs

Leo Szilard was a Hungarian-German-American physicist and inventor. He conceived the nuclear chain reaction in 1933, patented the idea in 1936, and in late 1939 wrote the letter for Albert Einstein's signature that resulted in the Manhattan Project that built the atomic bomb.

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1935, In December of 1935 an announcement in the Annals of Mathematical Statistics reported that:  "For some time there has been a feeling that the theory of statistics would be advanced in the United States by the formation of an organization of those persons especially interested in the mathematical aspects of the subject. As a consequence, a meeting of interested persons was arranged for September 12, 1935, at Ann Arbor, Michigan. At the meeting, it was decided to form an organization to be known as the Institute of Mathematical Statistics."  

The Institute was founded in 1935 with Harry C. Carver and Henry L. Rietz as its two most important supporters. 

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1958, Jack Kilby demonstrated his invention of a miniaturized electronic circuit to his supervisor at Texas Instruments, now recognized as the first integrated circuit to be built and operated. On 6 Feb 1959, he applied for a patent, which was eventually issued on 23 Jun 1964. *TIS 

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1959 The Soviet spaceship LUNA 2 was launched. It was the first spacecraft to land on the moon. Exactly eleven years later, LUNA 12 was launched. It was the first spacecraft to land on the moon, collect samples, and return to Earth.*VFR  "Land" may be a gentler phrase than crashed into the surface of the moon.   

Prior to impact, two sphere-shaped pennants with USSR and the launch date engraved in Cyrillic were detonated, sending pentagonal shields in all directions. Luna 2 did not detect radiation or magnetic belts around the Moon.

Model of the Luna II, *Wik

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In 1962, President John F. Kennedy delivered perhaps the most famous space speech he gave. Speaking at the stadium of Rice University, the text of his speech included these memorable lines, "We choose to go to the moon. We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too. It is for these reasons that I regard the decision last year to shift our efforts in space from low to high gear as among the most important decisions that will be made during my incumbency in the office of the Presidency." (the entire text of his speech is here)*TIS

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1992 Mae Carol Jemison (born October 17, 1956) is an American engineer, physician,  and

former  astronaut. She became the first African American woman to travel into space when she served as a mission specialist aboard the Endeavor space shuttle for eight days. 

Born in Alabama and raised in Chicago, Jemison graduated from Stanford University with degrees in chemical engineering as well as African and African-American studies. She then earned her medical degree from Cornell University. Jemison was a doctor for the Peace Corps in Liberia and Sierra Leone from 1983 until 1985 and worked as a general practitioner. In pursuit of becoming an astronaut, she applied to NASA.

Jemison left NASA in 1993 and founded a technology research company. She later formed a non-profit educational foundation and through the foundation is the principal of the 100 Year Starship project funded by DARPA. Jemison also wrote several books for children and appeared on television several times, including in a 1993 episode of Star Trek: The Next Generation. She holds several honorary doctorates and has been inducted into the National Women's Hall of Fame and the International Space Hall of Fame.

*Wik 

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BIRTHS
1725 Guillaume-Joseph-Hyacinthe-Jean-Baptiste Le Gentil de la Galaziere(12 Sep 1725; 22 Oct 1792) was a French astronomer. He discovered what are now known as the Messier objects M32, M36 and M38, as well as the nebulosity in M8, and he was the first to catalogue the dark nebula sometimes known as Le Gentil 3 (in the constellation Cygnus).&Wik He attempted to observe the transit of Venus across the sun by travelling to India in 1761. He failed to arrive in time due to an outbreak of war. He stayed in India to see the next transit which came eight years later. This time, he was denied a view because of cloudy weather, and so returned to France. There, he found his heirs had assumed he was dead and taken his property.*TIS A more detailed blog about his life is at Renaissance Mathematicus

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1771 Antoine-André-Louis Reynaud (12 Sept 1771, 24 Feb 1844) Reynaud published a number of extremely influential textbooks. He published a mathematics manual for surveyors as well as Traité d'algèbre, Trigonométrie rectiligne et sphérique, Théorèmes et problèmes de géométrie and Traité de statistique. His best known texts, however, were his editions of Bézout's Traité d'arithmétique which appeared in at least 26 versions containing much original work by Reynaud.
It appears that Reynaud became interested in algorithms when he was working with de Prony. At this time de Prony was very much involved in trying to get his logarithmic and trigonometric tables published and it seems to have made Reynaud think about analysing algorithms. Certainly Reynaud, although his results in this area were rather trivial, must get the credit for being one of the first people to give an explicit analysis of an algorithm, an area of mathematics which is of major importance today. *SAU

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1838 Arthur von Auwers (12 Sep 1838; 24 Jan 1915) Georg Friedrich Julius Arthur von Auwers was a German astronomer known for his life's work making extremely accurate catalogs of stellar positions and motions. He also researched solar and stellar parallaxes, making a new reduction of James Bradley's 18th century Greenwich observations and measurements of star distances. Auwers also observed double stars, and accurately calculated the orbits of the Sirius and Procyon systems before the faint companions to the bright stars were seen. He redetermined the distance to the sun several times, making use of transits of Venus and an approach of a minor planet.*TIS

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1851 Sir Franz Arthur Friedrich Schuster FRS (12 September 1851 – 17 October 1934) He discovered and photographed a comet during an eclipse in Egypt: first time a comet discovered in this way has been photographed. *NSEC Schuster is perhaps most widely remembered for his periodogram analysis, a technique which was long the main practical tool for identifying statistically important frequencies present in a time series of observations. He first used this form of harmonic analysis in 1897 to disprove C. G. Knott's claim of periodicity in earthquake occurrences. He went on to apply the technique to analyzing sunspot activity. This was an old interest. In 1875 Stewart's friend and Roscoe's cousin, the economist Jevons, reported, "Mr. A Schuster of Owens College has ingeniously pointed out that the periods of good vintage in Western Europe have occurred at intervals somewhat approximating to eleven years, the average length of the principal sun-spot cycle."
Schuster is credited by Chandrasekhar to have given a fresh start to the radiative transfer problem. Schuster formulated in 1905 a problem in radiative transfer in an attempt to explain the appearance of absorption and emission lines in stellar spectra.*Wik

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1877 Georg Karl Wilhelm Hamel (12 September 1877 – 4 October 1954) was a German mathematician with interests in mechanics, the foundations of mathematics and function theory.*Wik

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1894 Dorothy Maud Wrinch (12 September 1894 – 11 February 1976) married names Nicholson, Glaser) was a mathematician and biochemical theorist best known for her attempt to deduce protein structure using mathematical principles.

Wrinch often attended meetings of the Heretics Club run by Charles Kay Ogden, and it was through a 1914 lecture organised by Ogden that she first heard Bertrand Russell speak. She graduated in 1916 as a wrangler.

For the academic year 1916–1917, Wrinch took the Cambridge Moral Sciences tripos and studied mathematical logic with Russell in London. In December she was invited to Garsington Manor, the home of Russell's then mistress Ottoline Morell, and there encountered Clive Bell and other Bloomsbury Group members, and in 1917 she introduced Russell to Dora Black who would later become his second wife.

Wrinch's first paper was a 1917 defence of Russell's philosophy, and between 1918 and 1932 she published 20 papers on pure and applied mathematics and 16 on scientific methodology and on the philosophy of science. At the 1928 International Congress of Mathematics in Bologna she delivered the paper "On a method for constructing harmonics for surfaces of revolution." She also presented on "Harmonics Associated with Certain Inverted Spheroids" at the 1932 ICM in Zürich." The papers she wrote with Harold Jeffreys on scientific method formed the basis of his 1931 book Scientific Inference. In the Nature obituary Jeffreys wrote, "I should like to put on record my appreciation of the substantial contribution she made to [our joint] work, which is the basis of all my later work on scientific inference.*Wik

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1897 Irène Joliot-Curie (12 Sep 1897; 17 Mar 1956) French physicist and physical chemist, wife of Frédéric Joliot-Curie, who shared the 1935 Nobel Prize for Chemistry "in recognition of their synthesis of new radioactive elements." For example, in their joint research they discovered that aluminum atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. She was the daughter of Nobel Prize winners Pierre and Marie Curie. From 1946, she was director of the Radium Institute, Paris, founded by her mother. She died of leukemia, like her mother, resulting from radiation exposure during research.*TIS

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1900 Haskell Brooks Curry (12 Sep 1900; 1 Sep 1982)American mathematician who was a pioneer of modern mathematical logic. His research in the foundations of mathematics led him to the development of combinatory logic. Later, this seminal work found significant application in computer science, especially in the design of programming languages. Curry worked on the first electronic computer, called ENIAC, during WW II. He also formulated a logical calculus using inferential rules. In 1942, he published Curry's paradox, which occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules.*TIS

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1921 Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number theory.
He was a member of the Bourbaki group, and filmed some of their meetings. A French television documentary on Bourbaki broadcast some of this footage in 2000.*Wik

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1960 Nassim Nicholas Taleb( 12 September 1960 - ) is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist. His work concerns problems of randomness, probability, complexity, and uncertainty.

Taleb is the author of the Incerto, a five-volume work on the nature of uncertainty published between 2001 and 2018 (notably, The Black Swan and Antifragile). He has taught at several universities, serving as a Distinguished Professor of Risk Engineering at the New York University Tandon School of Engineering since September 2008. He has also been a practitioner of mathematical finance and is currently an adviser at Universa Investments. The Sunday Times described his 2007 book The Black Swan as one of the 12 most influential books since World War II.

Taleb criticized risk management methods used by the finance industry and warned about financial crises, subsequently profiting from the Black Monday in 1987 and late-2000s financial crisis. He advocates what he calls a "black swan robust" society, meaning a society that can withstand difficult-to-predict events. He proposes what he has termed "antifragility" in systems; that is, an ability to benefit and grow from a certain class of random events, errors, and volatility, as well as "convex tinkering" as a method of scientific discovery, by which he means that decentralized experimentation outperforms directed research. *Wik

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DEATHS
1869 Peter Mark Roget (18 Jan 1779, 12 Sep 1869) English physician who, in 1814, invented a "log-log" slide rule for calculating the roots and powers of numbers. After studying medicine at the University of Edinburgh, he helped establish a medical school at Manchester, and practiced in London (1808-40). Upon retirement, from age 61 to 73, he produced his famous Thesaurus of English Words and Phrases (1852). He was a fellow of the Royal Society from 1815, and its secretary from 1827.*TIS

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1888 Richard Anthony Proctor (23 Mar 1837, 12 Sep 1888) English astronomer who first suggested (1873) that meteor impacts caused lunar craters, rather than volcanic action. He studied the motion of stars, their distribution, and their relation to the nebulae. In 1867 he prepared a map of the surface of Mars on which he named continents, seas, bays and straits (in the same manner that Riccioli used on his map of the moon). However, he did not perceive "canals" on the surface, which later Schiaparelli identified. Proctor participated in expeditions of 1874 and 1882 to observe the transit of Venus. He was very successful popularizing astronomy by his writings in books, periodicals, and lectures he gave as far abroad as Australia and America (where he stayed after 1881).*TIS

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1906 Ernesto Cesaro (12 March 1859 , 12 Sept 1906) died of injuries sustained while aiding a drowning youth. In addition to differential geometry Cesàro worked on many topics such as number theory where, in addition to the topics we mentioned above, he studied the distribution of primes trying to improve on results obtained in this area by Chebyshev. He also contributed to the study of divergent series, a topic which interested him early in his career, and we should note that in his work on mathematical physics he was a staunch follower of Maxwell. This helped to spread Maxwell's ideas to the Continent which was important since, although it it hard to realise this now, it took a long time for scientists to realize the importance of his theories.
Cesàro's interest in mathematical physics is also evident in two very successful calculus texts which he wrote. He then went on to write further texts on mathematical physics, completing one on elasticity. Two further works, one on the mathematical theory of heat and the other on hydrodynamics, were in preparation at the time of his death.
Cesàro died in tragic circumstances. His seventeen year old son went swimming in the sea near Torre Annunziata and got into difficulties in rough water. Cesàro went to rescue his son but sustained injuries which led to his death. *SAU

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1918 Maxime Bochner  (August 28, 1867 – September 12, 1918) was an American mathematician who published about 100 papers on differential equations, series, and algebra. He also wrote elementary texts such as Trigonometry and Analytic Geometry. Bôcher's theorem, Bôcher's equation, and the Bôcher Memorial Prize are named after him. *Wik

After receiving his doctorate under Felix Klein in 1891 he returned to Harvard for a lifetime of teaching and research in differential equations. *VFR

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1933 Leonard James Rogers (30 March 1862, 12 Sept 1933) Rogers was a man of extraordinary gifts in many fields, and everything he did, he did well. Besides his mathematics and music he had many interests; he was a born linguist and phonetician, a wonderful mimic who delighted to talk broad Yorkshire, a first-class skater, and a maker of rock gardens. He did things well because he liked doing them. Music was the first necessity in his intellectual life, and after that came mathematics. He had very little ambition or desire for recognition.

Rogers is now remembered for a remarkable set of identities which are special cases of results which he had published in 1894. Such names as Rogers-Ramanujan identities, Rogers-Ramanujan continued fractions and Rogers transformations are known in the theory of partitions, combinatorics and hypergeometric series. *SAU

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1940 Annie Louise MacKinnon Fitch (June 1, 1868 – September 12, 1940) was a Canadian-born American mathematician who worked with Felix Klein and became a professor of mathematics at Wells College. She was the third woman to earn a mathematics doctorate at an American university.

She graduated in 1889, and remained at the University of Kansas for graduate study in mathematics, becoming the third mathematics graduate student at the university and the first woman. She earned a master's degree in 1891, remaining one more year at the university to work there with Henry Byron Newson.

In 1892, MacKinnon transferred to Cornell University. She finished her doctorate there in 1894, supported as an Erastus Brooks fellow. Her dissertation, Concomitant Binary Forms in Terms of the Roots, was supervised by James Edward Oliver, and also thanked James McMahon as a faculty mentor. This made her the third woman to earn a mathematics doctorate at an American university, following Winifred Edgerton Merrill in 1886 at Columbia University in 1886 and Ida Martha Metcalf at Cornell in 1893.

MacKinnon taught high school mathematics in Lawrence, Kansas from 1890 to 1892. After her return from Europe in 1896, she became professor of mathematics at Wells College, a women's college in Aurora, New York; she was the only mathematician on the faculty. She also served as registrar for the college for 1900–1901.

In 1901, MacKinnon married Edward Fitch, an American classics scholar who had been at Göttingen at roughly the same time as MacKinnon, and later taught at Hamilton College. After marrying, she gave up her mathematical career.[2]

She died on September 12, 1940, in Clinton, New York. A scholarship in mathematics at Hamilton College was established in her name by her husband.

2005 Serge Lang  (May 19, 1927 – September 12, 2005) was a French-born mathematician who spent most of his life in the USA. He is best-known for his outstanding undergraduate text-books.*SAU He was a member of the Bourbaki group. Lang was born in Paris in 1927, and moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated from the California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951. He held faculty positions at the University of Chicago and Columbia University (from 1955, leaving in 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University. *Wik
Lang's Algebra, a graduate-level introduction to abstract algebra, was a highly influential text that ran through numerous updated editions. His Steele prize citation stated, "Lang's Algebra changed the way graduate algebra is taught...It has affected all subsequent graduate-level algebra books." It contained ideas of his teacher, Artin; some of the most interesting passages in Algebraic Number Theory also reflect Artin's influence and ideas that might otherwise not have been published in that or any form. *Wik

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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