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

---

EVENTS

1662: 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.

---

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

---

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

---

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

---

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. 

---

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.

---

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. 

---

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 

---

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

---

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

---

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 

------------------------------------------------------------------------------------------------------------------------------

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

---

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

---

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

---

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

---

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.

Hamel was born in Düren, Rhenish Prussia. He studied at Aachen, Berlin, Göttingen, and Karlsruhe. His doctoral adviser was David Hilbert. He taught at Brünn in 1905, Aachen in 1912, and at Technische Universität Berlin in 1919. In 1927, Hamel studied the size of the key space for the Kryha encryption device. He was an Invited Speaker of the International Congress of Mathematicians in 1932 at Zurich and in 1936 at Oslo. He was the author of several important treatises on mechanics. He became a member of the Prussian Academy of Sciences in 1938 and the Bavarian Academy of Sciences in 1953.[5] He died in Landshut, Bavaria. *Wik

---

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

---

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

---

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

---

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

---

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

---

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

---

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

---

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

---

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

---

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

---

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.

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

---

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

Some History of a Weighty Problem (repost from 2012)

  A while back my blog got a nice mention on Gary Antonick’s “Numberplay” in the New York Times. That seems only fair as I was in the process of writing this post about one of the problems in his column which relates back to a nice old recreational problem from way back.

Gary’s version of the problem reads like this:

You have a balance scale and a single chain with thirteen links.
Each link of the chain weighs one ounce. How many links of the chain
do you need to break in order to be able to weigh items from 1 to 13 ounces
in 1-ounce increments?

This is a complication of the ancient problem in two ways, first by having to divide up the chain to get links, but also because it does not say how the weighing is to be performed.

In recreational history such “balance scale” problems have two basic forms, one in which all the weights have to go on one side to balance the unknown object, and a more clever approach (my bias) that allows known weights to be on both pans of the balance. In the end Gary’s solution goes for the both-sides solution which allows the chain to be cleverly cut in only one place (producing three sections of one, three, and nine lengths) allowing the weighing of any integer weight as requested.(Cut the fourth link and remove it for the one, leaving three on one end of it, and nine on the other)

Searching for older versions of the problem, I quickly found a post in the Problem of the Week section of a 1961 Popular Science.

This one particularly allows the weights to be placed on both pans of the balance.
The solution a month later not only provides the same solution approach as Gary’s column, but also gives a bit of (not quite correct) history of the problem.

The credits to Tartaglia and Bachet are not wrong, they are just not complete. This is understandable because the attributions probably came from one of the outstanding recreational mathematics books of the early 20th century, Mathematical Recreations and Essays by W.W.Rouse BALL, in which he also credits Bachet and Tartaglia:

Both solutions were given over three hundred years earlier than Tartaglia, by Leonardo of Pisa, often known now as Fibonacci. From Sigler’s translation of the famous Liber Abaci I find:

Fibonacci also posted a version avoiding the use of weights in both pans by requiring that the total weight for each increment must be presented on a given day, in this case where each ounce was represented in a valuable metal, requiring the powers of two solution.

From David Singmaster's notes on the Chronology of Recreational Mathematics I found an earlier reference, but do could find no more about the subject named there

"c1075 Tabar_: Mift_h al-mu`_mal_t - first Use of 1,3,9,... as Weights."

If some reader knowledgeable about this source can provide more information I would be very grateful.

Even among those whose historical education has fully informed them of the earlier usages, the use of Bachet’s name is still common, as illustrated in a relatively new article which suggests a newer version of the problem from Edwin O’Shea’s BACHET’S PROBLEM: AS FEW WEIGHTS TO WEIGH THEM ALL

The generalized Bachet’s problem that we will explore here is that of finding appropriate weights when one replaces 40 with any positive integer. The full generalization, due to Park and studied further by Rødseth, not only tells us the minimum number of parts needed when 40 is replaced by any m but all possible ways to accordingly break up a given m. Furthermore, we can also count the number of distinct ways to break up such an m. For example, when we replace 40 by m = 25 we’ll still need no more than four parts but there are now nine ways to break up 25 to solve Bachet’s problem. Written as partitions with four parts, these are:
25 = 1 + 3 + 9 + 12 = 1 + 3 + 8 + 13 = 1 + 3 + 7 + 14
= 1 + 3 + 6 + 15 = 1 + 3 + 5 + 16 = 1 + 3 + 4 + 17
= 1 + 2 + 7 + 15 = 1 + 2 + 6 + 16 = 1 + 2 + 5 + 17

This brings us back to the NY Times version of the problem, but we might ask, how would you split the 13 link chain if you had to be able to pay any amount from 1 to 13 ounces of gold on a given day, as in the Fibonacci's second version of the problem?

On This Day in Math - September 11

  

We have already considered with disfavour the possibility of the universe having been planned by a biologist or an engineer; from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
~Sir James Jeans

The 254th day of the year; 254 is the maximum number of pieces a flat pizza could be cut into with n straight lines.... find n. (for help, see bottom of this post, a good quadratic problem)

254 is the average of consecutive primes,

and 254 = 2⁸ - 2¹

Probability Fact @ProbFact points out that: Odds of drawing a straight in a 5-card hand: 254 to 1.

---

EVENTS 

1632 Torricelli's first letter to Galileo. "We have direct evidence on the scope and trend of Torricelli’s scientific studies during his stay at Rome in the first letter (11 September 1632) of his surviving correspondence, addressed to Galileo on behalf of Castelli, who was away from Rome. In acknowledging receipt of a letter from Galileo to Castelli, Torricelli seized the opportunity to introduce himself as a mathematician by profession, well versed in the geometry of Apollonius, Archimedes, and Theodosius; he added that he had studied Ptolemy and had seen “nearly everything” by Brahe, Kepler, and Longomontanus. These studies had compelled him to accept the Copernican doctrine and to become “a Galileist by profession and sect”; he had been the first in Rome to make a careful study of Galileo’s Dialogo sopra i due massimi sistemi, published in February of that year (1632).*encyclopedia.com

After Torricelli's father died, between 1626 and 1627 he traveled to Rome with his whole family (his mother and two brothers) to study with the Benedictine friar, Benedetto Castelli.

Torricelli would be assigned the position of private secretary of Castelli. He used the money obtained with work to pay for his studies so he could stay in the position and studying at the University College of Sapienza until 1632. Later, Castelli appointed Torricelli to replace him as the teacher in mathematics, mechanics, hydraulics, and astronomy in the University College of Sapienza. 

*Torricelli w/ barometer *Chemistry World

---

1789 Alexander Hamilton appointed the first secretary of the U.S. Treasury. It is because of him that we did not adopt the English system of counting money, but a decimal system instead. *VFR Certainly it is hazardous to give one person credit for any decision in a democracy. For example, in 1784 Thomas Jefferson had proposed a decimal currency system based on the Spanish dollar, with coins for 10 dollars, 1 dollar, 1/10 dollar, and 1/100 dollar; possibly supplemented by a half-dollar, "double tenth", and "five copper piece". One argument he advanced in favor of this system was that the 1/100-dollar coin would be similar in value to existing copper coins. The Spanish Dollar was already in fairly common use in the US. *Wik

The name "dollar" originates from Bohemia and a 29 g silver-coin called the Joachimsthaler. North American colonist commonly used the Spanish peso or "piece of eight" (its value was 8 reales) has always held first place, and this coin was also called the "dollar" as early as 1581. Spanish dollars or "pieces of eight" were distributed widely in the Spanish colonies in the New World.  The dollar was derived from shortening the name of the city in the valley where the silver was mined named after Saint Joachim.  The coins were called Joachimsthaler (From the valley of Saint Joachim).  This mouthful became shortened in common usage to thaler or taler, and then eventually to dollar.  

The origin of the dollar symbol, $, was adopted from the Spanish abbreviation for pesos, "p^s".  There seem to have been much flexibility in how it was written as the 1776 diary of  Ezra l'Hommedieu, a member of the New York Provencial Assembly had over a dozen different symbols in his diary beginning with a single vertical bar and proceeding to two vertical bars. *F Carjori 

The image of l'Hommedieu's diary from Cajori's History of Mathematical Notations

The earliest U.S. dollar coins did not have any dollar symbol. The first occurrence in print is claimed to be from 1790s, by a Philadelphia printer Archibald Binny. The $1 United States Note issued by the United States in 1869 included a large symbol consisting of a "U" with the right bar overlapping an "S" like a single-bar dollar sign, as well as a very small double-stroke dollar sign in the legal warning against forgery.

(If any one has an image of this coin I would love a copy.  Many early U S Dollar coins had no denomination on them at all, and no sign of the dollar symbol on any I have seen.

---

1820 André Marie Ampere (1775-1836) was professor of mathematics at the École Polytechnique from 1809. On 11 September 1820 he heard of H. C. Ørsted's discovery that a magnetic needle is acted on by a voltaic current. Only a week later, on 18 September, Ampère presented a paper to the Academy containing a much more complete exposition of that and kindred phenomena. On the same day, Ampère also demonstrated before the Academy that parallel wires carrying currents attract or repel each other, depending on whether currents are in the same (attraction) or in opposite directions (repulsion). This laid the foundation of electrodynamics.*Wik

---

In 1822, it was announced by the College of Cardinals that henceforth "the printing and publication of works treating of the motion of the earth and the stability of the sun, in accordance with the opinion of modern astronomers, is permitted." When in two weeks pope Pius VII ratified the Cardinals' decree, the Catholic Church finally officially accepted the Copernican principle that on 22 Jun 1633 Italian scientist Galileo had been imprisoned for championing. (This is an over-generalization of the charges against Galileo.) It was not until 1835 that the Vatican removed Galileo's Dialogue Concerning the Two Chief World Systems from its list of banned books. Finally 31 Oct 1992, the Catholic Church admitted that Galileo had been correct. *TIS

---

In 1831, Charles Darwin and Captain Robert Fitzroy traveled from London to Plymouth to inspect the Beagle. This was Darwin's first sight of the ship on which he would sail on a voyage of discovery leading to his famous theory of evolution. *TIS

---

1831 After a four hour disputation in Latin, Jacobi was appointed professor at the University of K¨onigsburg. While there he inaugurated what was then a complete novelty in mathematics— research seminars—assembling the more advanced students and interested colleagues. [DSB 7, 50] *VFR

Jacobi’s seminars at Königsberg are widely seen as the birth of the modern mathematical research seminar, a practice that was soon emulated in other universities across Germany and eventually throughout the world.

This model became especially influential in the German mathematical tradition, laying the groundwork for the vibrant research culture that would develop in places like Göttingen under figures like Gauss, Riemann, and later Hilbert.

His initiative also influenced the structure of doctoral education, emphasizing collaborative research and discussion, not just individual study.

---

1893 Edgeworth sends greetings to Karl Pearson, "I hope that you flourish in Probabilities." *The History of Statistics: The Measurement of Uncertainty Before 1900
By Stephen M. Stigle

---

1923 Sixteen year old Donald Coxeter writes to Eric H. Neville (who had worked with Ramanujan) at the request of Literary scholar and suffragette, Edith Morley. "I am going to buy your book on the Fourth Dimension as I am awfully keen on that sort of thing. I am writing a book on 'Dimensional Analogy' of which I enclose an outline." Neville met with Coxeter and after a brief interview advised that, "You must leave school at once! They're not teaching you right!" He had him tutored by Alan Robson, Master at Marlborough College near Stonehenge. *Siobhan Roberts, King of Infinite Space

---

1933 In a speech at British Association meeting, Ernest Rutherford confidently dismissed the possibility of atomic energy. In a 2011 paper , John G Jenkins wrote "In the 1930s Ernest Rutherford (1871–1937) repeatedly suggested, sometimes angrily, that the possibility of harnessing atomic energy was “moonshine.” Yet, as war approached he secretly advised the British government to “keep an eye on the matter.” I suggest that Rutherford did not really believe his “moonshine” claim but did have profound reasons for making it. If I am correct, then this casts additional light on his personality, stature, and career." *Physics in Perspective

---

1940 The first remote computation -- from Dartmouth College to AT&T Bell Laboratories -- is demonstrated during a meeting of the American Mathematical Association. At Dartmouth, George Stibitz​ set up a terminal that allowed attendees to perform remote calculation by telegraph wire with the Complex Calculator in New York City. Stibitz had first tested the connection on September 9, an event memorialized by a plaque in front of McNutt Hall at Dartmouth College.*CHM

---

1958  Jack Kilby successfully tests the first integrated circuit at Texas Instruments to prove that resistors and capacitors could exist on the same piece of semiconductor material. His circuit consisted of a sliver of germanium with five components linked by wires. Along with Bob Noyce, he is considered the inventor of the integrated circuit (IC). *CHM

---

1981 NBC Magazine broadcasts a story about Rubik's cube on TV. The cube had begun production in 1977 in Hungary and after a couple of years began to sweep across Europe. In 1981, the rage hit the US. In November of 1981, the US would hold 1st American Rubik's Cube Championships. *Mark Longridge, A Rubik's Cube Chronology 

---

In 1997, the Mars Global Surveyor, launched in Nov 1996, went into an elliptical orbit around Mars. To drop into a lower orbit the original mission plan was to use a braking effect by dipping into the upper Martian atmosphere. The lower orbit was a better position for mapping purposes. However, the aerobraking method originally planned was suspended for several weeks to give engineers time to develop more gentle manoeuvers to protect the craft when a solar array failed to deploy correctly, and was flexing excessively. It was to spend two years mapping the surface of Mars. *TIS

*Gunter's Space Page

2001   Let's Roll!: Ordinary People, Extraordinary Courage,

Todd Morgan Beamer's work required him to travel up to four times a month, sometimes for as long as a week. In 2001, he earned a five-day trip to Italy with his wife for being a top sales performer. They returned home on Monday, September 10, at 5:00 pm EDT. Although Beamer could have left that night for a Tuesday business meeting in California, he chose instead to spend time with his pregnant wife, who was due with their third child the following January. He left home at 6:15 the next morning to take an early flight from Newark to San Francisco to meet with representatives of the Sony Corporation at 1:00 pm, planning to return on a red-eye flight that night.

Flight 93 was scheduled to depart at 8:00 am, but the Boeing 757 did not leave until 42 minutes later because of runway traffic delays. Four minutes later, American Airlines Flight 11 crashed into the World Trade Center's North Tower. At 9:03 am, 17 minutes later, as United Airlines Flight 175 struck the South Tower, Flight 93 was climbing to cruising altitude, heading west over New Jersey and into Pennsylvania. At 9:25 am, while above eastern Ohio, its pilot radioed Cleveland controllers to ask about an alert that had appeared on his cockpit screen to "beware of cockpit intrusion." Three minutes later, Cleveland controllers heard screams over the cockpit's open microphone. Moments after that, the hijackers, led by Lebanese national Ziad Jarrah, took control of the plane, disengaged the autopilot, and told passengers, "Keep remaining sitting [sic]. We have a bomb on board." Beamer and the other passengers were moved to the back of the plane. Within six minutes, the aircraft changed course and headed for Washington, 

Several passengers made phone calls to loved ones, who told them about the two planes that had crashed into the World Trade Center in New York City and the third into the Pentagon in Arlington County, Virginia. Beamer tried to place a credit-card call through a phone on the back of a plane seat, but was routed to a customer-service representative, who transferred him to GTE airphone supervisor Lisa Jefferson. With FBI agents listening to the call, Beamer told Jefferson that hijackers had taken over Flight 93 and that one passenger had been killed. He said two of the hijackers had knives and that one appeared to have a bomb strapped around his waist. When the hijackers veered the plane sharply south, Beamer exclaimed, "We're going down! We're going down!"

After this, the passengers and flight crew decided to act. According to accounts of cell-phone conversations, Beamer, Mark Bingham, Tom Burnett, and Jeremy Glick formed a plan to retake the plane. They were joined by other passengers, including Lou Nacke, Rich Guadagno, Alan Beaven, Honor Elizabeth Wainio, Linda Gronlund, and William Cashman, along with flight attendants Sandra Bradshaw and CeeCee Lyles, in discussing their options and voting on a course of action, ultimately deciding to storm the cockpit. Beamer told Jefferson that the group planned to "jump on" the hijackers and crash the plane before the hijackers could carry out their plan. He recited the Lord's Prayer and the 23rd Psalm with Jefferson, prompting others to join in. He asked Jefferson, "If I don't make it, please call my family and let them know how much I love them." After this, Jefferson heard muffled voices and Beamer clearly answering, "Are you ready? Okay. Let's roll." These were the last words from Beamer that Jefferson heard.

According to the 9/11 Commission Report, the cockpit voice recorder revealed pounding and crashing against the cockpit door and shouts and screams in English. "Let's get them!" a passenger cried. A hijacker shouted, "Allahu akbar." Jarrah repeatedly pitched the plane to throw passengers off their feet, but they continued their assault. At 10:02:17, a male passenger said, "Turn it up!" A second later, a hijacker said, "Pull it down! Pull it down!" At 10:02:33, Jarrah was heard pleading, "Hey! Hey! Give it to me. Give it to me. Give it to me. Give it to me. Give it to me. Give it to me. Give it to me. Give it to me." The plane crashed upside down[12] into an empty field in Shanksville, Pennsylvania, at 563 miles per hour (906 km/h), killing everyone on board. It was 20 minutes of flying time from its suspected target, either the White House or the U.S. Capitol in Washington, D.C. According to Vice President Dick Cheney, President George W. Bush had given an order to shoot the plane down if it continued toward Washington.

Todd Morgan Beamer was born on November 24, 1968, in Flint, Michigan, to David Beamer, an IBM sales representative, and Peggy Jackson Beamer, a muralist. He was the middle child of three and the only son. Beamer and his sisters, Melissa and Michele, were raised "with a strong biblical value system and work ethic".[citation needed] The family relocated to Poughkeepsie, New York, and later to Wheaton, Illinois, a suburb west of Chicago, where David worked at Amdahl, a computer technology company.

Beamer married Lisa Brosious on May 14, 1994, in Peekskill, New York, and they moved to Plainsboro, New Jersey, where Beamer began working with Oracle Corporation, selling systems applications and database software as a field marketing representative. Within months, he was promoted to account manager. He held that position until his death. They had two sons, and their daughter was born in January 2002. *Wik 

---

BIRTHS

1623 Stephano Angeli (21 Sept 1623 in Venice - 11 Oct 1697 )was an Italian mathematician who worked on infinitesimals and used them to study spirals, parabolas and hyperbolas.(James)Gregory studied with Angeli in Padua from 1664 to 1668 and learnt from him about series expansions of functions. *SAU The word abscissa is first recorded in 1659 Angeli, according to Moritz Cantor.

---

1798 Franz Ernst Neumann (September 11, 1798 – May 23, 1895) was a German mineralogist, physicist and mathematician.
Neumann was born in Joachimsthal, Margraviate of Brandenburg, located not far from Berlin. In 1815 he interrupted his studies at Berlin to serve as a volunteer in the Hundred Days against Napoleon, and was wounded in the Battle of Ligny. Subsequently he entered Berlin University as a student of theology, but soon turned to scientific subjects. His earlier papers were mostly concerned with crystallography, and the reputation they gained him led to his appointment as Privatdozent at the University of Königsberg, where in 1828 he became extraordinary, and in 1829 ordinary, professor of mineralogy and physics. His 1831 study on the specific heats of compounds included what is now known as Neumann's Law: the molecular heat of a compound is equal to the sum of the atomic heats of its constituents.

Devoting himself next to optics, he produced memoirs which entitle him to a high place among the early searchers after a true dynamical theory of light. In 1832, by the aid of a particular hypothesis as to the constitution of the ether, he reached by a rigorous dynamical calculation results agreeing with those obtained by Augustin Louis Cauchy, and succeeded in deducing laws of double refraction closely resembling those of Augustin-Jean Fresnel. In studying double refraction, with his deduction of the elastic constants (on which the optical properties depend) Neumann employed the assumption that the symmetry of the elastic behavior of a crystal was equal to that of its form. In other words, he assumed that the magnitudes of the components of a physical property in symmetric positions are equivalent. This assumption substantially reduced the number of independent constants and greatly simplified the elastic equations. However, four decades passed before Neumann elaborated his application of symmetry in a course on elasticity in 1873. This principle was later formalized by his student Woldemar Voigt (1850–1918) in 1885: ‘‘the symmetry of the physical phenomenon is at least as high as the crystallographic symmetry,’’ which became a fundamental postulate of crystal physics known as ‘‘Neumann’s principle’’. In 1900, Voigt attributed this principle to Neumann’s 1832 paper even though, at most, all that was present in that work was an implicit assumption that the symmetry of the phenomenon was equal to that of the crystal. Bernhard Minnigerode (1837–1896), another student of Neumann, first expressed this relation in written form in 1887 in the journal Neues Jahrb. Mineral Geol. Paleontol. (Vol. 5, p. 145).

Later, Neumann attacked the problem of giving mathematical expression to the conditions holding for a surface separating two crystalline media, and worked out from theory the laws of double refraction in strained crystalline bodies. He also made important contributions to the mathematical theory of electrodynamics, and in papers published in 1845 and 1847 established mathematically the laws of the induction of electric currents. His last publication, which appeared in 1878, was on spherical harmonics (Beiträge zur Theorie der Kugelfunctionen). *Wik

---

1816 Carl Zeiss ( 11 September 1816 – 3 December 1888) was a German scientific instrument maker, optician and businessman. In 1846 he founded his workshop, which is still in business as Carl Zeiss AG. Zeiss gathered a group of gifted practical and theoretical opticians and glass makers to reshape most aspects of optical instrument production. His collaboration with Ernst Abbe revolutionized optical theory and practical design of microscopes. Their quest to extend these advances brought Otto Schott into the enterprises to revolutionize optical glass manufacture. The firm of Carl Zeiss grew to one of the largest and most respected optical firms in the world.*Wik

---

1847 Mary Watson Whitney (11 Sep 1847; 20 Jan 1921) American astronomer who trained with Maria Mitchell and succeeded her as professor and director of the Vassar College Observatory. Mary Whitney was in the first Vassar class and became Maria's first student. As Mitchell had before her, Whitney championed science education the advancement of professional opportunities for women. She developed the astronomy department. Four years before her 1910 retirement, there were 160 students and eight different astronomy courses, including some of the first courses anywhere on astrophysics and on variable stars. During her tenure as director, the Observatory staff published 102 papers in major astronomical journals reporting their work on comets, asteroids, and variable stars. From 1896, photographic plates were used to study and measure star clusters.*TIS

photograph, probably from the 1880s, shows Maria (left) and Mary (right) in front of Vassar’s Almost Great Refractor. *Linda Hall org

---

1877 Sir James Hopwood Jeans (11 Sep 1877; 16 Sep 1946) was an English physicist, astronomer, and mathematician who was the first to propose that matter is continuously created throughout the universe. He made other innovations in astronomical theory but is perhaps best known as a writer of popular books about astronomy. Died in Dorking, Surrey.*TIS  Famous quote, "We have already considered with disfavour the possibility of the universe having been planned by a biologist or an engineer; from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician."

---

1884 Harvey Fletcher (11 Sep 1884; 23 Jul 1981) American acoustical engineer who was the first to demonstrate stereophonic sound (1934). He was a trail blazing investigator of the nature of speech and hearing, noted for his contributions in acoustics, electrical engineering, speech, medicine, music, atomic physics, sound pictures, and education. He guided the development of the Western Electric Hearing Aid, the first such device to use vacuum tubes. He developed a group survey method using recorded sound of decreasing volume which has wide acceptance in schools throughout the nation.*TIS

---

1890 Euphemia Lofton Haynes (September 11, 1890 - July 25, 1980) After graduating from Washington D.C. Miner Normal School with distinction, she went on to earn an undergraduate mathematics major (and psychology minor) from Smith College in 1914. In 1917 she married Harold Appo Haynes.

[He earned a bachelor's degree in electrical engineering at the University of Pittsburgh, master's degree in education at the University of Chicago, and a doctorate in education at New York University. Dr. Haynes was named associate superintendent of schools in 1948 and became the first assistant superintendent of schools - head of black public schools - in 1951.]

Euphemia pursued graduate studies in mathematics and education at the University of Chicago, earning a masters degree in education in 1930. She continued her graduate work in mathematics at the Catholic University of America where in 1943 she became the first African-American woman to earn a Ph.D. in mathematics. Her dissertation on "The Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences" was written under the supervision of Professor Aubrey Landrey.

Euphemia Haynes devoted her life to education in the Washington, D.C. area for forty-seven years, including teaching mathematics at Armstrong High School and Dunbar High School. She became a professor of mathematics at Miner Teachers College in 1930 where she established the mathematics department and served as chair of the Division of Mathematics and Business Education (in 1955 Minor Teachers College and Wilson Teachers College united to form the District of Columbia Teachers College.) From July 1966 to July 1967, Haynes served as the first woman to chair the District of Columbia School Board. She played a central role in the integration of the DC public schools. Upon her death, she left $700,000 to the Catholic University of America which was used to establish the Euphemia Lofton Haynes Chair in the Department of Education and to support a student loan fund in the School of Education. *ASC

---

1930 Vera Turán Sós (11 September 1930 – 22 March 2023) was a Hungarian mathematician who specialized in number theory and combinatorics. She was a student and close collaborator of both Paul Erdős and Alfréd Rényi. She also collaborated frequently with her husband Pál Turán, an analyst, number theorist, and combinatorist. Until 1987, she worked at the Department of Analysis at the Eötvös Loránd University, Budapest. Afterwards, she was employed by the Alfréd Rényi Institute of Mathematics. She was elected a corresponding member (1985) and member (1990) of the Hungarian Academy of Sciences. In 1997, Sós was awarded the Széchenyi Prize.

One of her contributions is the Kővári–Sós–Turán theorem concerning the maximum possible number of edges in a bipartite graph that does not contain certain complete subgraphs. Another is the following so-called friendship theorem proved with Paul Erdős and Alfréd Rényi: if, in a finite graph, any two vertices have exactly one common neighbor, then some vertex is joined to all others. In number theory, Sós proved the three-gap theorem, conjectured by Hugo Steinhaus and proved independently by Stanisław Świerczkowski.

---

1998 Kenkichi Iwasawa (11 Sept 1917 in Shinshuku-mura (near Kiryu), Gumma Prefecture, Japan - 26 Oct 1998 in Tokyo, Japan ) In the late 1960s Iwasawa made a conjecture for algebraic number fields which, in some sense, was the analogue of the relationship which Weil had found between the zeta function and the divisor class group of an algebraic function field. This conjecture became known as "the main conjecture on cyclotomic fields" and it remained one of the most outstanding conjectures in algebraic number theory until it was solved by Mazur and Wiles in 1984 using modular curves. "it is no exaggeration to say that Iwasawa's ideas have played a pivotal role in many of the finest achievements of modern arithmetical algebraic geometry on such questions as the conjecture of B Birch and H Swinnerton-Dyer on elliptic curve; the conjecture of B Birch, J Tate, and S Lichtenbaum on the orders of the K-groups of the rings of integers of number fields; and the work of A Wiles on the modularity of elliptic curves and Fermat's Last Theorem." *SAU

---

DEATHS

1760 Louis Godin (28 February 1704 Paris – 11 September 1760 Cadiz) was a French astronomer and member of the French Academy of Sciences. He worked in Peru, Spain, Portugal and France.
He was graduated at the College of Louis le Grand, and studied astronomy under Joseph-Nicolas Delisle. His astronomical tables (1724) gave him reputation, and the French Academy of Sciences elected him a pensionary member. He was commissioned to write a continuation of the history of the academy, left uncompleted by Bernard le Bovier de Fontenelle, and was also authorized to submit to the minister, Cardinal André-Hercule de Fleury, the best means of discovering the truth in regard to the figure of the earth, and proposed sending expeditions to the equator and the polar sea. The minister approved the plan and appropriated the necessary means, the academy designating Charles Marie de La Condamine, Pierre Bouguer, and Godin to go to Peru in 1734.
When they had finished their task in 1738, at the invitation of the Viceroy of Peru, Godin accepted the professorship in mathematics in Lima, where he also established a course of astronomical lectures. When in 1746 an earthquake destroyed the greater part of Lima, he took valuable seismological observations, assisted the sufferers, and made plans by the use of which the new buildings would be less exposed to danger from renewed shocks.
In 1751 he returned to Europe, but found that he had been nearly forgotten, and superseded as pensioner of the academy; and, as his fortune had been lost in unfortunate speculations, he accepted the presidency of the college for midshipmen in Cadiz in 1752. During the earthquake of Lisbon, 1755, which was distinctly felt at Cadiz, he took observations and did much to allay the apprehensions of the public, for which he was ennobled by the king of Spain. In 1759 he was called to Paris and reinstated as pensionary member of the academy, but he died on his return to Cadiz. *Wik

---

1768 Joseph-Nicolas Delisle (4 Apr 1688, 11 Sep 1768) French astronomer who proposed that the series of coloured rings sometimes observed around the Sun is caused by diffraction of sunlight through water droplets in a cloud. He also worked to find the distance of the Sun from the Earth by observing transits of Venus and Mercury across the face of the Sun.*TIS

---

1843 Joseph Nicolas Nicollet (24 Jul 1786, 11 Sep 1843) Joseph Nicolas Nicollet was a French mathematician, explorer, and cartographer with an interest in astronomy. He was born in France, but financially ruined by the 1830 Revolution, he left for the U.S. in 1831. He made a private survey of the Mississippi region (1836-7), the results of which he presented in Washington. In 1838, he led a surveying expedition for the U.S. government party mapping out the lakes and waterways of north central Minnesota. He stressed to map publishers the importance of elevation marks on published maps. His maps were considered among the most accurate and useful until the surveyors for the great logging companies arrived in Minnesota's vast pine forests.*TIS

---

1861 Johann Martin Zacharias Dase (June 23, 1824, Hamburg – September 11, 1861, Hamburg) was a German mental calculator.
He used to spend a lot of time playing dominoes, and suggested that this played a significant role in developing his calculating skills. Dase suffered from epilepsy from early childhood throughout his life.

At age 15 he began to travel extensively, giving exhibitions in Germany, Austria and England. Among his most impressive feats, he multiplied 79532853 × 93758479 in 54 seconds. He multiplied two 20-digit numbers in 6 minutes; two 40-digit numbers in 40 minutes; and two 100-digit numbers in 8 hours 45 minutes. The famous mathematician Carl Friedrich Gauss commented that someone skilled in calculation could have done the 100-digit calculation in about half that time with pencil and paper.

These exhibitions however did not earn him enough money, so he tried to find other employments. In 1844 he obtained a position in the Railway Department of Vienna, but this didn't last long since in 1845 he was reported in Mannheim and in 1846 in Berlin.

In 1844, Dase calculated π to 200 decimal places over the course of approximately two months, a record for the time, from the Machin-like formula:

\( \frac{\pi}{4} = \arctan \frac{1}{2} + \arctan \frac{1}{5} + \arctan \frac{1}{8} \)

He also calculated a 7-digit logarithm table and extended a table of integer factorizations from 7,000,000 to 10,000,000.

Dase had very little knowledge of mathematical theory. The mathematician Julius Petersen tried to teach him some of Euclid's theorems, but gave up the task once he realized that their comprehension was beyond Dase's capabilities. Gauss however was very impressed with his calculating skill, and he recommended that the Hamburg Academy of Sciences should allow Dase to do mathematical work on a full-time basis, but Dase died shortly thereafter.

The book "Gödel, Escher, Bach" by Douglas Hofstadter mentions his calculating abilities. "... he also had an uncanny sense of quantity. That is, he could just 'tell', without counting (subitizing), how many sheep were in a field, or words in a sentence, and so forth, up to about 30." *Wik

---

1890 Felice Casorati (17 Dec 1835, 11 Sept 1890). He is best remembered for the Casorati-Weierstrass theorem characterizing the behavior of a function near an essential singularity.*SAU

The theorem, named for Casorati and Karl Theodor Wilhelm Weierstrass, describes the remarkable behaviour of holomorphic functions near essential singularities, which is that every holomorphic function gets values from any complex neighbourhood, in any neighbourhood of the singularity.

The Casorati matrix is useful in the study of linear difference equations, just as the Wronskian is useful with linear differential equations. It is calculated based on n functions of the single input variable. *Wik

Look at the signature below his image???? What do you think?

---

1943 Oswald Teichmüller (18 June 1913, Nordhausen, Germany - 11 Sept 1943 on Eastern Front, WWII) His main contribution is in the area of geometric function theory.*SAU  He introduced quasiconformal mappings and differential geometric methods into complex analysis.
He joined the Nazi Party in July 1931. In 1933 he organized the boycott of his Jewish professor Edmund Landau.In 1936 and 1937 he attended lectures by Nevanlinna, who sympathized with the Third Reich, where he was a guest professor and, like Brouwer, was considered by the Nazis as "politically reliable" 
Much of Teichmüller's work was published in Deutsche Mathematik, a highly ideological journal founded by Ludwig Bieberbach that contained not only scholarly articles but also race propaganda. Because of the nature of the journal, his papers were hard to find in modern libraries before the publication of his collected works. 

---

1972 Johannes de Groot (7 May 1914 , 11 Sept 1972) De Groot worked in topology and group theory. In group theory one of the topics he studied was that of groups with only trivial automorphisms. Later de Groot worked on set-theoretic topology. He introduced the concept of co-compactness and other topological concepts. *SAU

---

1989 W. W. Chandler (December 1, 1913, Bridport, Dorset, England;  September 11, 1989)  He obtained his B.Sc. from London University in 1938 by private study while working as a telephone engineer at the British Post Office Research Department. During the war he was responsible for the installation and maintenance of the Colossus at Bletchley Park. The Colossus represented the first electronic computer, however it was programmed by a mechanical switchboard. Its was used to crack the German Fish codes which guarded the highest levels of German communication. Winston Churchill characterized the Bletchley Park team as the geese who laid the golden eggs but never cackled.
After the war Chandler participated in development and installation of the MOSAIC computer and worked on optical character recognition. He died on September 11, 1989. *CHM

The Colossus team in 1981. A.W.M. Coombs, T.H. Flowers, A.C. Lynch, W.W. Chandler, N.T. Thurlow, H.W. Fensom

---

2012 Irving Stoy Reed (November 12, 1923 in Seattle, Washington- September 11, 2012) is a mathematician and engineer. He is best known for co-inventing a class of algebraic error-correcting and error-detecting codes known as Reed-Solomon codes in collaboration with Gustave Solomon. He also co-invented the Reed-Muller code.
Reed has made many contributions to areas of electrical engineering including radar, signal processing, and image processing. He was part of the team that built the MADDIDA, guidance system for Northrop's Snark cruise missile - one of the first digital computers. He developed and introduced the now-standard Register Transfer Language to the computer community while at M.I.T. Lincoln Laboratory. He had been a faculty member of the Electrical Engineering-Systems Department of the University of Southern California from 1962 to 1993. *Wik

---

****   the maximal number of pieces in which a pancake (or a circle) can be divided into by    linear cuts. They are the bidimensional version of cake numbers.

In general,

Pancake numbers are often called lazy caterer numbers, or, more formally, central polygonal numbers.

---

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