On This Day in Math - April 14

 

Can  you guess what joke about Topology this was supposed to represent?  

The 'control of nature' is a phrase conceived in arrogance, born of the Neanderthal age of biology and the convenience of man.
~Rachel Carson


The 104th day of the year; 104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex. *What's Special About  Number   

HT Jesse Hammer

  
104 is the sum of eight consecutive even numbers, 104 = 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20
Douglas W Boone noted that "_Every_ odd multiple of eight greater than 56 is the sum of eight consecutive positive even numbers. (The smallest sum of eight consecutive positive even numbers is 72 = 2+4+6+8+10+12+14+16.) Allowing zero and negative numbers, every odd multiple of eight, period, is the sum of eight consecutive even numbers. The _even_ multiples of eight (that is, multiples of sixteen) are the sum of eight consecutive _odd_ numbers."  

The reversal of 104 is a prime, 401.  It is the largest year day that has a prime reversal that is too large to be a year date

13 straight lines through an annulus can produce a maximum of 104 pieces (students might try to create the maximum for smaller numbers of lines, the sequence is 2, 5, 9, 14, 20,... https://oeis.org/A000096 the differences give a clue to the complete pattern.)

Douglas W Boone pointed out that The formula for the number of pieces can be stated as (n^2 + 3n)/2, or (1/2) × n × (n+3), which is an integer for integral n; exactly one of n and n+3 will be even, i.e. divisible by 2.(Students might like another way involving the counting numbers.)

There are 588939451 "left and right" truncatable primes (truncate the two outside digits at once) with an even number of digits. The largest is the 104-digited prime number 91617596742869619884432721391145374777686825634291523771171391111313737919133977331737137933773713713973.

Just introduced to these by a comment from William Gosnell, thanks. sum of number and cube of its digits is a square.(wonder if there are other power sums?)

104+1^3+0^3+4^3 = 13^2 .  There is another smaller year day with this property, (Hint, it is prime),

but wait..104 + 1^2 + 0^2 + 4^2 = 11^2  Don't you wonder if there are more like this?

Japanese Route 104 ran from Hachinohe, near my former home in Misawa, Japan  on the Pacific, to go across the mountains to  Noshiro on the Sea of Japan in Akita prefecture.  One of the better places to find the prized 36 inch green glass fishing floats washed up along the coast. (perhaps no more, almost all plastic in last two decades)

*************** Lots of additional math facts for days 91-120 at https://mathdaypballew.blogspot.com/

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EVENTS

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

The first sunspot drawing, John of Worcester around 1128 *Wik

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1527  Abraham Ortelius, a Flemish cartographer, was born Apr. 14, 1527. In 1570, Ortelius published Theatrum Orbis Terrarum, or Theater of the World. This was the first modern world atlas. It contained 53 maps, and its novelty lay in the fact that the maps were uniform in style, size, and lettering; had been engraved especially for this work; had descriptive text on the back of each map; and covered the entire world, region by region. Most of the maps were not original with Ortelius—he borrowed freely from previous cartographers and he fully credited all his sources—but many of the maps, such as the world map, are brand new.

The Theatrum was an immediate publishing success, and it went through 23 editions and translations in Ortelius’ own lifetime (he died in 1598).  *Linda Hall Library

  

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1561 One of the earliest recorded citations of UFO's:
At sunrise on the 14th April 1561, the citizens of Nuremberg beheld "A very frightful spectacle." The sky appeared to fill with cylindrical objects from which red, black, orange and blue white disks and globes emerged. Crosses and tubes resembling cannon barrels also appeared whereupon the objects promptly "began to fight one another." This event is depicted in a famous 16th century woodcut by Hans Glaser.
*UFO Evidence Org

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1611 Galileo (1564 1642) visited Rome at the height of his fame and was made the sixth member of the Accademia dei Lincei (Lynx Society) at a banquet on 14 Apr. The word 'telescopium' was first applied to his instrument at this dinner. He showed sunspots to several people. The term “telescope” was introduced by Prince Federico Cesi at a banquet given in Galileo’s honor. It derives from the Greek “tele” meaning “far away” and “skop´eo” meaning “to look intently.” For a change, a term which derives from the Greek was actually coined by a Greek, namely Ioannes Demisiani. [Willy Ley, Watchers of the Skies, p. 112]*VFR Thony Christie at the Renaissance Mathematicus blog has an enjoyable review of the telescope and how it got its name.  This account of he events that evening by Girolamo Sirtori was published in his Telescopium, printed in 1618 but written in 1612. "I went to Rome... Galileo was there with his unforgettable telescope. By chance, on a certain day, Prince Federico Cesi,Marquis of Monticello, a learned man and benefactor of the sciences, had invited him [Galil eo] to dinner... Before sunset... they began to look through the telescope at the inscription of

Pope Sixtus Vii above the Lateran portal, which was about a mile distant. I took my turn and looked and read the inscription to my satisfaction. Later that night, after dinner, we observed Jupiter and the motion of his companion stars, after which, sufficiently invigorated by the sight of such brilliance and by the curiosity of the matter, they withdrew in order to examine the telescope. And Galileo himself, in order to satisfy their curiosity, took out the lens and the concave glass, and showed them openly."

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1685 It's easy for students of Math History to get the impression that John Wallis was totally immersed in mathematics, but a perusal of his writing on religion, or  his many varied contributions to the Royal Society paint the picture of a polymath.

“A Relation Concerning the Late Earthquake Neer Oxford: Together with Some Observations of the Sealed Weatherglass, and the Barometer Both upon That Phænomenon, and in General,” Phil Trans 1 (1665-1666):
166-171; Wallis, “A Discourse concerning the Air’s Gravity, Observd in the Baroscope, Occasioned by That of Dr. Garden: Presented to the Phil. Soc. of Oxford, by the Reverend Dr. Wallis, President of That Society. April, 14, 1685,” Phil Trans 15 (1685): 1002-1014; WC II, 282; WC III, 281-287.

This is almost certainly concerning the earthquake of 6 Oct, 1683 at Derbyshire. This earthquake also has the distinction of being the first British earthquake surveyed by the British Geological Survey.

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1760 Four years after leaving the coal pits near Newcastle, 22 year old Charles Hutton advertises the opening of his private school.

"To Be Opened

On Monday, April 14, 1760, at the head of the Flesh Market, down the entry formerly known by the name of the Salutation Entry, Newcastle, A Writing and Mathematical School, where persons may be fully and expeditiously qualified for business, and where such as intend to go through a regular course of Arts and Sciences, may be completely grounded  therein at large.  "  Four years later he would publish his first math text. It would still be in print 100 years later. *Gunpowder and Geometry, Benjamin Waedhaugh.

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1790 Mathurin Jacques Brisson (1723–1806) proposed to the Paris Academy the establishment of a system of measurement resting on a natural unit of length. The general idea of decimal subdivision was obtained from a work of Thomas Williams, London, 1788. *F Cajori, History of Mathematics

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1822 In a letter to Gauss, Bessell recommends his student, Heinrich Ferdinand Scherk. Gauss considered Scherk one of the best students he ever had. Scherk would go on to great educational success and Kummer was one of his students. * Dunnington, Gray, & Dohse , Carl Friedrich Gauss: Titan of Science

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1845 First Light for Western Hemispheres Largest Refractor.   

The Cincinnati Observatory is known as ‘The Birthplace of American Astronomy.’  It houses one of the oldest working telescopes in the world and was the first public observatory in the western hemisphere.  Recently restored to its original beauty, the Observatory is a fully functioning 19th century observatory used daily by the public and amateur astronomers.  The main telescopes are an 11-inch Merz and Mahler refractor from 1845 and a 16-inch Alvan Clark and Sons refractor from 1904.  The historic buildings are designated as a National Historic Landmark, and the grounds provide a serene, park-like setting while still being centrally located in the city of Cincinnati.  

The observatory originally sat on four acres of land at the top of Mt. Ida, which was donated to the Society by Nicholas Longworth.  On the 9th of November, 1843, a crowd of thousands witnessed former president John Quincy Adams preside over the dedication of the observatory, “The Lighthouse of the Sky,” and the laying of the cornerstone.  It was at the dedication that Adams gave his last public speech.  Mt Ida was renamed Mt. Adams following this event.

When the great refractor saw first light on April 14, 1845 it was the largest refractor in the Western Hemisphere and third largest in the world.  Mitchel, the first director, wrote and edited the first astronomical publication in the United States, The Sidereal Messenger.  The second director, Cleveland Abbe, published the nation’s first weather forecasts and he later assisted in the founding of the National Weather Service. *Cincinnati Observatory

The 11-inch Merz & Mahler refractor at Cincinnati Observatory, installed in 1842, and still in operation, recent photograph, Observatories of Ohio *Linda Hall Org

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1855 The first chess problem of Sam Loyd, age fourteen, was published in the New York Saturday Courier. Within a few years he was recognized as the nation’s foremost composer of chess problems. Once he announced that he had discovered a way to mate a lone king in the center of the board with a knight and two rooks. Readers were first furious, afterwards amused, by his preposterous solution: line them up in the order knight, rook, king, rook. [Mathematical Puzzles of Sam Loyd, edited by Martin Gardner, Dover 1959, p. xi-xii]

His first published puzzle is below:

  

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1860 A printed article on the Four Color theorem (perhaps only the second public statement about it, see June 10, 1854) was printed on this date and spread knowledge of the problem to America. In the unusual form of an Atheaneum book review of The Philosophy of Discovery by William Whewell, the unsigned, but almost surely written by DeMorgan, review launched in to a discussion of the Four Color problem. The review treats the four color necessity as obvious to cartographers, and makes no mention of either Guthrie, since he most surely knew the mathematical community in England were aware of his contribution from DeMorgan's own letters.
The review of Whewell's book came to the attention of American Philosopher/Logician C. S. Peirce, son of Harvard Professor Benjamin Peirce, and became a lifelong fascination. He immediately crafted a proof, which is still unknown, to my knowledge. He wrote later that it had been the Atheanenum review which first ignited his interest, and that his own proof was never printed. Shortly before DeMorgan's death in 1871, he was visited by Peirce, but no record is known of what they talked.

See the story of DeMorgan and Guthrie at the origin of the four color problem, 1852.

Letter of De Morgan to Hamilton, 23 Oct. 1852

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1894  The first ever commercial motion picture house opens in New York City, United States. It uses ten Kinetoscopes, devices for peep-show viewing of films.

*The Painter Flynn

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1914 Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras. He arrived in London on 14 April, with E. H. Neville waiting for him with a car. I received a tweet from @amanicdroid who pointed out that, "this was significant for him culturally as a high-caste Hindu as crossing the ocean was taboo. "

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1931 The first issue of the review journal Zentralblatt f¨ur Mathematik was published by Springer. Otto Neugebauer, then a young professor at G¨ottingen, conceived the idea of a journal that would publish the reviews of
articles as soon as possible after the papers had appeared and persuaded the publishing house of J. Springer to publish such a journal. The first issue of Zentralblatt f¨ur Mathematik und ihre Grenzgebiete, as the new journal was called, dated April 14, 1931, had Neugebauer as its editor. It also had a very distinguished and international editorial committee (consisting of P. Alexandroff, J. Bartels, W. Blaschke, R. Courant, H. Hahn, G. H. Hardy, F. Hund, G. Julia, O. Kellogg, H. Kienle, T.Levi-Civita, R. Nevanlinna, H. Thirring and B. L. van der Waerden). The first volume consisted of seven issues plus an index, in 466 pages. (The very first item reviewed was the second edition
of Methoden der mathematischen Physik, by Courant and Hilbert.) The classification system used was very similar to the scheme used by Jahrbuch.
Mathematical Reviews. Zentralblatt flourished under Neugebauer’s direction and became the primary reviewing journal in mathematics. Jahrbuch valiantly continued until issue number 4 of its Volume 68, for the year 1942, ceasing publication in mid-1944, but it had already lost its prominence in the research community. But, just asWorldWar I damaged Jahrbuch, serious harm was done to Zentralblatt soon after its founding by political conditions beyond its control. The anti-Semitic and anti-Soviet policies of the Nazi regime generated pressures on the editorial policies of Zentralblatt concerning the use of Jewish and Russian reviewers. Although Neugebauer left G¨ottingen for the University of Copenhagen in 1934, he had continued to edit Zentralblatt. But by 1938 the intrusion of politics had become intolerable and he and other members of the editorial board resigned. Despite these difficulties Zentralblatt continued its operation and, except for a brief suspension of publication from November 1944 until June 1948, has continued to publish to the present day.

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1943  a proposal for an electronic computer was submitted to colleagues at the U.S. Army's Ballistics Research Laboratory by John Grist Brainerd, director of research at the University of Pennsylvania's Moore School, where the proposal was written by John Mauchly. In May 1943, the Army contracted the Moore School to build ENIAC, the first electronic computer. Although ENIAC was not finished until after the war had ended, it nevertheless marked a major step forward in computing. *TIS

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1995 Chinese Government Works to Purge Its Agencies of Illegal Software:
The Chinese government launches widespread efforts to purge governmental agencies of illegally copied software, a practice that had been costing U.S. software publishers millions of dollars. The plan calls for allotting more money to purchase software while giving an enforcement agency the power to prosecute anyone bootlegging software. The announcement follows a March meeting at which China had signed an accord with the United States vowing to crackdown on piracy.*CHM

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2014 Almost exactly a year after Yitang Zhang announced a proof (see April 17) that there are infinitely many pairs of prime numbers which differ by 70 million or less Terrance Tao's online group attack on the problem reduced the number to 243. Zhang's proof is the first to establish the existence of a finite bound for prime gaps, resolving a weak form of the twin prime conjecture.

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2014 A total Lunar eclipse visible in most of North and South America occurred on this night. The total eclipse began around 3am EDT and last for about 80 minutes. More information is here. *Michael Zeiler

Another lunar eclipse took place on Wednesday 8 October 2014. The April eclipse was the first of two total lunar eclipses in 2014, and the second in a tetrad (four total lunar eclipses in series). Other eclipses in the tetrad are those of 4 April 2015, and 28 September 2015.

*Wik

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BIRTHS

1629 Christiaan Huygens (14 Apr 1629; 8 Jul 1695 at age 66) Dutch physicist and astronomer who founded the wave theory of light, discovered the true shape of the rings of Saturn, and contributed to the science of dynamics - the study of the action of forces on bodies. Using a lens he ground for himself, on 25 Mar 1655, he discovered the first moon of Saturn, later named Titan. In 1656, he patented the first pendulum clock, which he developed to enable exact time measurement while observing the heavens. Cristiaan Huygens studied the relation of the length of a pendulum to its period of oscillation (1673) and stated theories on centrifugal force in circular motion which influenced Sir Isaac Newton in formulating his Law of Gravity. Huygens also studied and drew the first maps of Mars. On 14 Jan 2005, a NASA space probe, named after Huygens, landed on Titan. *TIS
Amazon has the Kindle version of his Treatise on Light for free.

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1868 Annie Scott Dill Maunder (née Russell) FRAS (14 April 1868 – 15 September 1947)

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

On the far side of the Moon lies the Maunder crater, named after two British astronomers - Annie and Walter Maunder.

Annie worked alongside her husband at the end of the 19th Century, recording the dark spots that pepper the Sun.

The name Maunder is still known in scientific circles, yet Annie has somehow slipped from history.

"I think the name Maunder is there and we have all rather forgotten that that's two people," says Dr Sue Bowler, editor of the Royal Astronomical Society magazine, Astronomy and Geophysics.

"She was acknowledged on papers, she published in her own name as well as with her husband, she wrote books, she was clearly doing a lot of work but she also clearly kept to the conventions of the day, I think." *By Helen Briggs BBC News

She is known to have worked closely with her husband on the study of sunspots, and she is often credited with discovering the butterfly pattern. *LH

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1898 Harold Stephen Black (14 Apr 1898; 11 Dec 1983 at age 85) American electrical engineer who discovered and developed the negative-feedback principle, in which amplification output is fed back into the input, thus producing nearly distortionless and steady amplification. In 1921, Black joined the forerunner of Bell Labs, in New York City, working on elimination of distortion. After six years of persistence, Black conceived his negative feedback amplifier in a flash commuting to work aboard the ferry. Basically, the concept involved feeding systems output back to the input as a method of system control. The principle has found widespread applications in electronics, including industrial, military, and consumer electronics, weaponry, analog computers, and such biomechanical devices as pacemakers. *TIS

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1922  Betty Shannon (née Mary Elizabeth Moore) (April 14, 1922 – May 1, 2017) was a mathematician and the main research collaborator of Claude Shannon. Betty inspired and assisted Claude in building some of his most famous inventions.

She was awarded a full scholarship to the New Jersey College for Women, where she graduated Phi Beta Kappa after studying mathematics.

She worked as a numerical analyst at Bell Labs, where as a computer she supported work on microwaves, and then on radar. She published her own research on "Composing Music by a Stochastic Process"; an "exceptional" accomplishment in an era when it was a "significant and unusual achievement for a woman to get her name on a research report".

While at Bell Labs she met the shy and insular Claude Shannon. Claude "didn’t have much patience with people who weren’t as smart as he was" and the two of them got on well. In 1948 he asked her on a date and they ended up dining each night together; they were married in 1949.

Many of his papers were written in her hand, and at her inspiration.  Shannon's mind had little patience with filling in the gaps between his leaps of intuitive brilliance.

She also was the partner and co creator of many of his unusual creations. 

In 1950, pioneering information theorist Claude Shannon engineered a mechanical mouse, theseus, that navigated a maze to find a hunk of metal “cheese.”  The mouse was made from an erector set given to Claude by Betty, and the final electrical connections were by her hand.

In addition to her research, Shannon was a member of the Weavers' Guild of Boston, served as Dean of the Guild from 1976 to 1978 and received the Guild's Distinguished Achievement Award.

Shannon had three children, Robert James Shannon, Andrew Moore Shannon, and Margarita Shannon, and raised their family in Winchester, Massachusetts. Her oldest son, Robert Shannon, died in 1998 at the age of 45. Betty died on May 1, 2017 at her home at Brookhaven in Lexington, Massachusetts.

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DEATHS

1792 Maximilian Hell (May 15, 1720 – April 14, 1792) was a Slovak astronomer and an ordained Jesuit priest from the Kingdom of Hungary.
Born as Rudolf Maximilian Höll in Selmecbánya, Kingdom of Hungary (present-day Banská Štiavnica, Slovakia)., but later changed his surname to Hell. He was the third son from the second marriage of his father Matthias Cornelius Hell (Matthäus Kornelius Hell) and his mother Julianna Staindl. The couple had a total of 22 children. Registry entries indicate that the family was of German descent, while Maximilian Hell later in life (ca 1750) is known to declare himself as Hungarian.
Hell became the director of the Vienna Observatory in 1756. He published the astronomical tables Ephemerides astronomicae ad meridianum Vindobonemsem ("Ephemerides for the Meridian of Vienna"). He and his assistant János Sajnovics went to Vardø in the far north of Norway (then part of Denmark-Norway) to observe the 1769 transit of Venus. He was elected as a foreign member of the Royal Danish Academy of Sciences and Letters on October 13, 1769. This society also funded the publication of his 1770 account of the Venus passage Observatio transitus Veneris ante discum Solis die 3. Junii anno 1769 (Copenhagen, 1770).
There was some controversy about Hell's observations of the transit of Venus because he stayed in Norway for eight months, collecting non-astronomical scientific data about the arctic regions for a planned encyclopedia (which never appeared, in part due to the suppression of the Jesuit order). The publication of his results was delayed, and some (notably Joseph Johann Littrow) accused Hell posthumously of falsifying his results. However, Simon Newcomb carefully studied Hell's notebooks and exonerated him a century after his death in Vienna.
Besides astronomy, Hell also had an interest in magnet therapy (the alleged healing power of magnets), although it was Franz Anton Mesmer who went further with this and received most of the credit.
In 1771, Hell was elected a foreign member of the Royal Swedish Academy of Sciences.
The crater Hell on the Moon is named after him. *Wik

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1935 Amalie Emmy Noether (23 Mar 1882, 14 Apr 1935 at age 53) was a German mathematician best known for her contributions to abstract algebra, in particular, her study of chain conditions on ideals of rings. In theoretical physics, she produced Noether's Theorem, which proves a relationship between symmetries in physics and conservation principles. This basic result in the general theory of relativity was praised by Einstein. It was her work in the theory of invariants which led to formulations for several concepts of Einstein's general theory of relativity. For her obituary in The New York Times, Albert Einstein wrote: “Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.”*TIS Emmy Noether’s house in Erlangen is shown in a blog at The Renaissance Mathematicus

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1964 Tatyana Alexeyevna Afanasyeva (Kiev, 19 November 1876 – Leiden, 14 April 1964) (also known as Tatiana Ehrenfest-Afanaseva) was a Russian/Dutch mathematician. On 21 December 1904 she was married to Paul Ehrenfest (1880–1933) an Austrian physicist. They had two daughters and two sons: one daughter, Tatyana Pavlovna Ehrenfest, also became a mathematician.
Afanasyeva was born in Kiev, Ukraine, then part of the Russian Empire. After her father died she was brought up by an uncle in St Petersburg, Russia, where she attended a women's pedagogical school and a Women's College. In 1902 she transferred to Göttingen, where she met Ehrenfest. The couple got married in 1904, and in 1907 they returned to St Petersburg. In 1912 they moved to Leiden, where Paul Ehrenfest was appointed to succeed H.A. Lorentz as professor at the University of Leiden.
Tatyana collaborated closely with her husband, most famously on their classic review of the statistical mechanics of Boltzmann. She published many papers on various topics such as randomness and entropy, and teaching geometry to children. *Wik

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1964 Rachel Louise Carson (27 May 1907, 14 Apr 1964 at age 56) was an American marine biologist, conservationist and writer well known for her writings on environmental pollution and the natural history of the sea. Embedded within all of Carson's writing was the view that human beings were but one part of nature distinguished primarily by their power to alter it, in some cases irreversibly. Disturbed by the profligate use of synthetic chemical pesticides after World War II, Carson reluctantly changed her focus in order to warn the public about the long term effects of misusing


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