nwr
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How much contribution did John Nash make to proving Riemann Hypothesis?
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16 votes

Nash was known to have been captivated by RH at an early age after reading E.T. Bell's Men of Mathematics. He had confided in some friends and colleagues that he had an idea that might work involving ...

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Alexander Grothendieck's "stolen" correspondence in 1985?
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14 votes

The Grothendieck Circle site suggests a more innocent explanation for the loss these letters. Having left Montpellier in 1984.... In May of that year [1985] a secretary informed him that his ...

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Why didn't Einstein win a second Nobel Prize, for relativity?
13 votes

The time when experimental evidence supporting relativity began to appear coincided with the rise of antisemitism in Germany following Germany's defeat in WWI. Antisemitism was on the rise in Germany;...

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Did the ancient Chinese know the earth is a sphere?
12 votes

There appear to be conflicting accounts of when the Chinese came to view the earth as spherical. Chinese sources might suggest the 11th century, while western sources suggest the 17th century. ...

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Why didn't Euclid's Elements treat conic sections?
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11 votes

While Elements contains no reference to conic sections it does define angled cones, given as definition 18 of Book XI, and it examines some of their properties in Book XII. History identifies ...

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Are there examples of influential scientific articles first rejected and later proved to be valid?
11 votes

As user njuffa has commented, my original answer was not strictly to the letter of the OP. Here are some other examples : Fermi's 1933 paper on the weak interaction. Gell-Mann's 1953 paper on the ...

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Who discovered the Jordan normal form?
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11 votes

According to the following linked text, Weierstrass defined his equivalent form in a memoir presented to the Berlin Academy in 1868, two years prior to Jordan's Traite being published. From Bartel L ...

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How did J.J. Thomson learn that what he discovered was different than an atom or a molecule?
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9 votes

Thomson drew his conclusion based on his calculation of the charge to mass ratio of the "corpuscular carriers of negative charge in cathode rays". Quoting Thomson's Nobel Lecture of 1906: ...

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How did Newton prove the generalised binomial theorem?
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9 votes

According to William Dunham in his Journey Through Genius [Newton's Binomial Theorem is] not a "theorem" in the sense of Euclid or Archimedes in that Newton did not furnish a complete proof. Yet ...

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Euler's first proof of $e^{ix}=\cos(x)+i\sin(x)$
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9 votes

According to Boyer's A History of Mathematics, the identity first appeared in Euler's Introductio in analysin infinitorum of 1748. Euler started from the infinite series for $e^x$, $\sin x$, and $\...

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History of poster sessions
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8 votes

The paper Lire debout. Le poster comme pratique de lecture dans le monde scientifique. writes: Les «premiers» posters ou des produits fort proches furent présentés dès 1967 pour le moins au Medical ...

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Failures in math
8 votes

Alexander Abian may fit the bill here. His most notable contribution to mathematics was proving consistency and independence of four of the Zermelo-Fraenkel axioms. source: Wolfram Mathworld. They ...

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Madhava and $\pi$
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8 votes

According to this page: Although almost all of Madhava's original work is lost, he is referred to in the work of later Kerala mathematicians as the source for several infinite series expansions (...

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History of the definition of Injective & Surjective Function
8 votes

According to this page on "earliest know uses of some mathematical words", the terms injective, surjective, and bijective were first introduced in Bourbaki's Théorie des ensembles, of 1954, page 80. ...

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Who was the first to prove the mean value theorem?
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7 votes

As per your comment requesting details of the linked paper : Besenyei's paper begins with a history of the development of Rolle's Theorem into its general form. It follows this with the history of ...

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Stern-Gerlach: oven, or filament?
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7 votes

The following diagram of the original setup is from Stern's private slide collection and was included in Stern and Gerlach's 1924 paper Über die Richtungsquantelung im Magnetfeld. Annalen der Physik, ...

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How did the Arabs determine the longitudes of cities?
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7 votes

Terrestrial longitudes were derived from the astronomical longitudes given in the "Hakimite Tables" of Ibn Yunus (d. 1009). Essentially, during a lunar eclipse (predicted by the astronomical tables) ...

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Are there any famous mathematicians who did regular physical workouts?
7 votes

Niels Bohr's brother, Harald Bohr, was a notable mathematician and football (soccer) player. Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and football player. ...

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Who invented or discovered the hyperbolic numbers?
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7 votes

According to the text Bicomplex Holomorphic Funtions by Luna-Elizarraras, et al, as far as we know Cockle was the first to introduce and study these objects, and their introduction was almost ...

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Where can I find Grothendieck's letter of resignation from Bourbaki?
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6 votes

Here is an English translation of Grothendieck's letter dated October 9, 1960. Here is the letter in its original French. May also be of interest, Grothendieck's stolen correspondence of 1985.

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Who were some mathematicians who have a musical background?
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6 votes

The MacTutor Article Mathematicians and Music provides an overview of this relationship. Amongst those mathematicians who were accomplished players and had performed in public, the article includes: ...

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When Indian mathematicians learn of Euclid's Elements?
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6 votes

According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma: It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s ...

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Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?
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6 votes

From the Earliest Known Uses of Some of the Words of Mathematics site : PENCIL OF LINES. Desargues coined the term ordonnance de lignes, which is translated an order of lines or a pencil of lines [...

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Einstein's readings of popular sciences as a kid
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6 votes

From Walter Isaacson's Einstein (page 116 of the linked pdf) : Einstein’s greatest intellectual stimulation came from a poor student who dined with his family once a week. It was an old Jewish ...

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Did Gödel consider himself primarily a philosopher who is interested in mathematics (instead of the other way round)?
6 votes

Since there is no record of Gödel's view, any response to this question is a matter of opinion. One of the few philosophers who has published opinions on the merits of Gödel's philosophical views, as ...

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Notations for Laplacian: $\nabla^2$ vs. $\Delta$
5 votes

Jeff Miller's site gives the first occurrence of $\Delta$ as The symbol $\Delta$ for the Laplacian operator (also represented by $\nabla^2$) was introduced by Robert Murphy in 1833 in Elementary ...

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Who was the first to say "Shut up and calculate!"?
5 votes

As noted, Mermin was probably the first to utter the exact words “Shut up and calculate”. However, the equivalent rallying cry of “Get the numbers out” has its origins some decades earlier. ...

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Definitions of continuity pre-Dedekind
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5 votes

Regrading the early consideration of density as a means of defining the continuum : William of Ockham (c. 1280–1349) brought a considerable degree of dialectical subtlety to his analysis of ...

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What did Farcas Bolyai write to his son?
5 votes

The wikiquote site gives the original quote from a letter of 4, April 1820: A parallelákat azon az útan ne próbáld: tudom én azt az utat is mind végig — megmértem azt a feneketlen éjszakát én, és ...

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Who first wrote down $S^6$'s standard almost complex structure? And who first proved that it is not integrable?
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5 votes

According to this arxiv paper by Atiyah, existence and construction dates from 1947; non-integrability from 1951. Here is Atiyah's history: Ehresmann 1947: Introduced the notion of almost complex ...

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