41 votes
Accepted

Timeline of measurements of the electron's charge

If anyone's still reading this thread, here's a few more data points that appear to back Feynmann's interpretation. Erik Bäcklin, Nature vol 123, no. 3098, p. 409 (1929): $1.59875 \cdot 10^{-19} \pm ...
Anonymaus's user avatar
  • 526
40 votes
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How did Eratosthenes know the Sun was very far away?

We do not know for sure what Eratosthenes read, but at his time this was a common knowledge. This can be inferred from the book of Archimedes, The sand reckoner (Archimedes was Eratosthenes' ...
Alexandre Eremenko's user avatar
19 votes

Who are the youngest mathematicians that published an original research article in a peer-reviewed journal?

George Bergman, "A number system with an irrational base," Mathematics Magazine, Vol. 31, No. 2, Nov.-Dec. 1957, pp. 98-110. George Mark Bergman is an American mathematician who was born on ...
njuffa's user avatar
  • 6,496
19 votes
Accepted

Why was the development of mathematics very slow between Ancient Greece and Descartes?

Making my comment into an answer: Was there a gap of knowledge or slow-down of progress in math as a whole between Ancient Greeks and the 17th century? The answer is probably no. Islamic Medieval ...
Mauricio's user avatar
  • 3,344
18 votes
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What did Fermat do as a lawyer?

Fermat wasn't so much a "lawyer" as a magistrat which means that he sat on successively higher levels of the Parlement of Toulouse, France. This period (17th century) was before the emergence of the ...
Mikhail Katz's user avatar
  • 5,506
17 votes
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What major areas of mathematics have been abandoned?

I would say that no area of mathematics has ever been completely abandoned. The areas go in and out of fashion, but nothing seems to be completely abandoned. For example, approximately in 1940's most ...
Alexandre Eremenko's user avatar
17 votes
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Did Newton say: "If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent"?

So far I have been unable to find substantially identical words in Newton's writings, and as usual, authors that use this quotation do not cite a source. The origin may be a remark of Newton's in ...
njuffa's user avatar
  • 6,496
16 votes
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What was Kolmogorov’s point of view in the philosophy of mathematics?

Kolmogorov was not exactly free to express his views considering the situation in the Soviet Union. Philosophical issues, even concerning mathematics, were ideologically sensitive, and everyone had to ...
Conifold's user avatar
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16 votes

How did Eratosthenes know the Sun was very far away?

This is a long answer, explaining more or less step to step why the data available to Eratosthenes indicted that the Sun should be a vast distance from the Earth, thus makings its diverging rays ...
M.A. Golding's user avatar
  • 1,288
15 votes

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

Some centuries before Mermin, Leibniz in the 17th century was seeking a solution to some of the denominational quarrels that were plaguing his generation by envisioning a calculus ratiocinator that ...
Mikhail Katz's user avatar
  • 5,506
15 votes

Who was L. Aubry?

I am Camille Aubry, granddaughter of Léon Aubry (1882-1947), and I thank you for your interest in my great-grandfather. He was a wine grower, farmer, beekeeper, in Jouy-lès-Reims (51). He was also a ...
Camille Aubry's user avatar
14 votes

What is the original source for Abel's quote about Gauss:"He is like the fox, who effaces his tracks in the sand with his tail"?

Bjerknes cites a letter from Abel to Christopher Hansteen, a fellow professor of Bjerknes at Christiania/Oslo, who had put up and mentored Abel in the beginning of his career. Den omgangskreds af ...
Michael E2's user avatar
  • 1,861
13 votes
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Who was the first to say "Shut up and calculate!"?

Mermin has a thorough analysis1 and traces the phrase to himself in a 1989 Physics Today column2 & makes a case that the numerous attributions to Feynman may or may not be mistaken. Mermin, Could ...
vzn's user avatar
  • 246
13 votes

Is Spivak right in what he says about Galileo?

Yes, indeed when trying to obtain the law of falling bodies, Galileo's first conjecture was that the speed is proportional to the distance traveled. After some contemplation, Galileo understood that ...
Alexandre Eremenko's user avatar
13 votes

Did Einstein say "We cannot solve our problems with the same thinking we used to create them"?

I am afraid there is no original source. Wikipedia has talk pages where sourcing is discussed, and its editors did extensive searches on this one and its variants. It is listed under the heading ...
Conifold's user avatar
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13 votes
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Some references for Vladimir Arnold's thesis "Mathematics is a part of physics"?

First, on the question in the narrow sense the answer is in the negative, I am afraid, although there are some other places where Arnold expresses his views on mathematics: An apologia for Applied ...
Conifold's user avatar
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13 votes

Who are the youngest mathematicians that published an original research article in a peer-reviewed journal?

Arthur Leonard Rubin submitted the following paper at age 12.5 -- he was born in Feb 1956 and the paper was submitted in Nov 1968: Arthur L. Rubin and Jean E. Rubin, Extended operations and relations ...
Dave L Renfro's user avatar
13 votes
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DeMorgan's commentary on Euclid's Elements

De Morgan's "Short Supplementary Remarks on the first Six Books of Euclid's Elements" is contained in the Companion to the (British) Almanac for the year 1849, pp.5–20, published by the ...
Alexander Campbell's user avatar
12 votes

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

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. According ...
nwr's user avatar
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12 votes
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Where did Rayleigh derive the ultraviolet catastrophe?

The short answer is that you can not find it because it does not exist, Rayleigh never derived the "ultraviolet catastrophe". Chapter VI of Kuhn's book on the history of quantum mechanics reads: "...
Conifold's user avatar
  • 75.2k
12 votes
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What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

Poincare refers to the Lie's solution of the so-called problem of space, a.k.a. the Helmholtz , or Riemann-Helmholtz, or Helmholtz-Lie problem of space, which amounts to characterizing all manifolds (...
Conifold's user avatar
  • 75.2k
11 votes
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An English copy of One Hundred Authors Against Einstein?

Here is a link to online version in German. As for the English translation, according to Milena Wazeck's Einstein's Opponents: The Public Controversy about the Theory of Relativity "nothing ever came ...
Conifold's user avatar
  • 75.2k
11 votes

Source for Hilbert's famous quote "Mathematics in Göttingen? There really is none anymore"

In my grandfather's book, lately translated from German: Recollections of a Jewish Mathematician in Germany, by Abraham A. Fraenkel, edited by Jiska Cohen-Mansfield, translated by Allison Brown. ...
Avraham Fraenkel's user avatar
11 votes
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What manuscript is depicted in the HSM advertisement?

User plannapus points out that the proposer of the ad links to the original source, which is the first page of Diophantus’s Arithmetica, specifically the 1621 translation by Claude Gaspard Bachet de ...
11 votes

Did Srinivasa Ramanujan have a surviving sibling?

There were actually two surviving brothers: source See also page 12 of Robert Kanigel's biography of Ramanujan.
Carlo Beenakker's user avatar
11 votes
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What was the main language in science/mathematics before 1850

For what it’s worth, here are the languages of the 1645 math/phys paper and book titles from the years 1690–1919 in a bibtex file I have. Of course unscientific with all kinds of biases, but I imagine ...
Francois Ziegler's user avatar
11 votes
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Origin of identity: $\int\limits_{-\infty}^{\infty} \exp\{ - \pi x^2 - 2 \pi^{1/2} a x\} \,da = \exp\left\{a^2\right\}$

This is a variation on the Gaussian integral $\int\limits_{-\infty}^{\infty} \exp\left\{-x^2\right\} \,dx=\sqrt{\pi}$, a.k.a. Poisson or Euler-Poisson integral, to which it reduces by completing the ...
Conifold's user avatar
  • 75.2k
11 votes
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History of irreducible polynomials and motivation for them

I will skip the pre-history of solving polynomial equations and factoring polynomials. Let me mention that the analogy between long division of numbers and polynomials goes back to medieval Islamic ...
Conifold's user avatar
  • 75.2k

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