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Questions tagged [debunking]

For questions about finding the truth in claims that give good reason to be skeptical.

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33 votes
2 answers
40k views

Story of Grothendieck's Prime Number

There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which goes roughly as follows (cf. this wikipedia article): In a mathematical conversation, someone suggested to ...
Moishe Kohan's user avatar
  • 1,746
30 votes
5 answers
7k views

In a popular anecdote, who took 20 minutes to decide that a thing was obvious?

The joke is found on this comment chain on Reddit. One user told the joke: The version I heard is that Pauli was lecturing, and he said "this is obvious". A student raises his hand and says "sorry ...
Ooker's user avatar
  • 1,228
25 votes
3 answers
5k views

Is Millikan's famous oil drop experiment a fraud?

I read in my mechanics textbook written by Goodstein that Robert Millikan cherry-picked his data in his famous oil drop experiment, and now I'm left wondering about the scientific value of his results....
Shing's user avatar
  • 664
19 votes
2 answers
1k views

Pythagoras vs. the idea of Pythagoras

Maybe we need some replies on current scholarly thinking. (Judging from some replies here, many of us are still using the myths current 100 years ago.) Is it true (as I have heard) that most, if not ...
Gerald Edgar's user avatar
  • 10.4k
18 votes
1 answer
2k views

How was the Möbius strip discovered?

Britannica is terse:"Möbius discovered this surface in 1858. The German mathematician Johann Benedict Listing had discovered it a few months earlier, but he did not publish his discovery until 1861". ...
Conifold's user avatar
  • 77.6k
17 votes
3 answers
2k views

Did light bulb companies commission Planck to study black body radiation?

Background When introducing Planck's switch to looking at black-body radiation, a number of sources -- like MinutePhysics, the Economist, random online encyclopaedias and even here on HSM.SE (plus ...
Artem Kaznatcheev's user avatar
17 votes
0 answers
816 views

Did Kontsevich start a lecture with "one I will not define, the other nobody knows how to define, and we will be proving that they are equivalent"?

The story was circulating in early 2000s, so presumably it happened in 1990s. Kontsevich, it goes, opened a lecture course on mirror symmetry with:"This course is about two categories. One I will not ...
Conifold's user avatar
  • 77.6k
15 votes
2 answers
18k views

Is the "ques­tions that can’t be an­swered over an­swers that can’t be ques­tioned" quote by Feynman authentic?

In a lot of places I find this quote from Feynman: I would rather have ques­tions that can’t be an­swered than an­swers that can’t be ques­tioned. However, I cannot find any source of where it ...
Nicola Gigante's user avatar
15 votes
1 answer
6k views

Is the anecdote about Niels Bohr keeping a horseshoe on his door true?

I recently came to know of an anecdote about Niels Bohr that the philosopher Slavoj Zizek claims to have read in a biography of Bohr. He doesn't specify the author or the biography. The anecdote ...
ACat's user avatar
  • 1
14 votes
2 answers
2k views

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"?

According to the editor of the German version of Ian Stewart's "The Problems of Mathematics", on page 226 of the biography of Gauß authored by Erich Worbs (C. F. Gauß: Ein Lebensbild. Koehler & ...
José Hdz. Stgo.'s user avatar
13 votes
2 answers
584 views

When did the people start using the portraits of the two Euclids interchangeably?

According to the folks of Wikipedia, this is the portrait of Euclid of Alexandria (the "Father of Geometry"): Yet, I read several years ago on MathOverflow that the individual in the ...
José Hdz. Stgo.'s user avatar
13 votes
1 answer
775 views

What were 12 year old Pitts' objections to Principia Mathematica?

In Wikipedia on the page dedicated to Walter Pitts (accesses today), it is written that, He is widely remembered to have spent three days in a library, at the age of 12, reading Principia ...
user avatar
13 votes
3 answers
481 views

Question on "What St. Augustine didn't say about mathematicians"

In the note "What St. Augustine didn't say about mathematicians" (which appeared sometime in 1991 in the pages of the Pi Mu Epsilon Journal), R. P. Boas, Jr. mentioned, among other things, that in the ...
José Hdz. Stgo.'s user avatar
12 votes
3 answers
3k views

Did Isaac Newton burn Robert Hooke's picture?

A well-known TV series hinted some time ago that Isaac Newton burnt the only known picture of Robert Hooke. Is it true?
rnrneverdies's user avatar
12 votes
3 answers
2k views

Poincaré and the baker: was the anecdote true?

There is a story featuring Henri Poincaré and an unscrupuolous baker. Every day Poincaré bought a piece of bread which should have weighted 1 kg. After an year, the mathematician brought the baker to ...
mau's user avatar
  • 1,277
12 votes
1 answer
575 views

Hawking on Newton and the famed apple

If I recall correctly, Stephen Hawking mentioned in A Brief History of Time that Newton remarked once that the famed apple actually distracted him from his lucubrations. Does anybody know where it ...
José Hdz. Stgo.'s user avatar
12 votes
1 answer
1k views

Did Cauchy forget or lose mathematical papers aside from Abel's and Galois's?

Augustin-Louis Cauchy was a prolific writer, his writings range widely in mathematics and mathematical physics. As a professor at École Polytechnique he came in contact and reviewed Abel's and Galois' ...
Ziezi's user avatar
  • 365
11 votes
5 answers
3k views

Who gets credit for the real numbers?

If Simon Stevin already pioneered the unending decimal representation for every number (rational, surd, etc.) at the end of the 16th century, why do Cantor and Dedekind (who certainly gave a more ...
Mikhail Katz's user avatar
  • 6,052
10 votes
2 answers
42k views

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

According to various sources on the Web, Albert Einstein is likely to have said or written one of the following: Probleme kann man niemals mit derselben Denkweise lösen, durch die sie entstanden ...
user avatar
9 votes
2 answers
2k views

What exactly was the Rutherford model of the atom?

I was recently doing research on the "Rutherford model" of the atom. I found that there seem to be three different accounts of Ernest Rutherford's theory circulating online: Electrons move ...
Mark Morales II's user avatar
9 votes
2 answers
2k views

Did Poincaré say that set theory is a disease?

This question has been discussed on several sites including MathOverflow but with not definite result. Presumely HSE is best suited. Jeremy Gray denies that Poincare said, "Later generations will ...
user avatar
9 votes
2 answers
2k views

Has Chinese Remainder Theorem ever been used by Chinese military?

The Chinese Remainder Theorem says, in rough terms, that if you know the remainders of an integer $n$ modulo $m_1,m_2,\dots,m_r$, you also know $n$ modulo $\mathrm{lcm}(m_1,m_2,\dots,m_r)$. In the ...
Jakub Konieczny's user avatar
9 votes
1 answer
1k views

Did Gauss say "there have been but three epoch-making mathematicians, Archimedes, Newton and Eisenstein"?

In Wikipedia I found this claim by E.T. Bell in his Men of Mathematics. However in the next paragraph it says that "it is doubtful that Gauss put Eisenstein in the same league as Newton", which makes ...
Nicco's user avatar
  • 263
9 votes
1 answer
399 views

How did Newton guess that the answer to the 3-dimensional "kissing problem" is 12?

I understand almost nothing about sphere packings and kissing numbers, but I am very curious to learn about the Newton - Gregory discussion of the problem. In particular, I wonder if Newton's guess ...
user2554's user avatar
  • 4,499
9 votes
1 answer
1k views

What is the origin of the cut and weigh method of integration, is it Galileo's?

I recently heard a story of a clever method of approximating an integral which, instead of using numerical techniques, relied on physically drawing out the graph of a function, cutting it out, and ...
Peter Woolfitt's user avatar
9 votes
1 answer
1k views

Why is the Sophie Germain Identity called thus?

Several authors (z.B.: Arthur Engel in his Problem-Solving Strategies, Alexander Bogomolny in this entry of the Cut the Knot website) refer to the following (straightforward) consequence of the ...
José Hdz. Stgo.'s user avatar
9 votes
1 answer
758 views

Did Galileo bet money on the ship experiment?

Galileo's writings describe two experiments involving ships. These are summarized in the Wikipedia article Galileo's ship. (A lot of the text in the article is mine, and if there are things I'm ...
user avatar
9 votes
2 answers
7k views

On Einstein's proof of the so-called Pythagorean theorem

Part I In E. Maor's book [2, p. 117] we read that, somewhere in his Autobiographical Notes, Einstein wrote this: An uncle told me about the Pythagorean theorem before the holy geometry booklet had ...
José Hdz. Stgo.'s user avatar
8 votes
2 answers
492 views

Is Spivak right in what he says about Galileo?

On chapter 9 of M. Spivak's book on calculus there is an exercise in which Spivak asks the reader to prove that Galileo "got his facts wrong". More specifically, Spivak asks one to to show if a body ...
Jamai-Con's user avatar
  • 271
8 votes
1 answer
441 views

Gauss accused of witchcraft: apocryphal?

I recall reading years ago in a linear algebra book that Gauss was accused of witchcraft for his (re)discovery of what we now call the row reduction algorithm for solving linear equations. Has anyone ...
Paul Siegel's user avatar
  • 1,041
8 votes
2 answers
469 views

What is the original source for Gelfand's problem on leading digits of the powers of 2?

The question of the distribution of the leading digits of the sequence $2^n$ is called Gelfand's problem or Gelfand's question. Is there any source that indicates Gelfand's own work on this, or the ...
KCd's user avatar
  • 5,689
8 votes
1 answer
13k views

Are there any extant letters backing up the famous anecdote about Edmund Landau and Fermat's Last Theorem?

I recall reading in several sources the story about the letter "template" with which Edmund Landau used to answer individuals that sent him their "proofs" of Fermat's Last Theorem.....
José Hdz. Stgo.'s user avatar
7 votes
1 answer
579 views

Who first proved the "Cantor-Heine theorem" on uniform continuity?

The theorem is that any continuous function on a compact is uniformly continuous. It is called "Heine", and sometimes also "Heine-Cantor" theorem. My question is: what is the contribution of Cantor ...
Phil-W's user avatar
  • 173
7 votes
1 answer
667 views

Did Cambridge change their BSc policy for Ramanujan?

I found this quote at Quora: In March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (This degree was later renamed as Ph.D. from 1920) for his work on Highly ...
students's user avatar
6 votes
4 answers
505 views

Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?

In the book What do you care what other people think?, Feynman talks about how in the 16th century Niccolo Tartaglia discovered a solution to cubic equations. He says while this was not a major ...
Steve Sether's user avatar
6 votes
6 answers
6k views

Where did the false "equal transit-time" explanation of lift originate from?

It's supposedly a "widely circulated" false claim that wings generate lift because of their asymmetric shape, forcing air above to travel faster so that they meet up on the trailing edge at the same ...
eugenhu's user avatar
  • 191
6 votes
2 answers
2k views

Question related to the legitimacy of a certain portrait of Christian Goldbach

According to what we read in footnote #2 of [I], no portrait of Christian Goldbach seems to be known. The author of the article under consideration even adds: ... Juskevič & Kopelevič's ...
José Hdz. Stgo.'s user avatar
6 votes
2 answers
428 views

Did Newton find the trajectory of a body moving in uniform gravity under the quadratic resistance law (the ballistic problem)?

I'm very confused by contradicting accounts of a supposed solution by Newton to the problem of finding the trajectory of a projectile moving under uniform gravity against resistance that is ...
user2554's user avatar
  • 4,499
6 votes
1 answer
1k views

Who discovered Napoleon's theorem?

I read about Napoleon's Theorem in geometry. Was this the same Napoleon as the great warrior? Was he a mathematician too?
Soham's user avatar
  • 911
6 votes
2 answers
796 views

A question on Gauss' "Vicimus GEGAN"

The 43rd entry(Oct. 1796) of Gauss' mathematical diary "Vicimus GEGAN" remained a mystery for a long time. K. R. Biermann found evidence that GEGAN is related the famous arithmetic-geometric mean(AGM) ...
zy_'s user avatar
  • 247
6 votes
2 answers
222 views

What mathematical problems did the Sicilians need Arab help with in 1229? Did the Arabs solve these problems?

An incident in the negotations of the Sixth Crusade is described as Frederick II asking help from Arab scholars with some mathematical problems: ... and the sultan graciously allowed Frederick to ...
gktscrk's user avatar
  • 328
6 votes
2 answers
331 views

Did Leibniz use infinite numbers?

Arthur's recent article Arthur, Richard T. W. Leibniz's actual infinite in relation to his analysis of matter. G. W. Leibniz, interrelations between mathematics and philosophy, 137–156, Archimedes,...
Mikhail Katz's user avatar
  • 6,052
5 votes
1 answer
6k views

What is the origin of the Chinese Stick Multiplication method?

A while back I came across an interesting method to do multiplication. I don't know what it's called and am interested in when (and who) developed this method. I don't know if it's a mathematical ...
Mayo's user avatar
  • 153
5 votes
1 answer
550 views

Beware the Ides of March!

Apropos of the murder of Gaius Julius Caesar, the late V. I. Arnold told the following amusing story in pages 89-90 of his "Yesterday and Long Ago": CAESAR AND GAULS: THE DEFENSE OF ROME FROM THE ...
José Hdz. Stgo.'s user avatar
5 votes
2 answers
344 views

What was Pauling's claim about vitamin C?

As I understand it after winning two (un-shared) Nobel prizes Linus Pauling began work which eventually had him recommending large amounts of vitamin C to all and sundry. When another scientist was ...
Elliot's user avatar
  • 242
4 votes
4 answers
799 views

Did Kronecker attribute immutable origin to the integers?

The familiar quote is often incorrectly attributed to Kronecker directly. Actually a colleague of his named Weber claimed after Kronecker's death that Kronecker said this. I have doubts about this ...
Mikhail Katz's user avatar
  • 6,052
4 votes
2 answers
607 views

What is the evidence for the existence of Geber?

In an unrelated question, some users started arguing about the existence of Geber (Jabir ibn Hayyan - جابر بن حيّان) from 806−816 AD and pseudo-Geber (probably from 13th-14th century). This ...
Mauricio's user avatar
  • 3,937
4 votes
1 answer
142 views

Source of a quote typically attributed to Proclus Lycaeus

The quote in question goes something like this: This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and ...
Jamai-Con's user avatar
  • 271
4 votes
1 answer
424 views

Is it true that Empress Elisabeth of Austria did math?

I have encountered a user on Math Stack Exchange with writing in his bio that Empress Elisabeth of Austria ("Sisi") did some math and she was famous for an unsolvable integral: $$\int_{0}^{1}...
SPARSE's user avatar
  • 248
3 votes
1 answer
1k views

Was Rayleigh the first to derive the drag equation?

I was reading about The Drag Equation: $$ F_D = \frac{1}{2} \rho v^2 C_D A $$ where: $ F_D $ is the drag force $ \rho $ is the mass density of the fluid $ v $ is the flow velocity relative to the ...
Nau's user avatar
  • 233