79 votes
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What's the famous story about a mathematician who gave a talk without saying a word?

You are most likely referring to the 1903 presentation by American mathematician Frank Cole. The original false conjecture was that the 67-th Mersenne number $M_{67}:=2^{67}-1$ is prime, and it goes ...
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  • 66k
76 votes
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What evidence is there that Fermat had a proof for his Last Theorem?

The other answer is correct. In addition, there is significant evidence that Fermat did not have a proof of the theorem now known as Fermat's Last Theorem. First, we should note that Fermat was not a ...
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  • 2,732
33 votes
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Is the story about Fermat's writing on a margin true?

Yes, it is true. Fermat's own copy was used in the publication of Diophantus by Fermat's son Samuel, and he included Fermat's notes. The original with Fermat's handwriting is lost. https://www.joh.cam....
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32 votes

What evidence is there that Fermat had a proof for his Last Theorem?

There is no way that Fermat could have had anything approaching the now commonly-accepted proof. Almost none of the concepts in that proof were known in any form in Fermat's time. Further, Fermat is ...
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  • 653
25 votes

Irrationality of the square root of 2

I do not agree on some details of the interpretation regarding the discovery of the irrationality of $\sqrt{2}$ as a confutation of the Pythagoreans [...] belief that all numbers could be ...
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25 votes
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Did ancient Greek mathematicians consider numbers independently of geometry?

The answer is yes. There was a split. First of all, for the Greek mathematics (and very long after them) "numbers" were integers. "Rational numbers" were called fractions, and no ...
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19 votes
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Ancient Chinese numbering system

It has been said that the invention of zero was a great leap forward, not only in abstract understanding, but in the ability to introduce place value notation and do computations; computing using ...
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17 votes
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How much did John Nash contribute to proving the Riemann hypothesis?

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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  • 6,004
15 votes

Irrationality of the square root of 2

According to this link, Legend has it that Hippasus first discovered the irrationality of $\sqrt{2}$. The second link in fact mentions a legend that held that supporters of Pythagoras murdered ...
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14 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 ...
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13 votes
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Have numbering systems other than base ten ever been used or popular?

To this day many people use various systems besides the decimal one. I was surprised to read that "Old Babylonians used the system based on 60":-) Do not we all use their system today? Not only for ...
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13 votes

Have numbering systems other than base ten ever been used or popular?

Old Babylonians used base 60 for calculations. (This is also where 60 seconds in a minute and 60 minutes in an hour come from.) According to Wikipedia, the main advantage of this was that it made ...
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13 votes
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Who first introduced the notation $\mathcal{O}$ in algebraic geometry or algebraic number theory

Your guess is right: the notation $\mathfrak o$ goes back to Dedekind. If you get a copy of Dirichlet-Dedekind's Vorlesungen über Zahlentheorie and look in Dedekind's famous XI-th Supplement, which ...
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  • 4,064
12 votes

Irrationality of the square root of 2

These legends do exist, and have for along time. But few if any specialist historians of the subject believe Pythagoreans discovered irrationality of $\sqrt{2}$. See: Pythagoras vs. the idea of ...
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12 votes
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What is the origin of the Collatz conjecture?

Wikipedia does not actually know that it is from 1937, my guess is that they picked a number between 1929 and 1950. According to Lagarias, who compiled an exhaustive bibliography on the problem, the ...
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  • 66k
12 votes
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History of Galois Theory after Galois

I suggest that you reed B. Melvin Kiernan's The Development of Galois Theory from Lagrange to Artin. In particular, it says there that: In the 1890's a few noteworthy expositions of GALOIS Theory ...
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11 votes

Were transcendental numbers considered rare, pre-Cantor?

As I understand, people did not think much about comparing the size of infinite sets before Cantor, so for most of them the question you are asking had no meaning, and they did not think about it. ...
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11 votes

Have numbering systems other than base ten ever been used or popular?

The Celts (ie. Iron Age Britons and their descendents) are reputed to have used a base 20 system. This is meant to be the origins of the Yan Tan Tethera counting system used by many upland sheep ...
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11 votes
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History of $0 \in \mathbb N$.

For modern times: Richard Dedekind, Was sind und was sollen die Zahlen? (1888), page 20: §71. Definition. A system $N$ [Ein system $N$] is said to be simply infinite when there exists a similar ...
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10 votes

Have numbering systems other than base ten ever been used or popular?

The French language still has the residue of a base-twenty system. Their word for 80 is 'quatre-vingts', which literally translates to 'four twenties'.
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  • 301
10 votes
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When was the first recorded occurence of irrational and imaginary number usage in number theory?

Irrational numbers were used by the ancient Greeks when they were discovered. The earliest texts did not survive but there are plenty of them in Euclid. Though they are not called numbers. The theory ...
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9 votes
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How did Mersenne discover Mersenne primes?

In Elements IX.36 Euclid proves:"If as many numbers as we please beginning from a unit are set out continuously in double proportion until the sum of all becomes prime, and if the sum multiplied into ...
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9 votes
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Who first identified $\frac{n}{\ln(n)}$ as an approximation of a prime counting function?

Gauss also came up with the more discrete $n/\ln (n)$- in volume 10 of his collected works appears a short (5-6 pages) fragment entitled "asymptotic laws of arithmetics", which is dated to the year ...
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9 votes
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What changes in mathematics resulted in the change of the definition of primes and exclusion of 1?

As to the primality of $1$, nothing really evolved. This is an illustration that some things in mathematics are not right or wrong, they are just a matter of taste. And some fraction of the population ...
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  • 66k
8 votes

Irrationality of the square root of 2

The fact that $\sqrt{2}$ existed and is irrational was a blow to the ancient Greeks who only believed in numbers that they could calculate to a certain degree of precision whenever required. Or in ...
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8 votes
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Why is Dirichlet's L-function called "L-function"?

It's the original notation used by Dirichlet. The reason why he chose L, without commenting on the choice, rather than some other letter is not known. Chances are there is not much of a reason, and he ...
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  • 1,421
8 votes
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Who influenced Gauss in his abstract approach to mathematics?

Gauss in Disquisitiones Arithmeticae (1799) does indeed express something close to what is now called mathematical formalism and structuralism. He writes: "What is calculated (in the sense of ...
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  • 66k
8 votes

Number theory: a quote

"It has been estimated that, at the present stage of our knowledge, one could give a 200 semester course on commutative algebra and algebraic geometry without ever repeating himself." These ...
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