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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
103
votes
Accepted
How do we know that Fermat wrote his famous note in 1637?
Not only do we not know the date, we don't even know whether he wrote the remark at all.
For all we know it might have been invented by his son Samuel, who published his father's comments.
In his le …
87
votes
Pseudonyms of famous mathematicians
William Sealy Gosset published a result under the pseudonym
Student.
(Because his employer, the Guinness brewing company, did not allow their employees to publish for fear of divulging trade secrets. …
52
votes
Accepted
What was the relative importance of FLT vs. higher reciprocity laws in Kummer's invention of...
When Kummer started working on research problems,he tried to solve what became known as "Kummer's problem", i.e., the determination cubic Gauss sums (its cube is easy to compute). Kummer asked Dirichl …
39
votes
Accepted
Euler's Master's Thesis
Martin Mattmüller, in his article Leonhard Euler, seine Heimatstadt und ihre
Universität on Euler's hometown Basel, writes that this public talk (not a dissertation or written thesis), which Euler gav …
32
votes
Why is "abelian" infrequently capitalized?
I don't think that there's a good answer to this. The following episode at least shows that people have been thinking about the problem of capitalizing Abelian for quite a while.
In her letter to Has …
31
votes
what mistakes did the Italian algebraic geometers actually make?
A beautiful survey article on the Italian school, with a discussion of several errors of all kinds by Severi, can be found in
The Legacy of Niels Henrik Abel (Oslo 2002), Springer-Verlag 2004:
Brig …
30
votes
Did Euler prove theorems by example?
"Proof by example" is a technique used by Euclid, who often proved results that hold e.g. for n integers in a typical case, say for 3 integers, as well as by Diophantus, who had to choose values for h …
27
votes
Did Emmy Noether ever publish under a man's name?
In absence of any evidence (she has collected works, and there are various people who have studied her biography) this is nonsense. In addition, this would not at all be compatible with Emmy Noether's …
27
votes
Fermat's proof for $x^3-y^2=2$
Fermat did not prove this result; he claimed that the only solution is the obvious one and conjectured (in words that seem to suggest he knew how to prove it, but without explicitly saying so) that th …
27
votes
Accepted
What is the "ray" in ray class group?
There are many introductions to number theory, but few are as original (my term for what others would call weird) as Fueter's "Synthetische Zahlentheorie" published in 1925.
It starts with elementary …
25
votes
Accepted
Did Gauss know Dirichlet's class number formula in 1801?
In 1801, Gauss certainly was aware of the general procedure to obtain the class
number formula (or asymptotic results) via counting lattice points. As a matter of fact, the approach using lattice poin …
25
votes
Definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel
In a letter to Gauss, on January 3, 1840 (Werke II), Dirichlet stated the unit theorem in the same version as he would later publish it, along with the comment that the proof was very easy and could b …
23
votes
Major mathematical advances past age fifty
Furtwängler proved the principal ideal theorem when he was almost 60. No small feat given that Artin and Schreier simultaneously were working on it.
20
votes
Meaning of Kronecker's comment to Lindemann
This story is apocryphal. In my review of Dauben's article The battle for Cantorian set theory, I wrote that Dauben repeats the well known claim that Kronecker, in a lecture at the Berliner Naturforsc …
19
votes
Accepted
Did Apollonius invent co-ordinate geometry?
Let V be the vertex of a parabola, F its focus, X a point on its symmetry axis, and A a point on the parabola such that AX is orthogonal to VX. It was well within the power of the Greeks to prove rela …