15 votes
Accepted

Who was N.M. Stephens who refuted the Stronger Feit-Thompson Conjecture?

I’m Nelson Stephens’ daughter. He was born on 6th May 1941 and was a Professor of Mathematics at the University of London. He passed away on 8th January 2024. Not sure I can be much help on the maths ...
Sophie's user avatar
  • 166
6 votes
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How did Gauss determine the number of primes?

For what it's worth: As Goldshtein writes, “Evidently Gauss considered the tabulation of primes as some sort of pastime and amused himself by compiling extensive tables on how the primes distribute ...
akhmeteli's user avatar
  • 961
5 votes

Why is the claim that $\pi$ contains all natural numbers thought by the general public to be proven, despite it being conjecture currently?

People without mathematical training have many mistaken beliefs. (Students studying higher math develop mistaken beliefs too, but on a higher level: see here). It is natural to think every non-...
KCd's user avatar
  • 5,617
4 votes
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David Hilbert's paper: Substitution of the group of cyclotomic field

I think in modern notation, the element $\Theta$ (which is literally defined as $\displaystyle e^{\frac{2\pi i}{l^h}}$ i.e. a primitive $l^h$-th root of unity; $l$ is a prime here) would often be ...
Torsten Schoeneberg's user avatar
4 votes

Implications of several unpublished "binomial congruences" of Gauss

I have seen papers and books on Gauss and Jacobi sums discuss such results, e.g., see https://core.ac.uk/download/pdf/82122545.pdf. The book "Gauss and Jacobi sums" by Berndt, Evans, and ...
KCd's user avatar
  • 5,617
3 votes

Background of 'Eisenstein series'

See the book "Elliptic and Modular Functions from Gauss to Dedekind to Hecke" by Ranjan Roy. It is a very rich source of material on the history of topics related to modular functions. ...
KCd's user avatar
  • 5,617
3 votes

How could the people of the past be sure that $a \times b = b \times a$?

The guesses that are ventured in this question are entirely wrong. (1) That our reason to think multiplication is commutative is that we have an axiom that says so is wrong. (2) That those without ...
Michael Hardy's user avatar
2 votes
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Teiji Takagi's Fondation of Class Field Theory in Terms of Norms

Honestly, I not see any mathematical connection, between these two objects - the ideal norm and Hilbert's norm residue - beside similar names as I remarked before. Does anybody see the connection ...
KCd's user avatar
  • 5,617
2 votes
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How did Fermat handle Frenicle's challenge to find a perfect number between $10^{20}$ and $10^{22}$?

Probably (I cannot easily verify...) Fermat knew a basic modular arithmetic device, that for prime $p$ dividing $b^n-1$, either $p|b^d-1$ for a proper divisor of $n$, or $p=1\mod n$. (This is related ...
paul garrett's user avatar
  • 1,064
2 votes

Finite fields as quotients

In the famous XI-th Supplement in Dirichlet-Dedekind's Vorlesungen über Zahlentheorie, quotient rings modulo an ideal (prime ideal or general nonzero ideal) are not used, but systems of ...
KCd's user avatar
  • 5,617
1 vote
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Question about Felix Klein's "Development of Mathematics in the 19th Century"

Regarding your second question: It is not clear what you mean by "the set of numbers divisible by the field $K\sqrt{-5}$". In any field, every element is divisible by every non-zero element ...
nwr's user avatar
  • 6,859

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