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The ancient Greeks were quite strict in their separation of pure mathematics (mathematics) and applied mathematics (logistics). Euclid in his elements covered the basics of pure mathematics: line segm …

Hilbert and Weber were more or less working simultaneously and independently on questions that led them to introduce "class fields". Weber was interested in extending Dirichlet's theorem on primes in …

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 …

Maarten Bullynck has studied relations between Lambert's philosophical ideas and his mathematics. See http://www.kuttaka.org/~JHL/About.html for a start.

Indeed Hermite did not prove what today usually is called Hermite's theorem. Translated into modern terms, he shows that there are finitely many number fields of given degree and given discriminant. S …

I certainly have read a lot of classics, and have learned a lot (mostly about historical developments) even from Euclid's elements. When it comes to research mathematics, I'd at least like to mention …

This "almost" answers Zoran Škoda's question: Otto Grün (his theorems in group theory are still well known) published his first paper at the age of 46.

The cuneiform tablet MS 2351 from the 19th century BC contains the 15-digit sexagesimal number 13 22 50 54 59 09 29 58 26 43 17 31 51 06 40, which happens to equal $20^{20}$. I also seem to remember t …

Let me add a few remarks concerning 2. If $p \equiv 3 \bmod 4$, then ${\mathbb F}_p(i) = {\mathbb F}_{p^2}$. The relative norm of $x+iy$ is the product of $x+iy$ and its conjugate $x-iy$, but the latt …

Let me address your questions 1. - 4. What were the original goals of class field theory? The question is a little bit anachronistic; class field theory describes the splitting of primes in abelian …

Let $p \equiv 1 \bmod 3$ be a prime number, let $g$ be a be a primitive root modulo $p$, and $\zeta$ a primitive $p$-th root of unity. The three cubic periods are \begin{align*} \eta_0 & = \zeta + …

My guess is that whoever translated the fragments did not distinguish carefully between Gauss's own results and the comments by Schlesinger in https://archive.org/details/fragmentezurtheo00gausuoft As …

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 …

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. …

This doesn't fly. If the powers that be would like to delete the question, please go ahead. For my defense I'd like to add that I wanted to see whether my guess that most people would use the name Gau …