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Consider that the question does not concern the origin of the ideas of equivalence relation and equivalence class. It exactly concerns the origin of the terms "equivalence relation" and "equivalence c …

You could not relate the equation $x^3+200x=20x^2+2000$ to the figures because, in fact, it does not originate from them. Here, Khayyam tries to find a point on the circle such that $ \frac{AE}{RH} = …

I came across an algebra problem book written in 1899 for students of Dar al-Fonun ([dɒːɾolfʊˈnuːn], meaning, "polytechnic college",) the only modern educational institute in Iran at the time (establ …

I was surprised not to see any mention of Lakatos' "Proofs and Refutations, The logic of Mathematical Discovery". At least, it uses the two words "discovery" and "proof" in the title! Here is an examp …

I was looking for the same claim about another mathematician (namely Vazgain Avanissian) that I came to this question. Following the clues left by the previous answer and the comments, I found a menti …

Here is a basic, though very important, example: Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of construct …

The longest-standing one of the sort is the "conjecture" that the parallel postulate can be proved using Euclid's first four postulates. I know that it is a far-fetched understanding of "conjecture". …

I guess, though I am not sure, the case of Albert Wormstein falls in your third category: Professional mathematicians writing mathematics under both their real name and a pseudonym. This paper: " …

[Migrated from Math Stack Exchange] More than a year ago, I posted the following on the Math Stack Exchange. Consider $2^n-1$. Based on checking a few small numbers for $n$ (in fact, the firs …

Recently I have "finished" a 13-year on and off research on the history of the mathematical notion of equivalence. At the end of which, I learned that we owe the nowadays rather elementary process of …

Warning. This is an attempt at an answer out of curiosity rather than an expert answer. Newton has the following passage in "Recomputation of surfaces of least resistance," (1694) (see Whiteside*, p …

Not sure if this answer adds anything to the ones already given. I write it because It is an example where Euler explicitly writes about the necessity of giving a proof, and more importantly, calls a …

Was Cantor Surprised? published in Monthly is debunking (or trying to do so) that Cantor was so surprised when he discovered $I=[0,1]$ and $I^2$ have the same cardinality that he said “I see it, but …

"The big picture" that can be seen in Carlo Beenakker's example is Rhetorical (verbal); Syncopated (abbreviated words); Symbolic. However, this well-known picture is very alge …

Just for the record, I thought this passage from Omar Khayyam's algebra book (p.49) should be here. In particular, it shows how hard it was to to tie the understanding of powers to geometry I say …