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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 …

[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 …

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 …

Mathematics: A Very Short Introduction by Timothy Gowers. It is very short and indeed very insightful. It is not a textbook, but includes some school-mathematics topics. From the cover: The aim o …

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 …

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 …

This is a historical question that needs some background to make sense. Let me start with the longer version of the question: When did negative numbers, algebra and coordinate plane come together? …

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 …

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} = …

"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 …

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 …

Is there any actual historical example in which a Cartesian plane with all four quadrants has been used, but with all axes marked with positive numbers? [Please see Sawyer's paper below for a "made-up …

You may enjoy Reviel Netz' book: The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge: Cambridge University Press, 1999. It examines the use of letters diagrams in …

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: " …