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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 …

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 …

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? …

"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 …

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 …

[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 …

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 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 …

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 …

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} = …

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 …

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: " …

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 …

This is to add something to Francois' answer to the UPDATE. This is from "Frege : philosophy of mathematics" by Dummett (1991), p. 50: One of the mental operations most frequently credited with cr …

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 …