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The flattering lie You Could Have Invented Spectral Sequences by Timothy Y. Chow.

Wrong! Here is Bourbaki document on algebraic geometry, taken from the now available Master's Archives: click on Autres rédactions, then on Chap.I Théorie globale élémentaire (91 p.) This prelimina …

In 1882 Kronecker proved that every algebraic subset in $\mathbb P^n$ can be cut out by $n+1$ polynomial equations. In 1891 Vahlen asserted that the result was best possible by exhibiting a curve in …

In 1908 Steinitz and Tietze formulated the Hauptvermutung ("principal conjecture"), according to which, given two triangulations of a simplicial complex, there exists a triangulation which is a common …

Certainly Bourbaki never wrote an introduction to algebraic geometry: we would have heard about it, right?

Rainich=Rabinowitsch (of trick fame : cf. Nullstellensatz). Here is an anecdote related by Bruce P. Palka, Editor of American Mathematical Monthly in Vol.111 (2004) of that journal (page460). Rai …

Projective geometry was introduced by fifteenth century Renaissance painters (like Alberti, da Vinci and Dürer) in the guise of perspective theory, although one could argue that Pappus was already doi …

Yes, he did. In his Récoltes et semailles, volume I posthumously edited by Gallimard in 2022 he reminisces (in footnote 68, page 522) about his first encounter with $\pi$ as a child: "La valeur appro …

It is usual in algebraic geometry to represent morphisms by vertical arrows pointing downwards, like that : $$\begin{matrix} X \\\\ \downarrow \\\\ S \end{matrix}$$ I suppose this stemmed from Grot …

If you look at the cross $C\subset \mathbb A^2_k$ given by $xy=0$ in the affine plane over the field $k$, you see or compute that it is exceptional at $O=(0,0)$ for many (obviously not independent) …

Dear Jérôme, I doubt that Grothendieck ever said that. However, in an analogous vein, Jean Leray, a brilliant French mathematician, was taken prisoner by the Germans in 1940 and sent to Oflag XVIIA …

Dear Charles, Dieudonné and Grothendieck themselves changed their terminology in the second edition of EGA I, published by Springer Verlag in 1971. At the end of their Avant-propos, on page 3, they wr …

In the theory of holomorphic functions of several variables, Hartogs's theorem that any holomorphic function on a punctured open set of $\mathbb C^n$ ($n\geqslant 2$) can holomorphically be continued …

There is a well-known story about Grothendieck being asked to explain concretely some result involving prime numbers and of his answering "You mean an actual number? All right, take 57". See here. Un …

I) The term exterior multiplication ("äussere Multiplication") is due to Grassmann, who introduced the term in his book (written in 1844) Die Wissenschaft der extensiven Grösse oder die Ausdehnungsl …