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I think one reason JSTOR doesn't have “loss of generality” before 1831 is that fewer scientists wrote in English. But one finds (with minor variants merged, translations *starred, and year first publi …

I can muddy the waters...! According to editor E. Scholz of Hausdorff’s Collected Works (2008, p. 884): In a note of 3/20/1933 (Nachlass, fasc. 449) and in a further undated note (fasc. 571), Hausdor …

Q1. Is there a sense in which the boundary operator $\partial$ is analogous to a derivative? It may be worth noting that de Rham in (1936) and especially (1938, pp. 317–323) already spelled out m …

I now believe that my question (and suggestion that proof $(1)$ should have become standard before Lacroix) relied on the misconception that tangent was easier to differentiate than arctangent. In fac …

In the manuscript "Determinationum progressio in infinitum" (pp. 668-675 of Sämtliche Schriften und Briefe, Reihe VII, Band 3, Teil C, available in pdf here), Leibniz writes on p. 673 (with "$\sqcap$" …

Although just beyond your 50-year scope, this may be of interest. Among the series $\mathsf A_n, \mathsf B_n, \mathsf C_n, \mathsf D_n$ in the Cartan-Killing classification of simple Lie groups, every …

Apparently first introduced by Weierstrass in Winter 1862/63 lectures published by H. A. Schwarz (1881, 1885, 1892, 1893), §9: Mit der Sigma-Function $\mathfrak Su$ ist die Pe-Function $\wp u=\wp(u\m …

Eduard Study in Von den Bewegungen und Umlegungen, Math. Ann. 39 (1891) 441-566, writes on p. 508: Here $g, g^*, g'$ are rays in space with polar planes $\gamma, \gamma^*, \gamma'$, $\mathfrak P$ i …

I think it's well known to have been introduced by Grassmann. He explains the word choice in Die lineale Ausdehnungslehre (1844, pp. x-xi): I have shown how one can understand as product of two se …

Despite the claims reported from Wikipedia and the “Earliest Uses” site, this notation certainly started much before Hurewicz-Steenrod (1940; 1941) or Ore (1935, p. 416; 1936) for, respectively, Domai …

On page 322 of Serre, Jean-Pierre, The works of Wiles (and Taylor,(\dots)). I., Séminaire Bourbaki. Volume 1994/95. Exposés 790-804. Paris: Société Mathématique de France, Astérisque. 237, 319-332, Ex …

$P=$ Calabi’s conjecture. Specifically, the link says “By the late 1960s, many were doubtful of the Calabi conjecture”, then Yau did “produce a "counterexample" to the conjecture. The "counterexample" …

Euler in Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie, 17-24 feb 1761, writes about objects he calls spaces (my emphasis): As a general notion encompasses an in …

Most ancient: Wikipedia has a daguerreotype of Gauss (1777–1855) on his deathbed. Or possibly Farkas Bolyai (1775–1856) in what look like similar circumstances. Less ancient, but allegedly photographe …

If a 25-year interlude will do, there is R. F. Coleman has sent me his preprint ["Manin's proof of the Mordell conjecture'', Preprint, 1988; per bibl.] concerning my proof of Mordell's conjecture …