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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 …

While irruption of cardinal in this context must somehow relate to Whittaker’s — also unexplained — use of the word (to name the functions subject to his sampling theorem), it seems far less clear tha …

Von Neumann uses "equivalence class" in Zur Prüferschen Theorie der idealen Zahlen, Acta Sci. Math. (Szeged) 2 (1926) 193-227, p. 197 (viewable after free registration): Wir nennen $R$ und $S$ äquiva …

The German word is treu, and I would look to papers by Hermann Weyl for its introduction. E.g. Quantenmechanik und Gruppentheorie (1927, p. 16): Da das Gruppenschema aus der Darstellung abstrahiert w …

Wilhelm Killing's program Zur Theorie der Lie'schen Transformations-Gruppen (Braunsberg, 1886) predates the accepted answer by 5 years. It is reprinted in his Correspondence with Friedrich Engel (1997 …

The letters $\mathrm X$ and $\mathrm Y$ are already used by Cayley in what Dieudonné (in MR) calls the first description of all finite-dimensional irreducible $\mathfrak{sl}_2$-modules: A Second Memoi …

The naming (attributed by Borel as quoted by @GjergjiZaimi) happened quite publicly, in Roger Godement : Groupes linéaires algébriques sur un corps parfait, Sémin. Bourbaki 13 (1960/61), Exp. No. 206, …

It’s far from true. For one thing, Crofton in his famous paper (1869, p. 198) speaks of points “distributed with uniform density over the plane” (my bold). Moreover he refers to prior discussion in Th …

From around 1900 to 1970, there was a highly-entrenched practice to write maps as $f:x\to y$ with an arrow between argument and value (e.g. Weyl 1913, p. 54). Starting in the 1930s, a programme arose …

Can someone explain, why in English the name "tempered" wins? Presumably because that’s how the inventor himself translated it (French past participle to English past participle), on e.g. p. 188 of …

Added: This terminology of Hirzebruch (1966), Steenrod (1951) translates the $\boldsymbol n$-Systeme of Stiefel (1936), $\boldsymbol n$-podes, $\boldsymbol n$-pèdes or multipèdes of Einstein (1931), Waelsch …

L. Kadison (2012, preprint p. 8) uses endo-operator. (That’s “attributive”, but I guess “predicative” use could still work, in the same way MacLane says an arrow is epi.)

French intellectuals of a certain period made à la limite into a widespread idiom (or verbal tic) meaning, not just “borderline” or “in a pinch” as dictionaries say, but the taking of an argument to s …

Borel (1951) definitely drew on an existing tradition. Besides de Saussure’s work unearthed in J.M. Selig’s answer, he could have learned « flag » from: van der Waerden (1936, pp. 15, 30) (they like …