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L'Hôpital's rule was first published in Analyse des Infiniment Petits. According to The Historical Development of The Calculus by Edwards (p. 269), L'Hospital's argument, which is stated verbally w …

Hilbert's finiteness theorem, which arguably "killed classical invariant theory" and resulted in the creation of abstract algebra. Hilbert's first work on invariant functions led him to the demonstra …

According to Weierstrass, Riemann knew about the existence of continuous nowhere differentiable functions. (Weierstrass' celebrated example was published in 1872, some 6 years after Riemann's death.) …

Weierstrass simply observed that not every problem in the calculus of variations would have a solution. He considered the example $$D[y]=\int_{-1}^{1}x^2\left(\frac{d y}{dx}\right)^2dx\to \min,$$ wher …

According to Hans Samelson's historical note "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by Poincaré (vol. 3, Gauthier-Villar …

Riemann's flawed proof of the Riemann mapping theorem which crucially relied on Dirichlet's principle. The theorem was stated by Bernhard Riemann in 1851 in his PhD thesis. Lars Ahlfors wrote once, c …

Jonathan M. Borwein, David H. Bailey and Roland Girgensohn discuss this and related formulae for $\pi$ in their book "Experimentation in Mathematics" (see Section 1.1, p. 3). They claim that The i …

The limit $$ \lim_{x\to 0}\frac { f(x) - g(x) } { f^{-1}(x) - g^{-1}(x)} = -\left(f'(0)\right)^6 $$ appears in the Problems section of Mathematics Magazine, where it is calculated under the assumptio …

Urysohn's example of a countable connected Hausdorff space with a countable base was published in his last paper «Über die Mächtigkeit der zusammenhängenden Mengen», Math Annalen 94 (1925), 262—295. …

There is a survey article by Berndt, Choi, and Kang devoted to the set of 58 Ramanujan's problems. They indicate that the questions had originally appeared in the problems section of the Journal and a …

Great Soviet mathematician N.I. Akhiezer mentions in his survey article "Чебышевское направление в теории функций" ("Function Theory According to Chebyshev") that the notation $$T_n(x)=\frac{1}{2^{n- …

According to these pages, the earliest known appearance of the term pole might be in "Théorie des fonctions elliptiques" (1875, p. 15) by Briot and Bouquet: Lorsqu'une fonction $u$ est holomorph …

From the introduction to History of the Central Limit Theorem: From Laplace to Donsker by Hans Fischer: The term “central limit theorem” most likely traces back to Georg Pólya. As he recapitulat …

"The determination of Gauss sums" by Berndt and Evans (Bull. Amer. Math. Soc., Vol. 5, Number 2 (1981), 107-129.) contains an exposition of the original proof due to Gauss. It also includes a short hi …

From The Fabulous Fibonacci Numbers by A.S. Posamentier and I. Lehmann (Prometheus Books, New York (2007), pp. 17-18): Leonardo Pisano - or Leonardo of Pisa, Fibonacci - his name as recorded in hi …