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I don't think there is a decisive answer to this question, because some mathematicians accepted negative coordinates long before others did. However, here is another landmark from the 1690s: Huygens' …

In recent times it has been claimed that Bhaskara I (around 700) and more definitely Ibn al-Haytham (965 - 1040) were aware of Wilson's theorem. This is much earlier than Wilson's theorem was previous …

Franel was a number theorist who gave introductory calculus lectures in French at the ETH. Maybe the ETH offered courses in different languages, because of its location in a multilingual country. Does …

Gödel 's failure to discover unsolvability of the decision problems for predicate logic and Peano arithmetic may be an example. Gödel had all necessary tools: arithmetization, diagonalization, and a …

If you count any inversion of a power series as a predecessor of Lagrange inversion, then I believe the earliest examples are Newton's inversion of the log series to obtain the exponential series, and …

As previous answers have pointed out, both the golden ratio and the Fibonacci numbers go back thousands of years. However, I believe the connection between the two was discovered around 1730. At that …

There is an English translation of the first 10 sections of Wessel's paper in the anthology edited by Henrietta Midonick, The Treasury of Mathematics, volume 2 (Penguin Books 1968) pp.321--329.

An earlier example than the Fermat primes is the class of primes of the form $2^n-1$, the so-called Mersenne primes. These occur in Euclid's theorem that $2^{n-1}(2^n-1)$ is perfect when $2^n-1$ is pr …

I imagine that Newton et al would have no trouble solving this teaser because they would say: let x be infinitesimal, in which case both numerator and denominator equal x-x; quotient equals 1 :)

The solution of the cubic equation by Scipione del Ferro and Tartaglia in the early 16th century. This was not only a great advance in algebra, but it also forced mathematicians to confront complex nu …

Cantor's diagonal argument first appears in his 1891 paper "Über eine elementare Frage der Mannigfaltigkeitslehre", Jahresbericht der Deutschen Mathematiker-Vereinigung 1: 75–78, in which he generali …

P. S. Novikov was 54 when he gave the first proof (143 pages!) of the unsolvability of the word problem for groups in 1955, and 58 when he co-solved the Burnside problem with S. I. Adian.

Since no one has mentioned A.N. Kolmogorov (born 1903), I hope I may be forgiven for a second answer. The following is from Kolmogorov's Wikipedia biography. In classical mechanics, he is best known …

Another point to consider is whether "Über den Rauminhalt" is in fact Dehn's first solution to Hilbert's 3rd Problem. I believe his first solution was in the paper "Über raumgleiche Polyeder" in the N …

The article is probably referring to Dedekind's Was sind und was sollen die Zahlen of 1888, in which point 64 is Dedekind's definition of infinite. This of course is after Cantor had been investigatin …