Resolves on the date after the first viable proof of the Riemann hypothesis is presented and accepted. Until then, a healthy discussion is appreciated.
1,000
3.00
@sixtynine do you want to extend the close date by a few years? The Riemann Hypothesis remains unproven.
Poincare, Riemann, Laplace, and Von Neumann were all undervalued here. But Gauss and Euler are the standard answers. Euclid, hard to know what mathematics he actually developed. Moreover, while he is known for the idea of establishing all of mathematics from a few axioms, many of his arguments were not rigorous, so this was only an aspiration.
@HarrisonNathan He basically established the formal idea of a mathematical proof as we understand it today and founded axiomatic geometry. It's hard to think of a more fundamental contribution to math than that coming from a single person (although Pythagoras deserves some credit here as well).
Note that most mathematicians were not rigorous by today's standards. The definition of limit was formalized by Cauchy and Weierstrass eg, a century after Newton died. And the set theoretical foundation of mathematics is very modern - early 20th century iirc
Newton should also be top 3
He pretty much founded modern mathematics with the development of calculus. John von Neumann (considered by many one of the smartest humans ever) said: "The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking"
And besides calculus "Newton's work has been said 'to distinctly advance every branch of mathematics then studied'" [...] "generalised binomial theorem, valid for any exponent. He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula) and was the first to use power series with confidence and to revert power series." https://en.wikipedia.org/wiki/Isaac_Newton
Archimedes should be top 3
Archimedes was using calculus concepts in 250 BC. He was thinking about the differences between different types of infinities, which was rediscovered only until Cantor in late 1800s and was not even accepted by main mathematicians then (Kronecker kept attacking Cantor and pretty much killed him because of that).
Wiki page says: "Considered the greatest mathematician of ancient history, and one of the greatest of all time" and has all these sources backing that claim: https://en.wikipedia.org/wiki/Archimedes#cite_note-LitList-5