Isaac Newton	Archimedes	Carl Gauss	Leonhard Euler	Bernhard Riemann	Henri Poincaré
J.-L. Lagrange	Euclid	David Hilbert	G.W. Leibniz	Alex. Grothendieck	Pierre de Fermat

The Greatest Mathematicians of the Past
ranked in approximate order of "greatness."
To qualify, the mathematician must be born before 1930 and his work must have
breadth, depth, and historical importance.
 

Isaac Newton Archimedes Carl F. Gauss Leonhard Euler Bernhard Riemann		Henri Poincaré Joseph-Louis Lagrange Euclid of Alexandria David Hilbert Gottfried W. Leibniz		Alexandre Grothendieck Pierre de Fermat Évariste Galois John von Neumann Srinivasa Ramanujan
René Descartes Karl W. T. Weierstrass Hermann K. H. Weyl Peter G. L. Dirichlet Georg Cantor		Brahmagupta Niels Abel Augustin Cauchy Emmy Noether Arthur Cayley		Pythagoras of Samos William R. Hamilton Carl G. J. Jacobi Apollonius of Perga Leonardo `Fibonacci'
At some point a longer list will become a List of Great Mathematicians rather than a List of Greatest Mathematicians. I've expanded my original List of Thirty to an even Hundred, but you may prefer to reduce it to a Top Seventy, Top Sixty, Top Fifty, Top Forty or Top Thirty list, or even Top Twenty, Top Fifteen or Top Ten List.
Charles Hermite Pierre-Simon Laplace Carl Ludwig Siegel Johannes Kepler Diophantus of Alexandria		Aryabhata Muhammed al-Khowârizmi Richard Dedekind Felix Christian Klein Kurt Gödel		Bháscara (II) Áchárya Blaise Pascal Élie Cartan Archytas of Tarentum Godfrey H. Hardy
Alhazen ibn al-Haytham Jean le Rond d'Alembert Andrey N. Kolmogorov Hipparchus of Nicaea F.E.J. Émile Borel		Julius Plücker Joseph Liouville Jacob Bernoulli F. Gotthold Eisenstein Giuseppe Peano		Stefan Banach Panini of Shalatula André Weil Jean-Pierre Serre Jacques Hadamard
Marius Sophus Lie Jakob Steiner F. L. Gottlob Frege Eudoxus of Cnidus M. E. Camille Jordan		François Viète Joseph Fourier Christiaan Huygens Bonaventura Cavalieri Hermann G. Grassmann		Albert Einstein James C. Maxwell Girolamo Cardano Aristotle Galileo Galilei
Einstein, Maxwell, Cardano, Aristotle and Galileo are among the greatest applied mathematicians in history, but lack the importance as pure mathematicians to qualify for The Top 70. Nevertheless I'd want to include them in any longer list, so I've tucked these ambiguous cases into the #71-#75 slots.
Michael F. Atiyah Atle Selberg Alfred Tarski Gaspard Monge L.E.J. Brouwer		Liu Hui Alan M. Turing Johann H. Lambert Israel M. Gelfand John E. Littlewood		Jean-Victor Poncelet Ernst E. Kummer Felix Hausdorff Henri Léon Lebesgue George Pólya
John F. Nash, Jr. Johann Bernoulli George D. Birkhoff Shiing-Shen Chern Adrien M. Legendre		James J. Sylvester John Wallis Pafnuti Chebyshev Omar al-Khayyám Thales of Miletus
This is primarily a list of Greatest Mathematicians of the Past, but I use 1930 birth as an arbitrary cutoff, and one of the "Top 100" (Jean-Pierre Serre) is still alive as of 2022. Click here for a longer List of 200 including many more 20th-century mathematicians.)