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

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		David Hilbert Joseph-Louis Lagrange Euclid of Alexandria Alexandre Grothendieck Gottfried W. Leibniz		John von Neumann Henri Poincaré Évariste Galois Srinivasa Ramanujan Pierre de Fermat
Hermann K. H. Weyl Karl W. T. Weierstrass Brahmagupta Niels Abel René Descartes		Georg Cantor Emmy Noether Peter G. L. Dirichlet Pythagoras of Samos Muhammed al-Khowârizmi		Carl Ludwig Siegel Augustin Cauchy Arthur Cayley William R. Hamilton Apollonius of Perga
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 Leonardo `Fibonacci' Carl G. J. Jacobi Diophantus of Alexandria Pierre-Simon Laplace		Élie Cartan Aryabhata Johannes Kepler Andrey N. Kolmogorov Giuseppe Peano		F.E.J. Émile Borel Felix Christian Klein Richard Dedekind Bháscara (II) Áchárya Kurt Gödel
Archytas of Tarentum Godfrey H. Hardy Hipparchus of Nicaea Alhazen ibn al-Haytham Marius Sophus Lie		Blaise Pascal Julius Plücker Panini of Shalatula Stefan Banach Jacob Bernoulli		André Weil F. L. Gottlob Frege F. Gotthold Eisenstein Jean-Pierre Serre Jean le Rond d'Alembert
Alfred Tarski Michael F. Atiyah Jakob Steiner Christiaan Huygens François Viète		Atle Selberg Jacques Hadamard Joseph Liouville Joseph Fourier M. E. Camille Jordan		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.
Johann H. Lambert Alan M. Turing Felix Hausdorff Israel M. Gelfand George Pólya		John F. Nash, Jr. John E. Littlewood Eudoxus of Cnidus L.E.J. Brouwer Hermann G. Grassmann		Bonaventura Cavalieri Ernst E. Kummer Shiing-Shen Chern James J. Sylvester Johann Bernoulli
George D. Birkhoff Gaspard Monge Henri Léon Lebesgue Andrei A. Markov Pafnuti Chebyshev		Omar al-Khayyám John Wallis Jean-Victor Poncelet Adrien M. Legendre 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 2023. Click here for a longer List of 200 including many more 20th-century mathematicians.)