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

The Greatest Mathematicians of All Time
ranked in approximate order of "greatness."
To qualify, the mathematician's work must have breadth, depth, and historical importance.
 

 

Isaac Newton Carl F. Gauss Archimedes Leonhard Euler Euclid		Bernhard Riemann Henri Poincaré David Hilbert Alexander Grothendieck Joseph-Louis Lagrange		Gottfried W. Leibniz Pierre de Fermat Niels Abel Évariste Galois John von Neumann
Srinivasa Ramanujan Karl W. T. Weierstrass Brahmagupta René Déscartes Augustin Cauchy		Hermann K. H. Weyl Leonardo `Fibonacci' Carl G. J. Jacobi Peter G. L. Dirichlet Georg Cantor		Arthur Cayley Emma Noether Eudoxus of Cnidus Kurt Gödel Pythagoras of Samos
At some point a longer list will become a List of Great Mathematicians rather than a List of Greatest Mathematicians. I've expanded the List to Seventy-five, but you may prefer to leave it at Forty or Thirty or even prune it back to just a Top Twenty or Top Fifteen or Top Ten List.
Bháscara Áchárya Blaise Pascal Apollonius of Perga Muhammed al-Khowârizmi Pierre-Simon Laplace		William Rowan Hamilton Richard Dedekind Charles Hermite André Weil Stefan Banach		Felix Christian Klein Diophantus of Alexandria George Boole Ferdinand Eisenstein François Viète
Girolamo Cardano Christiaan Huygens Pappus of Alexandria Gaspard Monge Johannes Kepler		Andrey N. Kolmogorov Alhazen ibn al-Haytham Jacques Hadamard L.E.J. Brouwer Hipparchus of Nicaea		Liu Hui Albert Einstein   (*) Jean-Victor Poncelet Jacob Bernoulli John Wallis
Aryabhatta Jean le Rond d'Alembert Godfrey H. Hardy Adrien M. Legendre Jakob Steiner		Joseph Liouville Joseph Fourier John E. Littlewood Simeon-Denis Poisson Johann Bernoulli		Émile Borel James J. Sylvester Thales of Miletus Omar al-Khayyám Henri Léon Lebesgue
Other contenders:       Archytas   Artin   Atiyah   D.Bernoulli   Bolyai   Bolzano   Cavalieri   Chang   Chasles   Chebyshev   Clairaut   deMoivre   Desargues   Erdös   Galileo   Germain   Heaviside   Heron   Hippocrates   Hypatia   ibnQurra   Jordan   Kowalewski   Kronecker   Kummer   Lambert   Landau   Lie   Lobachevsky   Maclaurin   Madhava   Minkowski   Napier   Nasir at-Tusi   Panini   Perelman   Plato   Polyà   Ptolemy   Regiomontanus   Seki   Serre   Shannon   Sturm   Turing   Zeno   et cetera