With so many blogs being written by members of the literati, it’s not surprising that a widespread meme involves compiling lists of writers and books.  I’ve even succumbed to it myself.   Lists of mathematicians are not as common, so I thought I’d present a list of the 20th century greats.    Some of these are famous for a small number of contributions, or for work which is only narrow, while others have had impacts across many parts of mathematics.
Each major area of mathematics represented here (eg, category theory, computer science) could equally do with its own list, which perhaps I’ll manage in due course.  I’ve included David Hilbert, Felix Hausdorff and Bertrand Russell because their most influential works were published in the 20th century.  Although Hilbert reached adulthood in the 19th century, his address to the 1900 International Congress of Mathematicians in Paris greatly influenced the research agenda of mathematicians for much of the 20th century, and his 1899 axiomatization of geometry (following the lead of Mario Pieri) influenced the century’s main style of doing mathematics.   For most of the 20th century, mathematics was much more abstract and more general than it had been in the previous two centuries.    This abstract style perhaps reached its zenith in the work of Bourbaki, Grothendieck, Eilenberg and Mac Lane, while the mathematics of Thurston, for example, was a throwback to the particularist, even perhaps anti-abstract, style of 19th century mathematics.  And Perelman’s major contributions have been in this century, of course.

• David Hilbert (1862-1943)
• Felix Hausdorff (1868-1942)
• Bertrand Russell (1872-1970)
• Henri Lebesgue (1875-1941)
• Godfrey Hardy (1877-1947)
• LEJ (“Bertus”) Brouwer (1881-1966)
• Srinivasa Ramanujan (1887-1920)
• Alonzo Church (1903-1995)
• Andrei Kolmogorov (1903-1987)
• John von Neumann (1903-1957)
• Henri Cartan (1904-2008)
• Kurt Gödel (1906-1978)
• Saunders Mac Lane (1909-2005)
• Leonid Kantorovich (1912-1986)
• Alan Turing (1912-1954)
• Samuel Eilenberg (1913-1998)
• René Thom (1923-2002)
• John Forbes Nash (1928-2015)
• Alexander Grothendieck (1928-2014)
• Michael Atiyah (1929- )
• Steven Smale (1930- )
• Paul Cohen (1934-2007)
• Nicolas Bourbaki (1935- )
• Sergei Novikov (1938- )
• Stephen Cook (1939- )
• William Thurston (1946-2012)
• Edward Witten (1951- )
• Andrew Wiles (1953- )
• Richard Borcherds (1959- )
• Grigori Perelman (1966- )
• Vladimir Voevodsky (1966- )
• Edward Frenkel (1968- )

And here’s my list of great mathematical ideas.