Mathematical Genius: Who Are Humanity's Current Mathematical Geniuses?

[Alexmahone]

I'm curious if anyone knows who today's greatest mathematicians are, or in your opinion, who are humanity's greatest mathematicians?  Do you think that any of them are on par with Gauss, Euler, Newton, Leibniz, and any other historical geniuses who greatly contributed to mathematics?  Also, how do you define mathematical genius, and in your opinion, is mathematical genius a rarity these days?

• Andrew Wiles - The British mathematician who proved Fermat's Last Theorem in 1994.
  
• Grigori Perelman - The Russian mathematician who proved the Poincare conjecture in 2003 and then turned down the Fields Medal and a 1 million dollar Millennium Prize. He has abandoned mathematics and is currently living with his mother in Russia.
  

These guys are probably on par with Leibniz, if not Newton, Gauss and Euler. All other Fields Medalists and Abel Prize winners are also mathematical geniuses. Solving a centuries' old math problem is a pretty strong sign of mathematical genius.

No, I don't think mathematical genius is a rarity these days. Given that the world population today is around 10 times what it was during Newton's time, mathematical genius should also be 10 times more common than it was then. If it isn't, something is seriously wrong...