+118609 I am going for Sir Isaac Newton because he is credited with inventing Calculus.
And I love Calculus! 
+128475 Archimedes was the greatest mathematician of ancient times. It is speculated that he was near to discovering Calculus, had he not been been killed by a Roman soldier's sword.....!!!
Newton was the co-inventor of Calculus - along with Leibniz. As to which " invented" [ or discovered ???] it first remains controversial. One thing that is not controversial - Leibniz's notation was superior to Newton's and continues to be used.
I'd rate two other mathematicians as possibly "The Greatest" - Euler and Gauss........ Which is "greater" is also debatable.!!!
[ One more person I might add to the list is the Hungarian-American, John von Neumann.......a participant in the development of the atomic bomb, von Neumann had a photgraphic memory and an IQ of something around 200...as an example, he could recite "The Tale of Two Cities" word for word !!!!....he was responsible for many early developments in the field of computer science.......a true genius....!!! ]
