For you who is the greatest mathematician? This was a question asked to me by a kin, a freshman who is currently studying a mathematics related course. This question is probably asked by many others who are just starting studying mathematics or those who are just simply curious.
Asking who the greatest mathematician is like asking who the greatest singer is. Singers have different genre that it is nearly impossible to tell. Pop lovers would probably suggest that it was Michael Jackson, but classical singers would probably disagree and would suggest some names like Luciano Pavarotti.
I think, determining the greatest mathematician is even more complicated than determining the greatest singer. Mathematicians lived in different times and the maturity of mathematics at different times is enormously different. For example, during the time of Euclid, it takes a high-caliber mathematician to prove that the inscribed triangle in a circle containing its diameter is right, while they can be easily proved by eighth graders of the present time. Of course, we cannot claim that our eighth graders are better than or even at the same level as Euclid because mathematics has changed so much. Those who are only read by mathematicians during the time of Euclid are now taught in the elementary and high school levels. In addition, mathematicians study different fields and it is impossible to compare the level of difficulty or even to quantify the effect of their contributions.
Further, the complexity of mathematics has dramatically increased making the problems solved by mathematicians now relatively more difficult than the problems before. On the contrary, mathematicians today have more tools to use especially with the existence of powerful computers. But even though the mathematicians today can solve more difficult problems, they cannot entirely take all the credits because they have also to build on works of mathematicians before them. For instance, many will probably agree that Newton is greater than Descartes, but had Descartes not invented the Cartesian Coordinates, Newton would probably have not invented Calculus.
To answer the question of who is the greatest mathematician, experts will probably give you a list that will include common names, but they will surely have second thoughts on giving a single name. The list will likely include Euclid, Archimedes, Newton, Euler, and Gauss along with a few others.