Re:Who Is Alexander Grothendieck? (2008) [pdf]
by GaussBonnet on Monday August 03, 2020 @10:02AM
(#24037871)
You aren't wrong. Until extremely recently, algebraic geometry was a field by and for the purest of the pure mathematicians. These days algebraic geometry has made its way into string theory.
1. A far reaching generalization of the Riemann-Roch theorem, which is now called the Grothendieck-Riemann-Roch theorem. As with a great deal of his work, it's about drawing conclusions about global structure from local data:
His work wasn't focused on solving particular problems so much as it was on finding the right language with which to describe problems. The philosophy is that, with the right language, your proofs should become obvious. This is somewhat in the same spirit as Leibniz's quest for the 'Universal Characteristic'.
https://en.wikipedia.org/wiki/Gromov%E2%80%93Witten_invarian...
A couple of his contributions:
1. A far reaching generalization of the Riemann-Roch theorem, which is now called the Grothendieck-Riemann-Roch theorem. As with a great deal of his work, it's about drawing conclusions about global structure from local data:
https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem
2. Creating the machinery used to solve the Riemann hypothesis for finite number fields.
https://en.wikipedia.org/wiki/Weil_conjectures
His work wasn't focused on solving particular problems so much as it was on finding the right language with which to describe problems. The philosophy is that, with the right language, your proofs should become obvious. This is somewhat in the same spirit as Leibniz's quest for the 'Universal Characteristic'.
https://en.wikipedia.org/wiki/Characteristica_universalis