(Working number theorist here.) What these guys are doing is definitely awesome. (A bit removed from my specialty, so I can't answer detailed questions about i

(Working number theorist here.) What these guys are doing is definitely awesome. (A bit removed from my specialty, so I can't answer detailed questions about it unfortunately.) But let me add that there are already a LOT of bridges between number theory and algebraic geometry. To get a sense of the scope, google "Arithmetic geometry" or "Diophantine geometry" and you will find much, including (large) books on these topics. Meanwhile, here is a classical one. How do you find all integer solutions to the equation a^2 + b^2 = c^2? First of all, it is fairly easy to see that this is the same problem as finding points on the circle x^2 + y^2 = 1 where both x and y are rational numbers. Now, to find these use "stereographic projection". See here (scroll down to "stereographic approach"): https://en.wikipedia.org/wiki/Pythagorean_triple https://en.wikipedia.org/wiki/Pythagorean_triple The bottom line is that there is a picture you can draw which graphically gives you an easy solution to this number theory problem -- and once you draw the right picture, it is easy to use it to write down the algebraic solution as well. These four mathematicians are continuing a long and wonderful tradition of finding applications of geometry to other areas of mathematics.