(Working number theorist here.)<p>What these guys are doing is definitely awesome. (A bit removed from my specialty, so I can&#x27;t answer detailed questions about it unfortunately.)<p>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 &quot;Arithmetic geometry&quot; or &quot;Diophantine geometry&quot; and you will find much, including (large) books on these topics.<p>Meanwhile, here is a classical one. How do you find all integer solutions to the equation a^2 + b^2 = c^2?<p>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 <i>rational</i> numbers. Now, to find these use &quot;stereographic projection&quot;. See here (scroll down to &quot;stereographic approach&quot;):<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Pythagorean_triple" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Pythagorean_triple</a><p>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.<p>These four mathematicians are continuing a long and wonderful tradition of finding applications of geometry to other areas of mathematics.