Hilbert’s 10th Problem

diophantineHow complicated can it be to find all the integer solutions to a set of polynomial equations? In fact, as complicated as you like! Given any output from a computer program (a list of all prime numbers, for example), you can find a set of equations whose only solutions occur when one of the variables takes any value in the list but no others. This project will look at the mathematics behind trying to make this statement precise. Along the way, it might well morph into some other aspect of mathematical logic (Goedel’s incompleteness theorem, the halting problem, etc.) as it takes your interest or not.

Supervisor: Dr Colin Christopher