Joseph Mileti

Joe's research interests lie in mathematical logic, which is a field that develops tools to calibrate the complexity of various mathematical objects.  By arguing that the objects guaranteed to exist by a theorem must be complicated, it is possible to conclude that any proof of that theorem must involve certain nonconstructive methods.  Joe has applied these techniques to a variety of theorems from algebra and combinatorics.  He has also worked with MAP students to prove that regular patterns must always exist in large structures, and that rings (a type of algebraic structure) can have exotic computational properties.  He recently completed his textbook Modern Mathematical Logic, which was published in September 2022.