>>7899020

>>7899048

>>7898995

>>7898930

Computability theory is very much a live and exist in the mathematics department at my undergraduate institution. The research done on the math department is different than what is taught in the computer science department. This is research looks into which set existence axioms are needed to prove theorems, which allows you to categorize the logical strength of theorems and differentiate between different proofs of theorems. All undergraduate mathematics can be done with transfinite inductive arguments.

But from what I've seen not many math departments outside of a core few have many mathematical logicians. Since computability theory is generally first exposed in an automata class I can see where the misconceptions come from. Based on what I've seen my math classes go into further mathematical meat in recursion theory than my automata classes and it connected it to other areas of mathematics like proof theory, combinatorics, real analysis and Ramsey theory.