Question

examples of math investigatory project

Answer 1

Universal Logic - The study the structures of logic systems, including what they have in common, what can be assumed from them, etc. It would seem like this would have been done centuries ago, but luckily we are starting to question ALL of our assumptions. Universal Logic could rewrite the foundations of mathematics. However, be assured, much of the higher level stuff would remain, just on stronger pillars.New Foundations - Type Theory over Set Theory. Again, this is an attempt to rewrite mathematics from the foundations. There is still more to do, but it also sets on top of logic, which means it could be rewritten by Universal Logic too.Theorems as Programs and the Calculus of Constructions - Using computers to encode all of the theories that we have. This allows us to use computers to help us prove theories, and use theories to help us rewrite code, to use in proving new theories, ad infinitum. It’s basically a new database of mathematical theory. You can see this in the results of Agda, Coq, Idris, etc.On the other end (branching out to the leaves, instead of the roots), follow Terrance Tao for new stuff.Also, we have things which are always growing: Fractional Calculus, Quantum mathematics, etc.