Only recently lightspeed as the ultimate limit of speed got challenged. It seems they have been challenging the Turing Machine for a while too.
If you start with studying mathematics you are only three or four centuries behind on contemporary mathematics. That's quite a lot of catching up to do. - Some fields started their development in the previous century though. Like mathematical logic, a field I have been studying this year, and have written about so now and then in this blog. Part of mathematical logic is the theory of computation which showed us what can be computed and what can't. That what can be computed is what can be computed on a Turing Machine, period. - That idea is challenged however in the theory of hypercomputation. A new field in mathematics which is trying to go beyond the limits of the Turing Machine.
A book with an overview of the theory is the following.
13-2016 Open letter to Open Source for You (OSFY)
5 months ago