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.
Sunday, October 9, 2011
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Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)
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