Thinking in unconventional/abstract ways allows for further development of the brain. Dedicating yourself to one field of science primes you toward thinking only in one sort of way. Since it is impossible to achieve any kind of meaningful level (that is, beyond simplifications apparent in much of the introductory material) in a subject, it follows that looking for alternative ways of mental engagement is preferable.
tl;dr
post recommendations for puzzle games, recreational mathematics, and so on

I have so far played Portal 1, Portal Rexaura, Portal 2, Portal Stories Mel. Don't bother with community chambers because they are all shit. Do you guys know of any other good mods to Portal?
As for recreational mathematics, so far I have only read 'The Lady Or the Tiger? And Other Logic Puzzles' by Smullyan.