(Also as a mathematician) Many constructive proofs involve what one could loosely categorize as algorithms. (Not to mention in some computational fields, some proofs can be strictly categorized as algorithms.) Now that I think about it, these can be patented too. Then one can "teach it, study it", but one's not allowed to prove without permission other results using constructions in the same spirit. Geez, thanks for letting people study it, I guess.