How would one calculate the $$$ value of exp2 multiplication? Eg if one finds a way, would it be worth keeping it a secret and creating a business around it?
First of all, you couldn't. The "fastest" multiplication algorithms for Matrix multiplication, which are roughly O(n^2.3), aren't used in practice. They're "galactic algorithms" (a term I just now learned), meaning that the size the problem would need to be for them to overtake the more common O(n^2.8) algorithm is too large for today's computers. O(n^2) might be theoretically valuable but practically useless.
Second of all, algorithms aren't patentable. The only way to keep it exclusive would be to keep it secret. I can't think of any examples of a private company making a major scientific or mathematical breakthrough and then keeping it secret long enough to profit off of it.
Algorithms absolutely are patentable because they are computing "machines." It's mathematical equations that aren't patentable, because they're closer to laws of nature.
Second of all, algorithms aren't patentable. The only way to keep it exclusive would be to keep it secret. I can't think of any examples of a private company making a major scientific or mathematical breakthrough and then keeping it secret long enough to profit off of it.