This seems like the kind of Feat he'd come up with.
#PATHFINDER SACRED GEOMETRY CALCULATOR PC#
He wrote a number of homebrew RPGs and optional rules which all amounted to "If you are really good at math and related subjects IRL, then your PC will also be, even if he is as dumb as a box of rocks on paper AND you will gain some special advantages!" (none of these ever actually got used, of course, because they were such obvious advantage-seeking BS). The other always felt that he was somehow being "short-changed" by RPGs, because he couldn't leverage his math/musical brilliance at all (beyond normal optimization, which even people like me could do! Peasants!). In the very late '80s/early '90s I played with two players who were actual, no-BS math geniuses (both also perfect pitch, played multiple instruments extremely well, etc.).
I would just let them know up front that I have reservations that it may be disruptive and I won't let it continue if it was disruptive. But as I said, I wouldn't be against letting a player try it. You do have some fair points on the other aspects, but largely, I feel them to be ancillary to the 'time to calculate' / testing player skill component. And one that benefits the not commonly used skill of number sense. Putting a cap on the time to solve definitely alleviates that problem, but it does very blatantly reduce it to player skill check as opposed to their character. After all, the player isn't going to try to find other solutions once they have one, it's when they lack a readily apparent solution that they will spend more time to find one. One of the things to remember however, making the numbers harder to work makes the feat more disruptive to the flow of combat. However, I think multiply by 1 may be advantageous in terms of identity cheese. It would reduce the ability to hit identity as easily.
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