I disagree. I'm more inclined to say:

philosophy = science - assumptions

Also, mathematics came from philosophy... So did Science, actually.

I'm not sure I follow you there. Quite a few philosophers are mathematicians-- René Descartes, Bertrand Russel, and Kurt Gödel are a few famous examples. It's also not at all clear the world would have been better off if they'd chosen to be engineers instead.