In the philosophy of mathematics, finitism is an extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps. (Most constructivists, in contrast, allow a countably infinite number of steps.) The most famous proponent of finitism was Leopold Kronecker, who said:
- "God created the integers, all else is the work of man."
Even stronger than finitism is the ultraintuitionism (or ultrafinitism as it is now more commonly known) of A. S. Esenin-Vol'pin.