Finitism

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."

Although most modern constructivists don't take such a strong view, they can trace the origins of constructivism back to Kronecker's finitist work.

Even stronger than finitism is the ultraintuitionism (or ultrafinitism as it is now more commonly known) of A. S. Esenin-Vol'pin.