Finitism
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. In her book Philosophy of Set Theory, Mary Tiles characterized those who allow countably infinite objects as classical finitists, and those who deny even countably infinite objects as strict finitists.
The most famous proponent of finitism was Leopold Kronecker, who said:
God created the natural numbers, all else is the work of man.Ultrafinitism is an even more extreme version of finitism, which rejects not only infinities but finite quantities that cannot feasibly be constructed with available resources.
Read more about this topic: Philosophers Of Mathematics, Contemporary Schools of Thought, Intuitionism