Brouwer–Hilbert controversy

The Brouwer–Hilbert controversy (German: Grundlagenstreit, lit. 'foundational debate') was a debate in twentieth-century mathematics over fundamental questions about the consistency of axioms and the role of semantics and syntax in mathematics. L. E. J. Brouwer, a proponent of the constructivist school of intuitionism, opposed David Hilbert, a proponent of formalism.

Source: Wikipedia — Brouwer–Hilbert controversy (CC BY-SA 4.0)