Brouwer–Hilbert controversy

In a foundational controversy in twentieth-century mathematics, L. E. J. Brouwer, a proponent of the constructivist school of intuitionism, opposed David Hilbert, a proponent of formalism. The debate concerned fundamental questions about the consistency of axioms and the role of semantics and syntax in mathematics. Much of the controversy took place while both were involved with the prestigious Mathematische Annalen journal, with Hilbert as editor-in-chief and Brouwer as a member of its editorial board.

Brouwer–Hilbert controversy

In a foundational controversy in twentieth-century mathematics, L. E. J. Brouwer, a proponent of the constructivist school of intuitionism, opposed David Hilbert, a proponent of formalism. The debate concerned fundamental questions about the consistency of axioms and the role of semantics and syntax in mathematics. Much of the controversy took place while both were involved with the prestigious Mathematische Annalen journal, with Hilbert as editor-in-chief and Brouwer as a member of its editorial board.