Brouwer–Hilbert controversy

The Brouwer-Hilbert Controversy was a debate between two mathematicians, Luitzen Brouwer and David Hilbert. They disagreed about whether mathematics should be based on what we can see (called intuition) or on logic (proofs). Brouwer believed that mathematics should be based on intuition, because he thought it would make the results more reliable. Hilbert disagreed, and argued that logic should be the basis of mathematics, because it could give us more certain results. This debate went on for a while, and it showed us that mathematics is a very complicated subject with lots of different opinions.