We rely on intuition every day, and we use mathematics every day.
Intuition is fast, powerful and omniapplicable, but sometimes wrong.
Mathematics is efficient, powerful and correct, when applicable. Whenever there is an uncertainty, a proof can be called in to settle the case.
With examples involving the use of intuition, mathematics and proof from philosophy, psychology, and so on, I will talk about the role of mathematics in these domains.
