Fermat's mean value theorem: a kind of mean value problem that can be solved by using the mean value theorem of continuous functions on closed intervals, that is, to prove the existence of ξ∈[a, b] and make a proposition hold. A mean value theorem that can be solved by Rolle's theorem and Fermat's theorem, that is, it is proved that ξ∈[a, b] exists, so that H(ξ, f(ξ), f'(ξ))=0.

History:

1995, andrew wiles and others published the proof process of Fermat's conjecture in Mathematical Yearbook, and successfully proved this theorem.

Although the expression of Fermat's Last Theorem is simple, it takes several generations to prove it. Many mathematicians have discovered many new mathematical theories and expanded new mathematical methods in the process of proving Fermat's Last Theorem. The process of proving Fermat's Last Theorem can be regarded as a history of mathematics.