Prove the three most important theorems in Mathematics.

 In Mathematics there are three main theorem.

The Theorem Fundamental of Arithmetic: It stats that any natural number, n (or integer positive) can be factorized in prime numbers, and this factorization is unique, respecting the number of primes with their relative exponents.

Euclid give a proof in its elements. 

The Theorem Fundamental of Algebra. A Polynomial which degree is n, have at most n different solutions.

Gauss release the first respectable proof. A simple proof can also be made using Complex Analysis.

The Theorem Fundamental of Calculus. The derivate of the Integral, is the function.

Any modern texbook of Calculus includes a proof. Michael Spivak, in is Calculus offers a good proof.