A mathematical proof is a logical argument that demonstrates the truth of a mathematical statement. It uses a series of deductive reasoning steps, starting from accepted principles, known as axioms or theorems, to arrive at a conclusion. Proofs can take various forms, including direct proofs, indirect proofs, and constructive proofs, each serving to validate different types of statements. The importance of mathematical proofs lies in their ability to provide certainty and clarity in mathematics. They ensure that results are not just based on intuition or observation but are rigorously established. Famous examples of proofs include Euclid's proof of the infinitude of prime numbers and Fermat's Last Theorem, which was proven by Andrew Wiles.