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 or axioms, to arrive at a conclusion. Proofs are essential in mathematics because they provide certainty and validation for theorems and propositions. There are various types of proofs, including direct proofs, indirect proofs, and proof by contradiction. Each method has its own approach to establishing the validity of a statement. Mathematicians rely on proofs to ensure that their findings are accurate and reliable, forming the foundation of mathematical knowledge.