A mathematical proof is a logical argument that demonstrates the truth of a mathematical statement or theorem. It uses a series of deductive reasoning steps, starting from accepted axioms and previously established results, to arrive at a conclusion. Proofs are essential in mathematics because they provide certainty and validation for mathematical concepts. 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.