A proof is a logical argument that demonstrates the truth of a statement or theorem in mathematics. It uses a series of deductive reasoning steps based on accepted principles, definitions, and previously established results. Proofs can take various forms, including direct proofs, indirect proofs, and constructive proofs, each serving to validate a claim rigorously. In addition to mathematics, the concept of proof is also relevant in fields like science and law. In science, proofs often come in the form of experiments and observations that support a hypothesis. In law, proof refers to the evidence presented to establish the truth of a claim in a court of law.