Proofs in mathematics

In mathematics, a proof is a logical argument that demonstrates the truth of a statement or theorem. It uses accepted principles, definitions, and previously established results to show that a conclusion follows necessarily. Proofs are essential because they provide certainty and assurance that mathematical concepts are valid and reliable. There are various types of proofs, such as direct proofs, proof by contradiction, and induction. Each type employs different strategies, but all aim to establish truths unambiguously, forming the foundation upon which further mathematical discoveries are built.