Sequent calculus is a formal system used in mathematical logic to represent proofs. It focuses on the relationships between statements, called sequents, which express that if certain premises are true, then a conclusion follows. This system allows for a structured way to derive conclusions from assumptions using rules of inference. Developed by Gerhard Gentzen in the 1930s, sequent calculus provides a framework for both classical and intuitionistic logic. It emphasizes the manipulation of sequents through various rules, making it easier to analyze the validity of arguments and the structure of logical reasoning.