Gerhard Gentzen was a German mathematician and logician who made significant contributions to the field of mathematical logic. He is best known for his work on proof theory, particularly his development of natural deduction systems. Gentzen's [[natural deduction]] is a method of reasoning that seeks to capture the intuitive way humans reason about logical arguments. It provides a formal system for constructing and analyzing proofs in a clear and straightforward manner. Natural deduction is characterized by its use of inference rules that mimic common patterns of reasoning, such as introduction and elimination rules for logical connectives (e.g., conjunction, disjunction, implication). One of Gentzen's most influential contributions to natural deduction was his formulation of the [[sequent calculus]]. The sequent calculus is an alternative proof system based on the idea of logical sequents, which are expressions involving multiple formulas separated by a symbol called the turnstile (∣-). This calculus allows for more flexibility in manipulating formulas and provides an elegant framework for analyzing proofs. Gentzen's work on natural deduction also extended beyond propositional logic to include quantifiers and predicate logic. He developed rules for quantifier introduction and elimination, which allow for reasoning about general statements involving variables. These additions made natural deduction a more comprehensive proof system capable of handling more complex logical arguments. Overall, Gerhard Gentzen's contributions to natural deduction revolutionized the field of proof theory and provided mathematicians and logicians with powerful tools for constructing and analyzing formal proofs in various branches of logic. His work laid the foundation for further developments in proof theory and has had a lasting impact on the field. # References ```dataview Table title as Title, authors as Authors where contains(authors, "Gerhard Gentzen") or contains(subject, "Gentzen") ```