Method
Metamath
Overview
Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.
By 2023, Metamath had been used to prove 74 of the 100 theorems of the "Formalizing 100 Theorems" challenge. At least 19 proof verifiers use the Metamath format.
The Metamath website provides a database of formalized theorems which can be browsed interactively.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
One of the chief ends served by mathematics, when rightly taught, is to awaken the learner's belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration. This purpose is not served by existing instruction; but it is easy to see ways in which it might be served. At present, in what concerns arithmetic, the boy or girl is given a set of rules, which present themselves…
Bertrand Russell, Mysticism and Logic and Other Essays
Close in meaning to Metamath; the term itself is not named.
Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Metamath is.
No; the name mathematicians give it would suffice to prove this. In mathematics logic is called _analysis_ and analysis means _division_, _dissection_. It can have, therefore, no tool other than the scalpel and the microscope. Thus logic and intuition have each their necessary rôle. Each is indispensable.
Henri Poincaré, The Foundations of Science
States what Metamath is.
Related ideas
- Formal language
- First-order logic
- Proof assistant
- Intuitionistic logic
- Algebra
- Modus ponens
- Number theory
- Peano axioms
- Set theory
- Topology
- YouTube
- Formal system
- Metalanguage
- Logic
- Gödel, Escher, Bach
- Mathematical analysis
- Natural deduction
- Substitution (logic)
- Higher-order logic
- Category theory
- New Foundations
Place in the tradition
Part of First-order logic.