Foundations of mathematics

In mathematics, foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathematics is however also the central question of the philosophy of mathematics: on what ultimate basis can mathematical statements be called "true"?

Sources

• The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Eugene Wigner, 1960;
• What is mathematical truth?, Hilary Putnam, 1975;
• Mathematics as an objective science, Nicholas D. Goodman, 1979;
• Some proposals for reviving the philosophy of mathematics, Reuben Hersh, 1979;
• Challenging foundations, Thomas Tymoczko, 1986, preface to first section of New Directions in the Philosophy of Mathematics, 1986 and (revised) 1998, which includes also Putnam, Goodman, Hersh.