After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana-Champaign. Takeuti was president (2003-2009) of the Kurt Gödel Society, having worked on the respected book Memoirs of a Proof Theorist: Godel and Other Logicians. His goal was to prove the consistency of the real numbers. To this end, Takeuti's conjecture speculates that a sequent formalisation of second-order logic has cut-elimination. He is also known for his work on ordinal diagrams with Akiko Kino.
- Takeuti, Gaisi (1953). "On a generalized logic calculus". Japanese Journal of Mathematics. 23: 39–96. ISSN 0075-3432.
- Takeuti, Gaisi; Zaring, Wilson M. (1971), Introduction to axiomatic set theory, Graduate Texts in Mathematics, 1, New York-Berlin: Springer-Verlag, ISBN 0-387-90683-5, MR 0349390
- Takeuti, Gaisi; Zaring, Wilson M. (1973), Axiomatic set theory, Graduate Texts in Mathematics, 8, New York-Berlin: Springer-Verlag, MR 0416914
- Takeuti, Gaisi (2013) . Proof theory (Second ed.). Mineola, New York: Dover Publications. ISBN 978-0-486-49073-1.
- Takeuti, Gaisi (1978), Two applications of logic to mathematics, Publications of the Mathematical Society of Japan, 13, Princeton, N.J.: Princeton University Press, ISBN 0-691-08212-X, MR 0505474
- Takeuti, Gaisi (2003) , Memoirs of a proof theorist. Gödel and other logicians, River Edge, NJ: World Scientific Publishing Co., Inc., ISBN 9789812382795, MR 1984952
- Takeuti 2013.
- Takeuti 1953. An erratum to this article was published in the same journal (24:149–156, 1954).
- Presidents of the Kurt Gödel Society
- Takeuti Symposium (contains relevant birthdate information)
- Logic Colloqium ’98 Proceedings (contains biography) at the Wayback Machine (archived September 26, 2006)
- Gaisi Takeuti at the Mathematics Genealogy Project