# Gaisi Takeuti

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Gaisi Takeuti | |
---|---|

Native name | 竹内 外史 |

Born | January 25, 1926 |

Died | May 10, 2017 | (aged 91)

Nationality | Japanese |

Education | Tokyo University |

Alma mater | Princeton |

Known for | Work in proof theory |

Scientific career | |

Fields | Mathematics |

Institutions | University of Illinois at Urbana-Champaign |

**Gaisi Takeuti** (竹内 外史 *Takeuchi, Gaishi*, January 25, 1926 – May 10, 2017^{[1]}) was a Japanese mathematician, known for his work in proof theory.^{[2]}

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 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.^{[3]} He is also known for his work on ordinal diagrams with Akiko Kino.

## Publications[edit]

- Takeuti, Gaisi (1953). "On a generalized logic calculus".
*Japanese Journal of Mathematics*.**23**: 39–96. doi:10.4099/jjm1924.23.0_39. ISSN 0075-3432. - Takeuti, Gaisi (1954). "Errata to 'On a Generalized Logic Calculus'".
*Japanese Journal of Mathematics*.**24**: 149–156. doi:10.4099/jjm1924.24.0_149. ISSN 0075-3432. - Takeuti, Gaisi; Zaring, Wilson M. (2011) [1982],
*Introduction to axiomatic set theory*, Graduate Texts in Mathematics,**1**(2nd ed.), New York-Berlin: Springer-Verlag, doi:10.1007/978-1-4613-8168-6, ISBN 978-1-4613-8170-9, MR 0349390 - Takeuti, Gaisi; Zaring, Wilson M. (1973),
*Axiomatic set theory*, Graduate Texts in Mathematics,**8**, New York-Berlin: Springer-Verlag, doi:10.1007/978-1-4684-8751-0, ISBN 978-0-387-90050-6, MR 0416914 - Takeuti, Gaisi (2013) [1975].
*Proof theory*(Second ed.). Mineola, New York: Dover Publications. ISBN 978-0-486-49073-1. - Takeuti, Gaisi (2015) [1978],
*Two applications of logic to mathematics*, Publications of the Mathematical Society of Japan,**13**, Princeton, N.J.: Princeton University Press, ISBN 978-0-69-161022-1, MR 0505474 - Takeuti, Gaisi (2003) [1998],
*Memoirs of a proof theorist. Gödel and other logicians*, River Edge, NJ: World Scientific Publishing Co., Inc., ISBN 978-981-238-279-5, MR 1984952

## Notes[edit]

**^**Sam Buss (2017-05-10). "[Proof Complexity] Gaisi Takeuti". Proof-Complexity mailing list. Retrieved 2019-01-13.**^**Takeuti 2013.**^**Takeuti 1953. An erratum to this article was published in the same journal as (Takeuti 1954).

## External links[edit]

- 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

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