# Mathematician:James Burton Ax

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## Mathematician

American mathematician who proved several results in algebra and number theory by using model theory.

## Nationality

American

## History

- Born: 10 January 1937
- Died: 11 June 2006

## Theorems and Definitions

- Ax-Grothendieck Theorem (independently of Alexander Grothendieck)
- Ax-Kochen Theorem (with Simon Bernhard Kochen)
- Ax-Katz Theorem (with Nicholas Michael Katz)

Results named for **James Burton Ax** can be found here.

## Publications

- 1965:
*Diophantine problems over local fields. I*(*American Journal of Mathematics***Vol. 87**: pp. 605 – 630) (with Simon B. Kochen) - 1965:
*Diophantine problems over local fields. II*(*American Journal of Mathematics***Vol. 87**: pp. 631 – 648) (with Simon B. Kochen) - 1966:
*Diophantine problems over local fields. III*(*Annals of Mathematics***Ser. 2****Vol. 83**: pp. 437 – 456) (with Simon B. Kochen)