# André Weil: His Book on Number Theory and Indian References

Chapter

## Summary

After giving a brief description of André Weil as a man and mathematician, the article concentrates on his book Number Theory: An Approach Through History, and particularly on Chap.IX, in which he discusses the history and the solution of Pell’s equation. It is shown that it was the Indian mathematician Brahmagupta who first attempted to solve the equation, in the seventh century c.e. He defined a binary composition on the set of all solutions of the equation, a work of genuine ingenuity, leading to the result that if the equation has a nontrivial solution, then it has infinitely many such solutions. Lagrange showed that the equation does indeed have a nontrivial solution, and Dirichlet later solved the equation completely.

## Keywords

Nontrivial Solution Riemann Hypothesis Binary Composition Transcendental Number General Riemann Hypothesis
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## References

1. 1.
Bombieri, E.: Problems of the Millennium: The Riemann Hypothesis.http://claymath.org/prizeproblems/riemann.htm
2. 2.
Chahal, J. S.: Pell’s Equation and the Unity of Mathematics. Proc. Inter. Conf. History of the Math. Sciences, Delhi, December 2001.Google Scholar
3. 3.
Colebrooke: Algebra with Arithmetic and Mensuration from Sanskrit of Brahmagupta and Bháscara. London (1817).Google Scholar
4. 4.
Datta, B., Singh, A. N.: History of Hindu Mathematics. Vol. II, Bharatiya Kala Prakashan, Delhi (2004).Google Scholar
5. 5.
Schlomiuk, Norbert: André Weil, The Man and the Historian of Mathematics. Proc. Inter. Conf., History of the Math. Sciences, Delhi, December 2001.Google Scholar
6. 6.
Shukla, K. S.: Ācarya Jayadeva the Mathematician. Gaṇita, Vol. 5, 1–20 (1954).
7. 7.
Weil, André: Number Theory: An Approach through History. Birkhäuser (1983).Google Scholar
8. 8.
Weil, André: Apprenticeship of a Mathematician. Birkhäuser (1992).Google Scholar
9. 9.
Weil, André: Œuvres Scientifiques. Collected Papers. Vol. 1, Springer, New York (1980).Google Scholar
10. 10.
Yadav, B. S.: André Weil’s India in the Early Thirties. Historia Scientiarum, Vol. 10, 84–91 (2000).