# André Weil

> French mathematician (1906-1998)

**Wikidata**: [Q323232](https://www.wikidata.org/wiki/Q323232)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/André_Weil)  
**Source**: https://4ort.xyz/entity/andre-weil

## Summary
André Weil was a French mathematician (1906–1998) known for his foundational contributions to algebraic geometry, number theory, and the Weil conjectures, which revolutionized the study of algebraic varieties. His work laid the groundwork for modern algebraic geometry and influenced global mathematical research.

## Biography
- Born: May 6, 1906, in Paris, France
- Nationality: French
- Education:
  - École Normale Supérieure (ENS Paris)
  - Lycée Saint-Louis
  - University of Göttingen
  - University of Chicago
- Known for: Pioneering work in algebraic geometry and number theory, including the Weil conjectures
- Employer(s):
  - École Normale Supérieure
  - University of São Paulo
  - Aligarh Muslim University
  - University of Strasbourg
  - Haverford College
  - Lehigh University
  - Institute for Advanced Study
- Field(s): Mathematics (algebraic geometry, number theory)

## Contributions
- **Weil Conjectures (1940s)**: Formulated a set of conjectures about the number of points on algebraic varieties over finite fields, which became a cornerstone of algebraic geometry and were later proven by Pierre Deligne.
- **Foundational Work in Algebraic Geometry**: Developed key theorems and concepts that shaped the field, including the Mordell–Weil theorem and the Chern–Weil homomorphism.
- **Hasse–Weil Zeta Function**: Introduced a zeta function associated with algebraic varieties, which became essential in number theory and algebraic geometry.
- **Weil Group**: Contributed to class field theory by introducing the concept of the Weil group.
- **Teaching and Mentorship**: Taught at prestigious institutions like the University of Chicago and the Institute for Advanced Study, mentoring numerous mathematicians.

## FAQs
### What was André Weil's most significant contribution to mathematics?
André Weil's most significant contribution was the formulation of the Weil conjectures, which provided deep insights into the number of points on algebraic varieties over finite fields and laid the foundation for modern algebraic geometry.

### Where did André Weil study and teach?
André Weil studied at the École Normale Supérieure, Lycée Saint-Louis, the University of Göttingen, and the University of Chicago. He taught at institutions including the University of São Paulo, Aligarh Muslim University, the University of Strasbourg, Haverford College, Lehigh University, and the Institute for Advanced Study.

### What awards and recognitions did André Weil receive?
André Weil received numerous awards, including the Guggenheim Fellowship, the Kyoto Prize in Basic Sciences, the Wolf Prize in Mathematics, and the Leroy P. Steele Prize. He was also a member of prestigious academic societies such as the Royal Society, the French Academy of Sciences, and the Bavarian Academy of Sciences and Humanities.

### What is the significance of the Weil conjectures?
The Weil conjectures are significant because they provided a framework for understanding the distribution of points on algebraic varieties over finite fields, leading to breakthroughs in number theory and algebraic geometry. They were later proven by Pierre Deligne, cementing Weil's legacy in mathematics.

## Why They Matter
André Weil's work fundamentally transformed algebraic geometry and number theory, influencing generations of mathematicians. His conjectures, though initially met with skepticism, became a cornerstone of modern algebraic geometry and were only fully proven decades later. Weil's interdisciplinary approach and mentorship at institutions like the Institute for Advanced Study and the University of Chicago helped shape mathematical research. His contributions continue to inspire research in algebraic geometry, number theory, and related fields, making him a pivotal figure in the history of mathematics.

## Notable For
- Formulating the Weil conjectures, which revolutionized algebraic geometry and number theory.
- Developing the Mordell–Weil theorem and the Chern–Weil homomorphism, foundational to algebraic geometry.
- Introducing the Hasse–Weil zeta function, essential in number theory and algebraic geometry.
- Teaching and mentoring at prestigious institutions, including the Institute for Advanced Study and the University of Chicago.
- Receiving major awards such as the Kyoto Prize, the Wolf Prize, and the Leroy P. Steele Prize.
- Being a member of elite academic societies, including the Royal Society and the French Academy of Sciences.

## Body
### Early Life and Education
André Weil was born on May 6, 1906, in Paris, France. He attended the Lycée Saint-Louis and later the École Normale Supérieure, where he studied under the guidance of prominent mathematicians. His early education laid the groundwork for his future contributions to algebraic geometry and number theory.

### Academic Career
Weil's academic career began at the University of Göttingen, where he studied under the supervision of mathematicians such as Emmy Noether and Richard Courant. He later moved to the University of Chicago, where he made significant contributions to algebraic geometry and number theory. His work at these institutions established him as a leading figure in the field.

### Contributions to Mathematics
Weil's most notable contribution was the formulation of the Weil conjectures in the 1940s. These conjectures provided deep insights into the number of points on algebraic varieties over finite fields and became a cornerstone of algebraic geometry. His work also included the development of the Mordell–Weil theorem and the Chern–Weil homomorphism, which are foundational to algebraic geometry.

### Teaching and Mentorship
Weil taught at numerous prestigious institutions, including the University of São Paulo, Aligarh Muslim University, the University of Strasbourg, Haverford College, Lehigh University, and the Institute for Advanced Study. His mentorship and teaching at these institutions helped shape the careers of many mathematicians.

### Awards and Recognition
Weil received numerous awards and honors throughout his career, including the Guggenheim Fellowship, the Kyoto Prize in Basic Sciences, the Wolf Prize in Mathematics, and the Leroy P. Steele Prize. He was also a member of prestigious academic societies such as the Royal Society, the French Academy of Sciences, and the Bavarian Academy of Sciences and Humanities.

### Legacy and Influence
André Weil's work continues to influence mathematical research in algebraic geometry, number theory, and related fields. His conjectures and theorems remain foundational to the study of algebraic varieties and have inspired generations of mathematicians. Weil's interdisciplinary approach and mentorship have left a lasting impact on the field of mathematics.

## References

1. BnF authorities
2. BeWeB
3. Integrated Authority File
4. [Source](https://www.ams.org/journals/notices/201801/rnoti-p54.pdf)
5. [André Abraham Weil. MacTutor History of Mathematics archive](http://www-history.mcs.st-andrews.ac.uk/Biographies/Weil.html)
6. MacTutor History of Mathematics archive
7. Find a Grave
8. [Source](http://www.cemeteryregister.com/search.asp?id=NJ_PRINCETON)
9. Guggenheim Fellows database
10. [Source](https://www.ams.org/prizes-awards/pabrowse.cgi?parent_id=28)
11. André Abraham Weil. Mathematics Genealogy Project
12. Mathematics Genealogy Project
13. International Standard Name Identifier
14. CiNii Research
15. SNAC
16. Solomon R. Guggenheim Museum
17. Roglo
18. Croatian Encyclopedia
19. La France savante
20. Freebase Data Dumps. 2013
21. Virtual International Authority File
22. CONOR.SI
23. Autoritats UB
24. Treccani's Enciclopedia on line
25. Enciclopedia Treccani
26. LIBRIS. 2012
27. Catalogo of the National Library of India