Wiles Proof of Fermat's Last Theorem

  • Context: Graduate 
  • Thread starter Thread starter fibonacci235
  • Start date Start date
  • Tags Tags
    Proof Theorem
Click For Summary
SUMMARY

To fully understand Andrew Wiles' proof of Fermat's Last Theorem, one must study several key areas of mathematics, including the Modularity Theorem, Elliptic Curves, algebraic geometry, arithmetic geometry, and Complex Analysis. Mastery of these subjects is essential for grasping the intricacies of Wiles' proof. Recommended literature includes "Invitation to the Mathematics of Fermat-Wiles" by Hellegouarch, "Rational Points on Elliptic Curves" by Silverman and Tate, and "Lectures on Curves, Surfaces and Projective Varieties" by Beltrametti.

PREREQUISITES
  • Modularity Theorem
  • Elliptic Curves
  • Algebraic Geometry
  • Arithmetic Geometry
NEXT STEPS
  • Study the Modularity Theorem in detail
  • Explore the properties and applications of Elliptic Curves
  • Learn about Algebraic Geometry fundamentals
  • Investigate Complex Analysis techniques relevant to number theory
USEFUL FOR

Mathematicians, students of advanced mathematics, and anyone interested in number theory and the historical significance of Fermat's Last Theorem.

fibonacci235
Messages
15
Reaction score
1
Just a quick question. What areas of mathematics would I have to study to understand Wiles' proof? I know his proof involves the Modularity Theorem, Elliptic Curves etc, but to really understand the proof what other topics would I need to master?
 
Physics news on Phys.org
You need to know algebraic and arithmetic geometry quite well. Complex Analysis is probably also used.

Here are some nice books to get you started:
- Invitation to the mathematics of Fermat-Wiles by Hellegouarch
- Rational points on elliptic curves by Silverman and Tate
- Lectures on Curves, Surfaces and Projective Varieties by Beltrametti
 

Similar threads

Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
8K
Graduate So is chike obo proof of fermat's last theorem
  • · Replies 3 ·
Replies
3
Views
6K
Graduate Question regarding proof of convex body theorem
  • · Replies 21 ·
Replies
21
Views
2K
MHB Fermat's Little Theorem .... Anderson and Feil, Theorem 8.7 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Fermat's Little Theorem .... Anderson and Feil, Theorem 8.7 .
  • · Replies 3 ·
Replies
3
Views
3K
Graduate What is a Possible Algebraic Proof of Case 1 of Fermat's Last Theorem?
  • · Replies 2 ·
Replies
2
Views
3K
Proving well ordering principle from Peano Axioms
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Can anyone give an intuitive proof of the theorem on polynomial factorization?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Fermat's Last Theorem, proof by Andrew Wiles
  • · Replies 20 ·
Replies
20
Views
37K
Graduate What Are Elliptic Curves and Their Connection to Fermat's Last Theorem?
  • · Replies 11 ·
Replies
11
Views
4K