Andrew Wiles

Born: 1953
Title: Prover of Fermat's Last Theorem

The Terminator Across Time and Space

Let us return to the beginning. The puzzle that Fermat left in 1637 was finally solved at the end of the 20th century.

In 1994, Andrew Wiles proved Fermat's Last Theorem—a problem that had puzzled mathematicians for 358 years. His proof, using deep connections between elliptic curves and modular forms, marked one of the greatest achievements in 20th-century mathematics.

Core Contributions - Deep Analysis

Fermat's Last Theorem: The Final Proof

Fermat's Last Theorem states: For $n > 2$ , the equation $x^n + y^n = z^n$ has no positive integer solutions.

Wiles didn't prove this directly. Instead, he proved the Taniyama-Shimura-Weil conjecture, which implies Fermat's Last Theorem. This connection was discovered by Gerhard Frey and proven by Ken Ribet.

The Modularity Theorem

Wiles (with Richard Taylor) proved that every elliptic curve over the rational numbers is modular. This means:

Elliptic curves (number theory) are connected to modular forms (analysis)
This connection is so deep it implies Fermat's Last Theorem
The proof uses techniques from many areas: algebraic geometry, number theory, representation theory

The Seven-Year Secret

The Process:

Wiles dreamed of solving this problem from age 10.
He worked in secret in his attic for 7 years, completely isolated from the world.
When he announced his proof in 1993, it shocked the world, but a gap was discovered.
He struggled painfully for another year to fix the gap.
In 1994, the proof was finally perfect. This moment is considered the most glorious finale of 20th-century mathematics.

Wiles worked on the problem in secret for seven years. He told almost no one, working alone in his attic. When he finally announced his proof in 1993, it was a mathematical event of historic proportions.

But there was a problem: his initial proof had a gap. It took another year of intense work with Richard Taylor to fix it.

The Dramatic Announcement

In June 1993, Wiles gave three lectures at Cambridge, ending with the announcement that he had proved Fermat's Last Theorem. The mathematical world was stunned.

When a gap was found, Wiles worked frantically for a year. In September 1994, he and Taylor found the fix. The corrected proof was published in 1995.

Legacy

Wiles's proof is a masterpiece of modern mathematics:

Number Theory: Connected elliptic curves and modular forms
Algebraic Geometry: Advanced techniques in the field
Mathematical Proof: Showed how deep connections can solve ancient problems

Wiles showed that problems that seem impossible can be solved by finding the right connections. His work demonstrates that mathematics is a unified whole—number theory, geometry, and analysis are all connected in ways we're still discovering.

The proof of Fermat's Last Theorem is not just about solving an old puzzle—it's about understanding the deep structure of mathematics itself.