Fermat's Last Theorem and Andrew Wiles
Fermat's Last Theorem is a statement in number theory that asserts that there are no three positive integers (a), (b), and (c) such that (a^n + b^n = c^n) for any integer value of (n) greater than two. This proposition was famously conjectured by the French mathematician Pierre de Fermat in 1637. Fermat jotted down the theorem in the margin of his copy of an ancient Greek text, claiming to have a "truly marvelous proof" which the margin was too small to contain. Despite its simplicity, the theorem eluded proof for over 350 years, becoming one of the most famous unsolved problems in mathematics.
The Journey to a Proof
The challenge of proving Fermat's Last Theorem captured the interest of many mathematicians over the centuries. Various attempts were made, but it wasn't until the late 20th century that a solution was finally achieved. The key breakthrough occurred through the work related to the modularity theorem and elliptic curves.
Andrew Wiles
The mathematician Andrew Wiles, born in 1953, was instrumental in proving Fermat's Last Theorem. Wiles, an English mathematician and a Royal Society Research Professor at the University of Oxford, dedicated much of his professional life to solving this problem. As a child, Wiles encountered Fermat's Last Theorem and became obsessed with finding a proof.
In the early 1990s, Wiles began working on a proof in secret, utilizing modern mathematical tools and concepts that were unavailable to previous generations. His work primarily involved the connection between elliptic curves and modular forms, a relationship conjectured in the Taniyama-Shimura-Weil conjecture, which later became part of the modularity theorem.
The Breakthrough
In 1993, Wiles announced his proof at a conference in Cambridge, England. However, a gap in the proof was discovered shortly thereafter. With the assistance of his former student, Richard Taylor, Wiles resolved the issue, and the corrected proof was published in 1995. This monumental achievement not only proved Fermat's Last Theorem but also demonstrated the power of modern mathematical techniques and collaboration.
Wiles's proof was heralded as a "stunning advance" in mathematics and contributed significantly to the field of number theory. For his accomplishment, Wiles was awarded numerous prizes, including the Abel Prize, often referred to as the "Nobel Prize of Mathematics".