What Is Fermat’s Last Theorem?

Learn English Phrases Through a Mathematical Mystery

Introduction

In the world of mathematics, Fermat’s Last Theorem is not just an equation — it is one of the most famous and enduring mathematical mysteries in history. For over 350 years, this problem puzzled the brightest minds. In this article, you’ll learn what the theorem is about, its fascinating history, and key English phrases related to the topic.

What Is Fermat’s Last Theorem?

Let’s begin with the statement of the theorem.

There are no three positive integers x, y, and z that satisfy the equation xⁿ + yⁿ = zⁿ for any integer value of n greater than 2.

Useful English Phrases:

positive integers – whole numbers greater than zero
satisfy the equation – make the equation true
for any integer value of n greater than 2 – when n is any whole number more than 2

Fermat’s Famous Note

The theorem was first proposed by the 17th-century French mathematician Pierre de Fermat. He scribbled a mysterious note in the margin of a book:

“I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.”

This short remark sparked centuries of curiosity and frustration among mathematicians.

Useful English Phrases:

a truly marvelous proof – an amazing or remarkable mathematical demonstration
margin – the edge or border of a page
too narrow to contain – not enough space to hold something

Unsolved for Over 300 Years

For more than 350 years, Fermat’s Last Theorem remained unproven.

No one could find the proof Fermat claimed to have, and many believed it might not even exist.

Useful English Phrases:

remained unproven – continued to lack a formal proof
for more than 350 years – spanning over three centuries

Who Solved It?

In 1994, British mathematician Andrew Wiles finally proved the theorem after years of secret research and collaboration.

“In 1994, British mathematician Andrew Wiles finally proved Fermat’s Last Theorem.”

His accomplishment was a landmark moment in mathematical history.

Useful English Phrases:

finally proved – succeeded in proving after much effort
historic achievement – a major success remembered in history

Why Was It So Hard?

Although the equation looks simple, the proof required deep knowledge of modern mathematics, including elliptic curves and modular forms.

“Despite its simple appearance, the proof required deep and complex mathematical theories.”

Useful English Phrases:

simple appearance – looks easy on the surface
deep and complex theories – difficult and advanced ideas
required – needed

Summary

Fermat’s Last Theorem is more than a math problem — it’s a story of persistence, curiosity, and human brilliance. Even if you’re not a math lover, the mystery and triumph surrounding this theorem are truly inspiring.