Today’s Wonder of the Day was inspired by Lucas. Lucas Wonders, “What is Fermat's Theorem?” Thanks for WONDERing with us, Lucas!

You probably know that 1 + 1 = 2. Maybe you’ve even learned that a² + b² = c² or that E = mc². These are all common equations in math and science. But have you ever seen the formula xⁿ + yⁿ = zⁿ?

If so, you’re probably a mathematician. That equation is part of an advanced topic in math called Fermat’s Last Theorem. It states that, when n>2, no non-zero integers may be equal to x, y, and z. 

The story behind this theorem has interested math experts for centuries. It was first written by Pierre de Fermat. Working as a lawyer, Fermat studied math in his spare time. When he died in 1665, his son found the theorem. Fermat had scribbled it in the margins of a book.

The book was “Arithmetica” by Diophantus, and experts estimate Fermat likely wrote his theorem in the 1630s. In his note, he claimed to have written a mathematical proof for the theorem. A proof is a statement that shows a particular math concept is true. In the case of Fermat’s Last Theorem, though, there was a problem: The proof was nowhere to be found.

This began a centuries-long mathematical mystery. For years, expert after expert worked to prove Fermat’s Last Theorem. Many made progress—including mathematicians like Leonhard Euler, Sophie Germain, and Peter Gustav Lejeune Dirichlet. However, over 300 years passed before anyone wrote a successful proof.

In 1993, British math expert Andrew Wiles wrote a proof for the theorem. However, others found holes in the work. At the end of 1994, though, Wiles released an updated version of his proof. It successfully solved the mystery of Fermat’s Last Theorem.

In 2000, Wiles was knighted and became Sir Andrew Wiles. In 2016, he won the Abel Prize for this accomplishment. In the math world, this honor is sometimes called the “Nobel of mathematics.” Today, Sir Wiles teaches mathematics at the University of Oxford.

Are you a budding mathematician? Many people find the subject of math difficult. For others, it’s a world of possibility. No matter which of these groups you fall into, it’s important to do your best in all subjects. Who knows? Maybe you’ll write the next major mathematical proof!


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