Fermat's Last Theorem: 8 key ideas
The core ideas of Fermat's Last Theorem, each in under a minute, written in our own words. Want the full depth? Get the book.
- IDEA 1 OF 8
A puzzle lasted 350 years
Singh tells the story of Fermat's Last Theorem, a simple-looking problem that defeated mathematicians for over three centuries.
It states that a certain equation has no whole-number solutions for powers above two.
- IDEA 2 OF 8
Fermat left a teasing note
Singh describes how Pierre de Fermat wrote in the margin of a book that he had a proof but no room to write it.
No one ever found his proof.
- IDEA 3 OF 8
The puzzle grew from Pythagoras
Singh explains that the theorem extends Pythagoras's famous equation about right-angled triangles.
With squares there are many solutions, but with higher powers there seem to be none. The question was whether the same trick works for powers above two.
- IDEA 4 OF 8
Many great minds tried
Singh describes attempts by mathematicians such as Leonhard Euler and Sophie Germain.
Germain, who had to hide her identity as a woman, made important progress. Each attempt solved only a few cases, and the full puzzle stayed unsolved.
- IDEA 5 OF 8
A link opened the door
Singh explains the Taniyama-Shimura conjecture, connecting two different areas of mathematics.
It was shown that proving it would also prove Fermat's theorem. This gave mathematicians a clear and new path toward solving the old puzzle.
- IDEA 6 OF 8
Wiles worked in secret
Singh tells how Andrew Wiles spent seven years working alone on the proof.
He announced it in 1993 to great excitement. Working alone let him focus deeply, without the pressure of others racing to the same result.
- IDEA 7 OF 8
A flaw nearly ended it
Singh describes how a gap was found in Wiles's proof.
After a painful year, Wiles and Richard Taylor repaired it. The setback showed how a single hidden error can threaten a proof that looks complete.
- IDEA 8 OF 8
Proof brings certainty
Singh explains that mathematical proof gives a kind of certainty unlike anything in science.
Once proved, a theorem is true forever. This is why mathematicians were willing to spend centuries working on a single statement.
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