Homer Simpson was ruining one of the most intriguing theorems in mathematics

The fascinating story of Fermat’s Last Theorem has been going on for hundreds of years. Since then, it has had major twists and turns, disappointing mistakes, and even the most unlikely mathematician has been caught up in the noise.

If, on the one hand, every young scientist’s dream is to make a discovery that changes the course of history; on the other, the nightmare is that, after having made the announcement and being featured in magazines and newspapers, someone discovers that they made a mistake and finds themselves ruined. That’s what happened to Andrew Wiles em 1993.

As explained by , Wiles worked secretly for seven years in his attic to try to solve a numerical puzzle that had defeated the greatest mathematicians for 350 years.

When he finally deciphered it (or so he thought), he described the proof in 3 hours of lectures, without anyone noticing a single thing. crucial flaw.

But later, when experts examined the structure of the test, they realized that the link connecting two of these steps was defective – and all it took was one weak link in a huge chain to break the entire structure.

Fortunately, the story had a happy ending, as Wiles’s resilience and ingenuity perfected the bond—and the .

The beauty of this theorem lies in the fact that it is extremely easy to understand. All children know Pythagoras theorem.

“The square of the hypotenuse is equal to the sum of the squares of the legs”

This fact inspired Fermat’s problem that frustrated mathematicians for three centuries, due to the fact that there are no integers that satisfy the equation aⁿ + bⁿ = cⁿ for n greater than 2.

For example, try to find three integers a, b and c that are solutions of a³ + b³ = c³. You can stop trying now. There are none.

Fermat and Wiles were right

Wiles first encountered Fermat’s Last Theorem in a library book at age 10 and decided to dedicate his life to it.

As New Scientist reports, the critical link that led to Wiles’ assault on the top happened in 1984, when Ken Ribet showed that if the Shimura-Taniyama conjecture were true, then Fermat’s Last Theorem would be true as well.

The way was then open for Andrew Wiles. If he could prove the Shimura-Taniyama conjecture, then, thanks to the work of Ken Ribet, he would also have proven Fermat.

This led to seven years of work in secret isolationhis moment of triumph when he announced his success, followed by months of agony as he tried to fix his broken theory. Finally, in 1995his triumph was complete.

Thanks to Pythagoras, the simple addition of integers, a + b = c, was elevated to the addition of their squares: a² + b² = c². There are an infinite number of integers that satisfy the first of these conditions, and likewise, there are an infinite number that satisfy the sums of squares.

Mathematicians love number symmetries, and have long sought examples in which cubes of non-zero whole numbers add up:³ + b³ = c³.

However, as Fermat suspected and Wiles eventually proved, There are no integers that satisfy this power or any higher power. Addition of whole numbers ends in squares.

Or at least it ends until someone finds a counterexample…

This is where Homer Simpson comes in…

In an episode of the television cartoon series The Simpsonsit looked like Fermat had been knocked down.

Homer Simpson, in a dream, wrote that 1782 raised to the 12th power plus 1841 raised to the 12th power equals 1922 raised to the 12th power:

1782¹² + 1841¹² = 1922¹²

A San Francisco Chronicle article in November 2005, cited by New Scientist, presented this remarkable equation and added confirmation that the numbers did, in fact, match.

“Have we found Fermat’s long-sought refutation?” asked the paper.

According to the calculator, the answer appears to be yes.

However, what was demonstrated was the limitation of a calculatorand not Fermat’s theorem.

Furthermore, you can see that the equation is not true without calculating the individual terms. The product of pairs (the first term) is even; the product of odd numbers (the second term) is odd. The sum of an even and an odd is odd (the left side of the equation).

As for the right side, a product of even powers must be even. Clearly something is wrong here.

The explanation is that the 12th power leads to numbers with forty integers; and after ten digits, Most hand calculators round the last digit up or down to keep an approximation of the answer.

In reality, the sum on the left of the equation is equal to the 12th power not of 1922, but of 1921.99999996, which on a hand calculator rounds to 1922. This may be great for practical computing – but not for the perfect precision required by a mathematical theorem .

Conclusion: Fermat’s theorem outlived mathematician Homer Simpson!