Failing for 130,000 Days Doesn’t Mean You Shouldn’t Try Again

A few decades ago, when I was in school, our math teacher gave us an assignment for homework. After a few days, the teacher came clean. This was what we had to prove:
It is impossible to separate any power higher than the second into two like powers.
You might recognize it in this form:
If an integer n is greater than 2, then the equation
an + bn = cn
has no solutions in non-zero integers a, b, and c.

In 1637, Pierre de Fermat wrote on the margin of a famous math book he owned, "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." This note eventually became known as Fermat's Last Theorem, probably the biggest most famous mathematical problem ever. It looks so simple and innocent, understandable even to kids, so it is only natural that all the mathematicians tried to prove this simple statement. They all tried. They all failed. For more than three and a half centuries, all the great mathematicians took a shot at this problem to no avail. It seemed like this problem was beyond human capabilities.

Then, one day out of the blue in 1993, an unknown mathematician named Andrew Wiles shocked the world. After working on the Taniyama-Shimura conjecture (the last huge impossible missing piece of the puzzle) alone and in secrecy for 7 years, he completed the proof using modular functions and elliptic curves. He achieved what was thought to be impossible for 358 years, in what is considered by many as the greatest most brilliant mathematical piece ever written. Later, a mistake was found in his proof, but he managed to fix it after another extremely frustrating year of failing. I’m skipping a lot of details, so I must recommend the fascinating book by Simon Singh.

So, the next time people tell you "Drop it, it’s too difficult", you can refer them to this.

p.s. Why fish don’t talk? ‘Cause they’re busy! (credit goes to my 3.5 year old son)


Inbar Shani said...

I didn't read the book and i'm kind of curious: does the Math world community believe Fermat had a proof? Or is it more likely that his proof was faulty, considering the proven difficulty of this theorm?

Uri Kalish said...

Andrew Wiles was asked the same question. He replied very politely and cautiously, but from his answer you can understand there is no way Fermat found a proof using 17th century math.

Miky Schreiber said...

I must disagree. Sometimes you can look for something and finally find that it was under your nose all of the time. Maybe the proof is very simple and still no-one found it with using 17th century math.

Child Person said...

My compliments to your son...
deeply profound, don't you think?
A Child is Waiting.
Take aware,
Child Person From The South

Uri Kalish said...

Considering the list of brilliant mathematicians who stormed this riddle for the last three and a half centuries, including every mathematician you've ever heard of, I would consider that highly unlikely. Wiles is always very polite during his interviews but make no mistake, he means there is no way in hell Fermat found a proof using 17th century math.

@Child Person,

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LAD said...

indeed fascinating.

perseverance will really get you there.

machinehuman said...

Wiles was introduced to Fermat's Last Theorem at the age of ten. Maybe your kid could take a look at it a little earlier.
Great blog Uri!

Daldianus said...

I've read the book by Simon Singh and liked it a lot. His other books, especially the one about cryptography, are great too.

Btw, that quote from your son about the fish is adorable!!!

Uri Kalish said...

I agree, The Code Book by Simon Singh is truly fascinating!

onn.benzvi said...

kagdila Mr. Kalish Man?

Tamera said...

Fantastic blog by the way. Trying again keeps mathematicians busy, alright. My husband is wound up in the world of Riemann, on the agreement that he comes out for food and sleep. lol. Yet, last time I saw him, he was chasing Goldbach. It's going to be a long haul!

Uri Kalish said...

If he will prove either the Goldbach conjecture or the Riemann hypothesis, I promise to dedicate a whole post to your husband... :p

Tamera said...

You got a deal. I'll get back to you in a few

Ray Gratzner said...

109 pages, that does not sound as if fermat had been right? May be he erred and he was wise enough not to bring the topic up again during his lifetime.