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# Pierre de Fermat’s Last Theorem Celebrated With A Google Doodle

## Famous theorem remained unproven for 358 years

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Google’s gone geeky for today’s Doodle.

If you look closely at the Google Doodle for today, you can see the faint outline of the company’s name, appearing as recently erased markings on a chalkboard. What takes center stage is the mathematical equation xn + yn ≠  zn (when n > 2)

If you mouse over the doodle, this message will pop up: “I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain.”

We have discovered a truly marvelous proof of this theorem, which today’s tweet is too small to contain. #Fermat http://t.co/9Tvx8A8 9 hours ago via web · powered by @socialditto

This equation is called Fermat’s Last Theorem and was first proposed in 1637 by Pierre de Fermat. Today is Fermat’s 410th birthday.

Fermat, a French lawyer and amateur mathematician, proposed the xn + yn ≠ zn theory as an extension of the concept of Pythagorean triples.

We all learned in basic algebra about using the Pythagorean Theorem to find the side lengths in right triangles – a2 + b2 = c2. where “c” is the hypotenuse.

Basically, the square of one shorter side plus the square of the other is equal to the square of the longest side.

Pythagorean triples are sets of positive integers a, b, and that fit the a2 + b2 = c2 equation. For instance – 3, 4, and 5 is a set:

32 (9) + 42 (16) = 52 (25)

There are many other sets of Pythagorean triples, including (5,12,and 13) (11, 60, and 61) and (65, 72, and 97).

That’s where Fermat’s Last Theorem take off. His xn + yn ≠ zn (when n > 2) states that there are no sets of integers for x, y, and z that satisfy the equation when n is greater than 2. Basically, the equation will never work for any set of integers when they are taken to any higher power than 2 (squared).

This theorem is said to be the basis of modern number theory.

Fermat simply stated this theorem and left it to other mathematicians to prove, and they tried – for 358 years. No mathematician could write a proof of Fermat’s equation until 1995 when British mathematician Andrew Wiles offered the first complete proof as part of the modularity theorem for semistable elliptic curves.

The proof was over 100 pages longs and took Wiles 7 years to complete. He was subsequently knighted for his accomplishment.

In other geeky Doodle news, Google recently honored the father of modern genetics Gregor Mendel with a Doodle referencing his famous pea experiments.

What do you think of today’s Google Doodle? Let us know in the comments.

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John Tomlinson

That is the coolest doodle I have ever seen. Unfortunately, most people will not understand the math symbolism nor be familiar with the story of Fermat writing the famous note in the page margin of his book. A great honorarium to a significant historical academic event.

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AMac

WOW! A big “props” to Google for this doodle! Perhaps a little much for my brain this early in the morning…. LOL

3. I have never been satisfied with the fact that the only available proof to Fermat’s famous theorem required advanced math that was not available to mathematicians alive when he was. Thus, the only available proof is not within the “spirit of Fermat” and I would hope that someone could prove his theorem w/mathematics that existed hundreds of years ago. If not, perhaps he was bluffing or he had made some error.

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Kenneth J. Kellar

Thanks. These little notes remind us why math is challenging and fun– sort of like basketball.

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Micheal

Ahh… The Pythagorean Theorem…. I remember i first mastered it in freshmen year…

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(Mr.) Lynn Davis

You (Google) refer to the algebraic expression as an “equation” when it is actually an “inequation”, not an inconsequential error, as the inequality is the crux of the theory. In a brief review of the info about the subject you (Google) display, I don’t see a reference to the Princeton mathematician (name?) who only a few years ago finally proved it. If this is geeky, then I want more geeky.

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(Mr.) Lynn Davis

Sorry. On a closer review it’s quite apparent that you do cite the epic proof developed by Andrew Wiles.

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Raisin

Major props indeed to Google for this doodle. It has been a loooong time since I was in highschool and studied the Pythagorean Theorem. I appreciate google’s refresher article and explanation of who the flip Fermat was and how important his theory was to the mathematic community.

9. Just a reminder, guys (v, vvv) – I’m not Google.

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Pat

Gotta love learning new things from Google Doodles! Thanks ;-j

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TommyZ

It’s good 2 see google using this type of info. Just explained simple algebra 2 my oldest niece and she loved it. “Jasmine 8yrs old” A big Thank you for giving me the inspiration to pass down knowledge.
TommyZ

12. 0 0
TommyZ

i know your Josh but, i was joshingyou by mentioning google so much….. lol
TommyZ

13. 0 0
macdhai

Can’t get my brain around it, but I love it!

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anonymous

Actually x^n + y^n = z^n has trivial solutions, so you need to mention there are no non-trivial solutions (i.e. (1,0,1), (0,1,1), and (0,0,0) will all work for all n)

• 0 0
TD

hence the n > 2 criteria

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math geek

please read the theorem. It states that n>2. All of the “solutions” you have proposed are less than 2.

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DH

“n>2″ refers to the value of the exponent, not the values of x, y, and z. 1^n + 0^n = 1^n.

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Loretta

This is a great one. It’s so much fun to find out the little known facts that your google crew dig up. Oh and btw, Congratulations on your purchase of Motorola Mobile!

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JERRY PALMER

LOVE IT!

17. 0 0
Story

Something for us math geeks. I love it!

18. 0 0
Mary Asher

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Suzanne

Things like this keep my mind strong. I LOVE the Google Doodles. They are as fun as finding the wishbone in a turkey!!! Keep up the good work!

20. We love the intellectual focus of Google and this particular story is riveting and entertaining because anyone with some brief intro to algebra can get it. The universe of numbers and mathematics is wild, and it raises epistemological questions about whether a falling tree makes a sound if nobody is there, how about all this math?

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John Smith

Google Doodles are great! I just found this all google doodle website. http://www.goologos.com

22. 0 0
heather

I think it is crap – I thought my computer had a virus.

23. 0 0
heather

Ah OK – was being thick. Hadn’t realised this kind of thing had been done before!