What a 358-year-old mathematical mystery can teach us about Creativity

The sum of the square of the legs is equal to the square of the hypotenuse. You probably learned in school about the Pythagorean Theorem, right?

That is, x² + y² = z².

But if you, like me, were not the most interested student in mathematics, I doubt that you have given much thought to this theorem. However, this theorem has a lot to teach us about Creativity.

In 1637, the mathematician Pierre de Fermat, while studying Arithmetic books, had an insight that led him to analyze the Pythagorean Theorem from another perspective: What if the power of the numbers were greater than 2? At this point, Fermat wrote in the margin of the book:

The equation xn+yn=zn has no integer solutions for n>2. I found it a wonderful demonstration, but the margin of this book is too small.

There is no record of what the demonstration proposed by Fermat would be. However, a simple statement in the corner of the page gave rise to one of the greatest mysteries of mathematics, known as Fermat’s Last Theorem.

What fascinated mathematicians over the centuries was the simplicity of the statement and the idea that there was a solution. Fermat’s Last Theorem provoked important mathematicians, but none of them were able to solve it. Given its complexity, most mathematicians thought that such proof did not exist and that it was simply impossible to solve it. After many unsuccessful attempts, the theorem was forgotten as other important questions of mathematics emerged.

The mystery remained unanswered for 358 years until it was finally solved in 1995 by a child. How was a child able to solve this problem? Well, let me explain.

In 1963, Andrew Wiles was just 10 years old when he found a copy of a book on Fermat’s Last Theorem in a local library in Cambridge, England. He was intrigued by the problem that even he at the age of 10 could understand, but that no one has been able to solve in more than 300 years.

“I knew at that moment that I would never give up. I had to resolve it.”

The boy Andrew grew up and devoted himself completely to mathematics. He graduated in mathematics at Oxford and completed his Ph.D. at Cambridge University. Today, Wiles is a research professor at the Royal Society at Oxford University.

After more than 30 years of study, in 1995, he finally managed to prove Fermat’s Last Theorem, putting an end to this almost 400-year mystery. Little Andrew’s curiosity has followed him all these years, and it is clear that it was thanks to his passion for the challenge that kept him steady throughout the journey. It is as if his whole life was dedicated to solving this theorem.

“It is a tremendous honor. Fermat’s equation has been my passion since I was a child, and solving it has given me an enormous sense of accomplishment. (…) I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.”

Achieving this result was not only the highlight of his career but also the outcome of a 10-year-old boy’s personal journey that began three decades earlier. The discovery earned Wiles the Abel Prize in 2016, considered the Nobel Prize in Mathematics, in addition to generating one of the most complex areas of Number Theory and considerable advances in the field of Mathematics.

But the question remains: did Fermat really have a solution for this theorem?

We will never know. However, it is believed not to. To arrive at the result, Wiles used the ideas of dozens of other mathematicians of the 20th century and, even today, only a tenth of the world’s mathematicians are able to fully understand Wiles’ solution.

Okay, and what does this have to do with Creativity?

Wiles could not rely on previous concepts, as there was no right answer to this situation. No one until then knew the answer, or even if an answer exists. When asked how he had the inspiration or ideas to solve this age-old problem, Wiles replied:

“I tried to find general patterns. I did calculations that explained small math results to me, then I tried to fit these calculations into my idea. Sometimes, this led me to consult some books to see how something similar had been done, other times I had to make changes and do more calculations. But I realized that these calculations had never been done before, so I had to work on something totally new.

This story shows us how various elements of Creativity operate, both in terms of the process of creating and generating ideas and in terms of personal and emotional attitudes and capacities. Are they:

Curiosity (generated mainly by the mystery of the problem);

· Question pre-established concepts;

· Look for a new perspective for the same problem;

· Change the context and/or conditions of a given situation;

· Explore possibilities by asking “what if …?”;

· Motivation to achieve a certain result;

· Resilience in the face of failure;

· Collaboration (the solution has only arrived thanks to all previous attempts);

· Ecstasy in finally getting the expected result;

Moral of the story: you still don’t know the practical application of the Pythagorean Theorem, but now you can at least use it to develop your Creativity!

P.S .: If you want to learn more about the story behind this mathematical mystery, I highly recommend watching the BBC’s award-winning documentary, Fermat’s Last Theorem (1996).

References

Abel Prize (2016). Sir Andrew J. Wiles receives the Abel Prize. <https://www.abelprize.no/nyheter/vis.html?tid=67106>.

McKenzie, S. (2016). Professor wins $700k for solving a 300-year-old math equation. <https://edition.cnn.com/2016/03/16/europe/fermats-last-theorem-solved-math-abel-prize/index.html>.

BBC Horizon (1996). Fermat’s Last Theorem.

Singh, S. (1998). Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem. New York, Anchor Books.

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