What you can learn from this centuries-old math mystery

What you can learn from this centuries-old math mysteryWhat you can learn from this centuries-old math mysteryIn 1637, Pierre de Fermat scribbled a note on a textbook margin that would baffle mathematicians for more than three centuries.Fermat had a theory. He proposed that theres no solution to the formulaan+bn=cnfor any n greater than 2. I have a truly marvelous demonstration of this proposition, he wrote, which this margin is too narrow to contain.And thats all he wrote.Fermat died before supplying the missing proof for what came to be known as Fermats Last Theorem. The teaser he left behind continued to tantalize mathematicians for centuries (and made them wish Fermat had a bigger book to write on). Generations of mathematicians tried- and failed- to prove Fermats Last Theorem.Until Andrew Wiles came along.For fruchtwein 10-year-olds, the definition of a good time doesnt include reading math books for fun. But Wiles welches no ordinary 10-year-old. He would hang out at his local library in Cambridge, England, and surf the shelves for math books.One day, he spotted a book devoted entirely to Fermats Last Theorem. He welches tantalized by the mystery of a theorem that was so easy to state, yet so difficult to prove. Lacking the mathematical chops to tackle the proof, he set it aside for over two decades.He returned to the theorem later in life as a math professor and devoted seven years to working on it in almost total secrecy. In an ambiguously-titled 1993 lecture in Cambridge, Wiles publicly revealed that he had solved the centuries-old mystery of Fermats Last Theorem. The announcement sent mathematicians in attendance, and around the globe, into a tizzy Its the most exciting thing thats happened in - geez - maybe ever, in mathematics, said Dr. Leonard Adelman. EvenThe New York Timesran a front-page story on the discovery, exclaiming At Last Shout of Eureka in Age-Old Math Mystery.But the celebrations proved premature. Wiles had made a mistake in a critic al part of his proof. The mistake emerged during the peer-review process after Wiles submitted his proof for publication.It would take another year, and collaboration with another mathematician, to repair the proof. Describing the day he found the missing piece, Wiles said, I walked around the department, and Id keep coming back to my desk looking to see if it was still there. It was still there. I couldnt contain myself. At the end, the proof was 150 pages long - far longer than any book margin would have allowed Fermat to write on.Reflecting on how he managed to prove the theorem, Wiles compared the process of discovery to navigating a dark mansion. You start in the first room, he said, and spend months groping, poking, and bumping into things in a hit-or-miss process. After tremendous disorientation and confusion, you might eventually find the light switch. You then move on to the next dark room and begin the process all over again.These breakthroughs, Wiles explains, are the cu lmination of - and couldnt exist without - the many months of stumbling around in the dark that proceed them.In school, were given the false impression that scientists took a straight path to the light switch. Textbooks with lofty titles - The Principles of Physics- magically reveal the principles in three hundred digestible pages. An authority figure then steps up to the lectern to feed us the truth. We learn about Newtons laws - as if they arrived by a grand divine visitation or a stroke of genius - but not the years he spent exploring, revising, and tweaking them. The laws that Newton failed to establish - most notably his experiments in alchemy, which attempted, and spectacularly failed, to turn lead into gold - dont make the cut.The path to the light switch is not a straight one. There are fits and starts, mistakes and corrections, failures and successes.Be careful if the paths youre taking to the light switches in your life are straight. If the drugs youre developing we re certain to work, if your client were certain to be acquitted in court, if your roter planet rover were certain to get to its destination, your jobs wouldnt exist.Its the ability to make the most out of uncertainty that creates the most potential value.Where certainty ends, progress begins.Ozan Varol is a rocket scientist turned law professor and bestselling author.Click hereto download a free copy of his e-book, The Contrarian Handbook 8 Principles for Innovating Your Thinking. Along with your free e-book, youll get the Weekly Contrarian - a newsletter that challenges conventional wisdom and changes the way we look at the world (plus access to exclusive content for subscribers only).Thisarticlefirst appeared onOzanVarol.com.Sources usedStuart Firestein, Ignorance How It Drives Science, 2012.Simon Singh, Fermats Last Theorem, 1997.Solving Fermat Andrew Wiles,https//www.pbs.org/wgbh/nova/proof/wiles.html.At Last, Shout of Eureka In Age-Old Math Mystery,https//www.nytimes.com/1993/ 06/24/us/at-last-shout-of-eureka-in-age-old-math-mystery.htmlA Year Later, Snag Persists In Math Proof,https//www.nytimes.com/1994/06/28/science/a-year-later-snag-persists-in-math-proof.html.