Why mathematicians find math thrilling


Mathematician Eduardo Sáenz de Cabezón suspects that when people ask him what’s the use of math, they’re really asking why they had to study math in school. As a mathematics professor at the University of La Rioja in northeastern Spain, Sáenz de Cabezón (TED Talk: Math is forever) has come up with a spirited defense of his chosen profession. Math, he believes, is nothing less than a quest for eternal truth. Here’s why:

Math reveals unfathomable truths. Take a regular sheet of paper and start folding. If the piece of paper were big enough to be folded 50 times, Sáenz de Cabezón says, “its thickness would extend almost the distance from the Earth to the Sun.” If you’re now trying to imagine how a sheet of paper, folded 50 times, can rise nearly 93 million miles into space, you’re experiencing the strange thrill of a mathematical proof. “Your intuition tells you it’s impossible,” he says. “Do the math and you’ll see it’s right. That’s what math is for.”

Math can be as beautiful as poetry — or love. “Science operates on intuition, creativity. Math controls intuition and tames creativity,” says Sáenz de Cabezón. He admits that his colleagues fall into two camps when they’re asked why math matters: attackers and defenders. “The attacking ones are mathematicians who would tell you this question makes no sense, because mathematics have a meaning all their own,” Sáenz de Cabezón says. “There’s no point in constantly searching for all possible applications. What’s the use of poetry? What’s the use of love? What’s the use of life itself?” They have a point, he says — and so do the defenders. “Those who stand in defense tell you, ‘Even if you don’t realize it, friend, math is behind everything.’ Those guys, they always bring up bridges and computers. ‘If you don’t know math, your bridge will collapse.’” Also true. But Sáenz de Cabezón suspects that neither answer conveys the private thrill that mathematicians experience with every breakthrough in their field — and every push to help us better understand the world.

Math endures. Anyone can posit a theory of how the universe works, but math leaves no room for conjecture. Consider how long mathematicians puzzled over a proposal by Pappus of Alexandria, who theorized in around 300 A.D. that a hexagon was surely the most efficient shape for covering an infinite flat field. “But he didn’t prove it,” says Sáenz de Cabezón. “It remained a conjecture: ‘Hexagons!’” The debate raged for 1,700 years, until in 1999 American mathematician Thomas Hales offered decisive proof of what Pappus had discovered and what bees instinctively know — the most efficient shape is indeed a hexagon. “We mathematicians devote ourselves to coming up with theorems,” says Sáenz de Cabezón. These, in essence, are “eternal truths,” discoveries that are possibly the most enduring things we will ever encounter in our lifetimes.” You probably said or were told at some point that diamonds are forever,” Sáenz de Cabezón says. “That depends on your definition of forever. A theorem? That really is forever.”

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Image credit: Emilie Soffe + How Big Is Infinity?/TED-Ed.

Editor’s note: This article is adapted for TED-Ed. A longer version appeared first on Ideas.ted.com.


  1. mcgregor

    no one can posit a theory on anything, they may hypothesize, but theories only happen when most of the scientific community agrees with you.

  2. That’s the difference between a “theory” and a “theorem.” A theory is considered true if people accept it as true. A theory can come into and out of acceptance. On the other hand, once a theorem is proven it is always true, whether people believe it or doubt it. A theorem can be forgotten and then rediscovered, but even when it is forgotten it is still true.

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