20151208 - hexagons

Hexagons! And other reasons to love math

One mathematician’s spirited answer to bored, frustrated and reluctant math students.

Eduardo Sáenz de Cabezón suspects that when people ask him what’s the use of math, they’re really asking a more pointed question. “They’re asking you, ‘Why did I have to study that bullshit I never used in my life again?’” he says. Sáenz de Cabezón (TED Talk: Math is forever) sympathizes, but as a mathematics professor at the University of La Rioja in northeastern Spain, he 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.”
Hexagons! Why they’re excellent. 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.”

 http://ideas.ted.com/hexagons-and-other-reasons-to-love-math/