Mathematician Proves Huge Result on ‘Dangerous’ Problem | Number Theory - Quanta Magazine

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades, writes Kevin Hartnett, senior writer at Quanta Magazine covering mathematics and computer science.

Terence Tao, inspired by a comment on his blog, made some of the biggest progress in decades on the Collatz conjecture.
Photo: Courtesy of UCLA

Experienced mathematicians warn up-and-comers to stay away from the Collatz conjecture. It’s a siren song, they say: Fall under its trance and you may never do meaningful work again.

The Collatz conjecture is quite possibly the simplest unsolved problem in mathematics — which is exactly what makes it so treacherously alluring.

“This is a really dangerous problem. People become obsessed with it and it really is impossible,” said Jeffrey Lagarias, a mathematician at the University of Michigan and an expert on the Collatz conjecture.

Earlier this year one of the top mathematicians in the world dared to confront the problem — and came away with one of the most significant results on the Collatz conjecture in decades.
 
On September 8, Terence Tao posted a proof showing that — at the very least — the Collatz conjecture is “almost” true for “almost” all numbers. While Tao’s result is not a full proof of the conjecture, it is a major advance on a problem that doesn’t give up its secrets easily...

Tao doesn’t normally spend time on impossible problems. In 2006 he won the Fields Medal, math’s highest honor, and he is widely regarded as one of the top mathematicians of his generation. He’s used to solving problems, not chasing pipe dreams.

“It’s actually an occupational hazard when you’re a mathematician,” he said. “You could get obsessed with these big famous problems that are way beyond anyone’s ability to touch, and you can waste a lot of time.”
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Source: Quanta Magazine