Over the years, many problem solvers have been drawn to the beguiling simplicity of the Collatz conjecture, or the “3 x + 1 problem,” as it’s also known. And once you hit 1, the rules of the Collatz conjecture confine you to a loop: 1, 4, 2, 1, 4, 2, 1, on and on forever. He conjectured that if you start with a positive whole number and run this process long enough, all starting values will lead to 1. Maybe others go marching off to infinity.īut Collatz predicted that’s not the case.
Maybe some numbers eventually spiral all the way down to 1. Intuition might suggest that the number you start with affects the number you end up with. The conjecture is about what happens as you keep repeating the process. Lothar Collatz likely posed the eponymous conjecture in the 1930s. “But what I did was more than I expected.” The Collatz Conundrum “I wasn’t expecting to solve this problem completely,” said Tao, a mathematician at the University of California, Los Angeles.
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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. On September 8, Terence Tao posted a proof showing that - at the very least - the Collatz conjecture is “almost” true for “almost” all numbers. 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.Įarlier 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. The Collatz conjecture is quite possibly the simplest unsolved problem in mathematics - which is exactly what makes it so treacherously alluring.
It’s a siren song, they say: Fall under its trance and you may never do meaningful work again.
Experienced mathematicians warn up-and-comers to stay away from the Collatz conjecture.
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