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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.
In the 1970s, mathematicians showed that almost all Collatz sequences — the list of numbers you get as you repeat the process — eventually reach a number that’s smaller than where you started — weak evidence, but evidence nonetheless, that almost all Collatz sequences incline toward 1.
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.
“I wasn’t expecting to solve this problem completely,” said Tao, a mathematician at the University of California, Los Angeles. “But what I did was more than I expected.”
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.
originally posted by: TEOTWAWKIAIFF
a reply to: sine.nomine
It is the “infinity” that makes this question so appealing to an answer.
I think the "unsolved" translates to "lacking rigorous proof", rather than "I don't know the answer". The unsolved conjectures seem to be of the form "here's what I think the answer is, how can we rigorously prove this is the correct answer?".
originally posted by: sine.nomine
To say the Collatz Conjecture is "unsolved" is kind of dumb. It is solved. It's 1.
originally posted by: TEOTWAWKIAIFF
a reply to: Peeple
My deepest Peeps,
The “conjecture” is more of a “conjuring trick” that makes people look at the leggy blonde assistant instead of the “magician” palming the card!
The weird thing is that this works. And people cannot understand why. It is kind of silly, like I said that it is a party trick, rather than a math puzzle.
Major hint to life... the answer is in the question!
Many math problems become easier when one allows a small number of exceptional cases to behave badly and one is willing to settle for controlling almost all cases, I showed that one could move this intermediate milestone to be as close as one wishes to the final goal 1… for almost all n.
Terrence Tao