09-12-2019, 08:46 PM
https://www.newscientist.com/article/221...st-solved/
We almost have a solution to an exceptionally tricky mathematical riddle first posed 82 years ago.
The problem, known as the Collatz conjecture, is easy to state:
The sequence can be depicted visually to show sequences of numbers all wiggling their way back to the same spot. The result looks a bit like waving seaweed or a pile of strange worms.
As well as being visually arresting, it is intensely difficult to prove true or false. The conjecture has been verified up to the starting number of 1020: that’s one hundred quintillion. But proving it holds in every case involves not just checking more and more numbers – the number line is infinite, after all – but finding a logically reasoned mathematical explanation.
I love this problem: it's simple enough that a schoolchild can understand it, but horrifically hard to solve: mathematicians have spent over 80 years looking for sequences that don't end in 1, and they haven't found any yet, but that doesn't mean they don't exist .
I will admit, while I was at university, I made a half-hearted attempt to solve this problem - which, needless to say, got nowhere. Now, I'm just hoping I live to see a solution !
We almost have a solution to an exceptionally tricky mathematical riddle first posed 82 years ago.
The problem, known as the Collatz conjecture, is easy to state:
- Start with any positive whole number;
- If it is even, divide it by two. If it’s odd, triple it and add 1.
- Whatever the result, follow the same steps as before, over and over again;
- The conjecture says that whatever number you start with, the sequence will always reach 1 eventually.
The sequence can be depicted visually to show sequences of numbers all wiggling their way back to the same spot. The result looks a bit like waving seaweed or a pile of strange worms.
As well as being visually arresting, it is intensely difficult to prove true or false. The conjecture has been verified up to the starting number of 1020: that’s one hundred quintillion. But proving it holds in every case involves not just checking more and more numbers – the number line is infinite, after all – but finding a logically reasoned mathematical explanation.
I love this problem: it's simple enough that a schoolchild can understand it, but horrifically hard to solve: mathematicians have spent over 80 years looking for sequences that don't end in 1, and they haven't found any yet, but that doesn't mean they don't exist .
I will admit, while I was at university, I made a half-hearted attempt to solve this problem - which, needless to say, got nowhere. Now, I'm just hoping I live to see a solution !
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