alt Hacker NewsIn my free time, I have taken to trying to prove the Collatz conjecture.
People much smarter and more educated than me have failed at this quest, so I will nearly certainly fail at it, but that's not really the point in my mind. Even if I'm not the one to actually prove it, I can at least try and contribute to the body of work towards proving it. Mathematics is, more than nearly anything else, the result of generations building upon previous generations work. It's never "done", always growing and refining and figuring out new things to look at.
I have a few ideas on how to prove Collatz that I have not seen done anywhere [1], and usually (at least for me) that means it's a bad idea, but it's worth a try.
One of the greatest things about humans is our willingness to have multi-generational projects. I think maybe the coolest thing humans have ever done was eliminate smallpox, and that took hundreds of years.
[1] Which I'm going to keep to myself for now because they're not very fleshed out.
Replies
And it’s not only never done, it’s always on the verge of dying off. Like Bill Thurston said, mathematical understanding basically lives in communities of mathematicians, every one of them a cell in the superorganism that is the field. You’re part of the distributed filesystem providing persistence as well as the possibility of new understanding.
https://mathoverflow.net/questions/43690/whats-a-mathematici...
Interesting new contender for simplest to state unsolved problem: The Antihydra
Does this program halt?
a = 8
b = 0
while b != -1:
if a % 2 == 0:
b += 2
else:
b -= 1
a += a//2
Reminds me of Stewart Brand and the Clock of the Long Now (and other longer time horizon projects they are working on).
Reminds me of a statement he made during a Tim Ferris interview that I think is quite profound for our mental health. ".... being proud is the most reliable source of happiness that I know."
A related thing occurs in academia for very niche topics on which only very few people are working. Perhaps nobody for most of the time. A paper might "reply" to another paper from years or decades ago, and receive itself a reply only years later, but from a different author.
The cool thing is that you can easily become the current world leading expert on such a niche topic, because there aren't that many papers. So it's easy to know every single one of them, and the few experts are spread out in time rather than space.
It's like a web forum thread on a very obscure question, where only every few years someone contributes a new comment, likely never to be read by most of the previous authors, but read by all that come later.