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Makes me think it would be neat to have a list of old conjectures that have been proven/disproven in the past year or so. Surely such a thing already exists?
A lot of recent math discoveries seem to be geometrical: circle packing, infinitely tiling patterns, neighbor coloring theorem, ... I don't seem to see as much discoveries in other areas like number theory, calculus, algebra etc... Is this a bias of what gets covered on HN, or are this type of geometrical problems the currently most active field of mathematics?
All of those new discoveries involve running code. More people are learning to code, more libraries are being written, compute costs are going down. It’s hard to break ground on a “sit and think” problem, especially one that is approachable enough that it’s also understandable news when you solve it.
Assume that something is true, write code to generate cases, run it, plot the generated data, expect that the plots show that everything matches the assertion, notice it doesn't, disprove the thing previously considered true. Nice and elegant.
These are my favorite kinds of things to learn. Once seen, they can't be unseen and can upend how I think of the world in some domain D.
Assume that something is true, write code to generate cases, run it, plot the generated data, expect that the plots show that everything matches the assertion, notice it doesn't, disprove the thing previously considered true. Nice and elegant.
Now try that on this problem: https://en.wikipedia.org/wiki/Riemann_hypothesis
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Earlier quoted context omitted.
Now try that on this problem: https://en.wikipedia.org/wiki/Riemann_hypothesis
This one is true though.
I'm sure lots of mathematicians have open bets about that. I still remember my supervisor hoping for no Higgs "because then physics will be boring for the foreseeable future".