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As someone not in the field of mathematics, I actually didn't realize there was such an emphasis on attempting to prove famous conjectures correct. I thought th

As someone not in the field of mathematics, I actually didn't realize there was such an emphasis on attempting to prove famous conjectures correct. I thought the famous conjectures were famous precisely because knowing the veracity of the conjecture (or independence with respect to some formal system) would be a monumental event in any case. I also assumed many mathematicians utilized the strategy of attempting to disprove something as a way to reveal the proof. Sort of like how the best chess players tend to spend most of their thinking time mentally challenging their planned move as opposed to novice chess players who tend to look for reasons confirming why their move will be a good one. Is this not the case?

feoren 2y ago
This article is one professor's mix of opinion and elementary introduction to the concept of conjecture, and IMO is quite rambling and inconsistent. Why are you generalizing this one random person's thoughts into a conclusion about mathematics as a discipline? Don't let one poor thinker (or perhaps merely poor writer) spoil it for you. The author seems to have completely missed the actual reason we find conjectures interesting: we're asking ourselves, "do we have the techniques to prove this kind of problem?" That's the fundamental reason disproving a conjecture is less celebrated than proving it, because disproving is often done by finding a single counterexample, which doesn't teach us much about our proof techniques -- unless, of course, the process of finding that counterexample was particularly new and interesting! The most interesting question to ponder with a conjecture is not "is this true?", but rather "why is this hard to prove?". The most boring answer to the latter is "oh, because it's false", while the most exciting answer is "because we were missing this fundamental idea that can spawn an entire new branch of mathematics." It's all about the journey, not the destination.

feoren 2y ago

This article is one professor's mix of opinion and elementary introduction to the concept of conjecture, and IMO is quite rambling and inconsistent. Why are you generalizing this one random person's thoughts into a conclusion about mathematics as a discipline? Don't let one poor thinker (or perhaps merely poor writer) spoil it for you. The author seems to have completely missed the actual reason we find conjectures interesting: we're asking ourselves, "do we have the techniques to prove this kind of problem?" That's the fundamental reason disproving a conjecture is less celebrated than proving it, because disproving is often done by finding a single counterexample, which doesn't teach us much about our proof techniques -- unless, of course, the process of finding that counterexample was particularly new and interesting! The most interesting question to ponder with a conjecture is not "is this true?", but rather "why is this hard to prove?". The most boring answer to the latter is "oh, because it's false", while the most exciting answer is "because we were missing this fundamental idea that can spawn an entire new branch of mathematics." It's all about the journey, not the destination.