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customguyyesterday at 11:58 PM0 repliesview on HN

I've been positively surprised by the result of a (overly?) thorough description, but at least to me as a math layman, this conjecture stuff is less impressive to me than a to-do app. Aren't they basically educated guesses that nobody put any real weight on, anyway? Asked differently, what does a disproven conjecture such as this change in the world that couldn't have been achieved by "Interesting idea, but you're just guessing, so let's circle back to this when you're not"? What does a disproven conjecture gain us that couldn't have been gotten more cheaply by not making it in the first place?