It's elegant if all you're concerned with is whether a conjecture is true or false. Answered, move along!

But mathematics is not a collection of facts. Mathematics is the study of abstraction. And what do you learn from a single data point? What can you abstract from that?

That's why just being a counterexample isn't really interesting. There has to be more than "counterexample" for there to be something to abstract. Was it generated from an analysis of the problem? Can the counterexample be generalized to explore the problem further? Is the counterexample a surprise in a way that suggests something is missing from current understanding?

Being a counterexample doesn't mean that something isn't interesting to a mathematician. But it's also not the interesting part.

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ATMLOTTOBEER 15 hours ago | parent [-]

You’re smuggling in a frame here which isn’t obviously true: that mathematics is not just a collection of facts

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chowells 11 hours ago | parent [-]

You have a weird definition of "smuggling". I say it outright. Because I follow it up with a description of the actual practice of math: it's the study of abstraction. That's not a frame. That's just what math is.

	▲	im3w1l 4 hours ago \| parent [-]
		I think the nature of mathematics is an interesting question without one clean answer. To present a radically different view of mathematics: It's a game of string transformations, where the goal is to produce specific strings given a set of rules. The (syntactically valid) strings would correspond to statements, a producible string a theorem, and the production the proof.