Apologies in advance for nitpicking, but the heuristic is to ask what are the real-world consequences of propositions in this discipline being right or wrong, not whether the discipline has real-world consequences. So what are the propositions of mathematics that can be right or wrong? Clearly a published theorem can be right or wrong, but most are correct. What can be right or wrong is what areas of pure mathematics people consider to be interesting. I would say that these propositions can be right or wrong, and do have “real world” consequences. People used to think graph theory was not interesting—they were wrong.
I’m not sure interestingness is really the focus of the issue. I’m sure feminist post-structuralist discourse analyses of the recent banking crisis are very interesting to people interested in the subject, but I still don’t think it has any power to deduce true facts about the universe.
I do have another heuristic which is a little less straightforward to apply, but a little more selective: would a society of humans kept isolated from our own for thousands of years develop a similar discipline with the same essential elements as our version? Pure maths definitely passes that one, while something like Jungian analysis probably wouldn’t.
Apologies in advance for nitpicking, but the heuristic is to ask what are the real-world consequences of propositions in this discipline being right or wrong, not whether the discipline has real-world consequences. So what are the propositions of mathematics that can be right or wrong? Clearly a published theorem can be right or wrong, but most are correct. What can be right or wrong is what areas of pure mathematics people consider to be interesting. I would say that these propositions can be right or wrong, and do have “real world” consequences. People used to think graph theory was not interesting—they were wrong.
I’m not sure interestingness is really the focus of the issue. I’m sure feminist post-structuralist discourse analyses of the recent banking crisis are very interesting to people interested in the subject, but I still don’t think it has any power to deduce true facts about the universe.
I do have another heuristic which is a little less straightforward to apply, but a little more selective: would a society of humans kept isolated from our own for thousands of years develop a similar discipline with the same essential elements as our version? Pure maths definitely passes that one, while something like Jungian analysis probably wouldn’t.