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Well, nobody said exactly what they meant by 'science', so there are indeed many ways to interpret that statement. I was referring to education, news reporting

Well, nobody said exactly what they meant by 'science', so there are indeed many ways to interpret that statement. I was referring to education, news reporting on paper, etc. This the main subject of the article, for which there is little difference between mathematics and other sciences. Even then, I don't think there are many mathematicians in the world who can claim they are paid to do pure mathematics without any connection to other sciences. Probability, modeling of some phenomena, programming are always supposed to be the final purposes. These different approaches are in competition with regards to grants, and thus need to argue how one or the other is better suited to tackle the real-world problems. For example in logic research, there are arguments between the two big camps of program certification and program verification; those ultimately rely on feasibility in terms of programmer training, financial cost, computational complexity. The camps have very different views and can use fundamentally different mathematical foundations. A great illustration is the HoTT project, often discussed on here.

Tainnor 4y ago
I mean, yes, you're right that many people just parrot whatever they learned in high school even in the case of maths (somehow it's surprisingly easy to get people on Facebook to argue about whether square roots of negative numbers exist). And if I interpret your second paragraph correctly that's more about the fact that deciding which research programs are getting grants is not a very "scientific" (or logical) matter but has a lot to do with how humans behave on a societal level. That's certainly true, although I'm not sure how to solve that. Nobody thought that we'd have any use for number theory for millenia and now cryptography is everywhere. Mathematics still has the unique property that it is, in principle, independently verifiable by anyone, even by a (relatively dumb) computer. The validity of results is rarely in question (Mochizuki notwithstanding), and if there are disagreements, they are mostly philosophical or concern the question of whether or not we should accept certain axioms. But I don't consider the latter a problem - working with different sets of axioms makes mathematics richer, not poorer.

Tainnor 4y ago

I mean, yes, you're right that many people just parrot whatever they learned in high school even in the case of maths (somehow it's surprisingly easy to get people on Facebook to argue about whether square roots of negative numbers exist). And if I interpret your second paragraph correctly that's more about the fact that deciding which research programs are getting grants is not a very "scientific" (or logical) matter but has a lot to do with how humans behave on a societal level. That's certainly true, although I'm not sure how to solve that. Nobody thought that we'd have any use for number theory for millenia and now cryptography is everywhere. Mathematics still has the unique property that it is, in principle, independently verifiable by anyone, even by a (relatively dumb) computer. The validity of results is rarely in question (Mochizuki notwithstanding), and if there are disagreements, they are mostly philosophical or concern the question of whether or not we should accept certain axioms. But I don't consider the latter a problem - working with different sets of axioms makes mathematics richer, not poorer.