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by drilldrive 2674 days ago
Coming from a mathematics background, I personally do not care so much for the 'beauty' of mathematics, and am moreso interested in clarity of properly abstracting and insight to the resulting formal theory. I feel that physicists care more about such intuitive ideas than anybody else.

Regardless, you only can become lost in math if you have bad premises. Mathematics is a relative subject, abstracting the arbitrary of reality to axioms. And if the axioms do not hold, the theory is bunk. It will always be the case that more granularity is required in real-life situations. Mathematics is precise and sound; it's not gospel.
2 comments
mikorym 2674 days ago
> And if the axioms do not hold, the theory is bunk.

You assume the axioms hold. That is what an axiom is: an assumption.

> Mathematics is precise and sound; it's not gospel.

We do think that mathematics is precise. We don't really know if it is sound (unless I am missing something). For example, what is a set? It is not a "collection of things". Rather, it is an object in some mathematical setting.

The topic of whether mathematics is "correct" is something else. We can all go out and build a DIY logical machine from scratch and see for ourselves that the mathematics we use give the results that we expect. Applied mathematics in this sense concerns itself with mathematics that suitably describe real situations.

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drilldrive 2673 days ago
>We don't really know if [mathematics] is sound. My apologies, I was hoping to be concise. I meant to say that mathematics is sound relative to the assumptions, which is exactly correct. But if the assumptions do not hold in reality (and they never quite do), then the theory as a whole is slightly off. I mean to say that mathematics is never 'correct' with reference to reality, but of course is always 'correct' with reference to the axioms.
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speedplane 2674 days ago
> Coming from a mathematics background, I personally do not care so much for the 'beauty' of mathematics, and am moreso interested in clarity and insight.

Beauty is a subjective emotion, it's not so easy to quantify. You may not find mathamatics beautiful due to it's clarity and insight, but many others would precisely because of that.

And it's not just math. Beautiful paintings, architecture, legal arguments, religions, etc., are often believed to be beautiful because of the clarity and insight they provide as well.

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