[wongarsu]

Academic math is a bit like basic research. You come up with funny ways to look at numbers or prove weird statements about this thing you came up with and call a "group", and a couple years or decades or centuries later it turns out that this solves real problems in electrical engineering or biology

Or it ends up never becoming useful. But you can't know that in advance

[tsunamifury]

Disagree, basic research, no matter how dull, is an observation of a measured reality. Math Theory are patterns of abstraction that may never be useful at all or representative of reality.

[lioeters]

> may never be useful at all

Nobody is qualified to judge the usefulness of mathematical, scientific, artistic, or any other kind of research that people choose to dedicate their time doing. And the world is better for it.

> or representative of reality

This so-called "reality" you speak of is some arbitrary representation in your head. It's your theory and patterns of abstraction, as you call it. Who knows how far or close you are to "objective" reality, whose existence we can only know through representations and abstractions. Mathematics and logic are some of the best tools we have of getting closer to that truth and understanding. All the sciences and even some of the arts are based on it.

[tsunamifury]

This is nonsense. Its the shared based case we can all test against, the things you think are the abstraction.

So wildly goofy train of thought here.

[card_zero]

I agree that rigorous logic shouldn't be assumed to get us closer to Ultimate Objective Truth than other forms of reasoning. It just gets us whatever peculiar oddments we can discover through rigorous logic, so far, here in our local, parochial patch of reality. Things that seem crucial powerful theories (theorems, whatever) to us here and now may not seem that way in the future, and arriving at them through logic doesn't provide a royal road to the Ultimate.

This means abstract mathematics is rooted in our current cultural concerns. I guess I'm saying that it isn't really useful or really abstract, but I also agree with the other poster that people can and should do what they like.

[fn-mote]

Parent seems to conflate “abstract” with “useless”. This comment addresses the “abstract” part only.

> Math Theory are patterns of abstraction that may never be useful at all or representative of reality.

This is a complete misunderstanding of (good) mathematical research.

The results look abstract, but they are based on concepts that are real and have truth or falsehood.

One example that comes to mind (sorry, technical): is it possible that all maps from a high dimensional sphere to a three dimensional sphere (S^2) might form a group that is not even finitely generated?

This is not just “abstract nonsense”, but understanding any of this takes effort.

[tsunamifury]

Abstraction is useless until its proves use in test against a base case of reality.

its the defition of useless most of the time.

[lyu07282]

“May never be useful“? You make it sound as if there aren't countless examples of those "abstractions" of theory/pure math turning out to be useful in all kinds of fields in the past. This feels like the more general anti-science argument of 90% of science is useless and never produces practical applications, the point people never understand is that nobody knows which 10% it's going to be so you have to do the 100% to get to the 10%.