I guess that the commentor meant that those kinds of thoughts don't get you jobs, and doesn't know how easy it is to get a job with a degree in either of those fields. Same for the upvoters.
Specifically, a language. It moves information from one place to another. It can reveal new information too, but that's more of a useful side effect imo.
Well, it depends on your definition of truth and it could be the absolute truth by definition. A theorem is absolutely true in the same way that "a bachelor is an unmarried man" is categorically true.
The test to know if anything is an absolute truth is if it is called an absolute truth. If it is called an absolute truth, then it isn't an absolute truth. If it isn't called an absolute truth, then it isn't an absolute truth. Absolute truths don't exist. If someone tells you something is an absolute truth, stop listening to them.
Theories can be a stepping stone to other theories. Until we explore those chains, we don't know if there is anything useful at the end.
E.g. initially, lasers were a solution looking for a problem. An interesting quirk possible due to some interesting bit of physics.
Maths explores idea spaces. Much of that is purely of interest to other mathematicians. However, it sometimes intersects with areas of interest to other scientists, at which point it becomes extremely useful.
But seriously though, yes, but useless isn't the same as pointless. Art by some definitions is useless, but it can still have a point, even if that point it just to be fun.
I agree. I'm pretty sure a bunch of stuff that Euler did was considered useless until it actually was used hundreds of years later. I'm pretty sure topology had a lot of people wondering what the hell to use it for until it was rediscovered multiple times.
Theory without application is often the entire point in certain academic circles and if someone comes along and finds a practical use for their mathematically based philosophical musings they delve deeper looking for the pureness
Models. Humans hold models of the world in their minds, math helps you understand and create more complex and consistent models. You always exist in a simulation of your own construction to make sense of the universe.
My feeling is that no model can ever fully capture a complete description of reality, the information isn't compressible to such a degree that approximations or abstractions can be lossless.
Most of what we consider to be invention is merely combinatoric novelty.
Math is definitely universal. The math behind things in science wouldn't suddenly change on different alien planets. Take things like V = IR. That relies on multiplication and division. It's gonna be the same on other planets. The units, notation, etc. will be different but the concepts would be the same.
I'm no STEM major, so I may be way off, but this is how I see it.
V = IR isn't math. It's a way of defining the relationship and outcome of two specific physical qualities. It says that we combine the resistance of a medium ( R) with the current flowing through it (I) into another joint emergent quality we call voltage (V). We do this because it makes our understanding of the physical world easier to manage since this relationship has helpful applications.
Math is simply patterns in the relationships of quantities. It excludes any physical units or qualities. In other words, math is the art of counting.
How we express math is particular to us, though it'd be commonly decipherable. Math is more and more globally standardized as more of it gets globally acknowledged as "the most useful" way to do math. E.g. place holder 0 vs Roman Numerals. Ratios are conceptually universal to any species that bothers measuring. Quantification maybe less so. Especially if their comprehension of advanced sciences/engineering is somehow intuitive instead of formally calculated.
If a space faring species has a concept of proportions/ratios, but not individual identity of numbers, presenting Meters as a portion of the speed of light might be a universal way discern the rest of our math. Water as Liters might be more accessible, depending on how they think of water.
Sets and Axioms are purely conceptually representative and so viable as long as they're capable of symbolic abstraction at all.