It is legitimately cool when a bunch of mathematicians get together in a room and say "Look at all the cool shapes and patterns we made," then show it to a physicist who goes all frantic and starts shouting "OMG! I understand how stuff works!"

Gotta love how the more "Applied" a field is, the more "Impure" it is.

There's a real gravity to that statement and it definitely adds up.

Because they are students? Both are high demand professions, I don't get it.

The way I see it, axioms and notation are made up but everything that follows is absolute truth

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.

They're made up constructs that reflect the absolute truth when applied correctly (from his perspective).

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.

Your a tool!

❤️

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.

Not as something we have access to but yeah!

All I know is that 1 = 0.9999…

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.

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.

Good thing physicists solved that problem already; if everything is made up and can only be observed through our preconceived notions and there's no way to prove a world beyond them, then it doesn't matter. The universe we can observe is reality and everything beyond that is beyond meaningful definition and is therefore useless, which is how we define "philosophy".

Universal. How else would you calculate or solve equations?

BURN THE HERETIC!

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.

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.

In social science, theory requires application. Otherwise, it's just a cool story, bro.

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