[tiffanyg]

The universe most certainly has a mysterious affinity with mathematics.

Is that really true?

Could it be more fair to say that mathematics has a (not so) mysterious affinity with the universe?

Specifically, where do our 'axioms' come from? Why did people spend centuries trying to prove the parallel postulate?

Partly, I'm being rhetorical, but, also, partly I'm really not. I would certainly not categorically dispute what you wrote, but I'd also not embrace it 'out-of-hand'.

... So, 'the floor is open', so-to-speak... if any have other perspectives on math-universe connection, rebuttals, etc. :)

[Salgat]

I think it's more just the fact that our universe seems to fit extremely rigid, unbreakable rules definable by math. If we lived in a simulation for example, you could have phenomena that "break" these rules at any given time.

[maxbond]

But wouldn't we just interpret that "break" as more rules for us to learn and study and build world models around? Why would we think "the simulation has broken" and not "physics is weird huh? Especially in edge cases like absurdly high energies or absurdly tiny scales."

(I don't think the universe is a simulation, to be clear.)

[Salgat]

In this case though there'd be nothing to learn, since math couldn't explain this phenomena.

[maxbond]

But that happens all the time in science, and we come up with different math that does explain it. Eg Jupiter's orbit couldn't be explained, the math didn't add up, so we came up with the idea that light had a speed and that Jupiter was far enough away that the speed impacted our calculations.

If you think about quantum mechanics, it's something that could sure look like a bug. Systems that you expect to be deterministic are stochastic if you look closely enough? If it were a program I was writing, I'd start wondering if there were rounding errors and/or concurrency issues. But we've come up with math to understand it.

Math is very general, I'm not sure there's a process that you couldn't describe with a complex enough mathematical system, and thereby conclude it had it's origins outside of our universe.

[Salgat]

The difference is that there's no possible model for this kind of hypothetical phenomena, it's by definition undefined behavior. Imagine a universe where the formula 𝜏=rF would just randomly be violated for no absolutely no reason, such as a person sometimes accidentally throwing a baseball that leaves the atmosphere, or a child accidentally lifting a house. Even the randomness of quantum mechanics can be explained using models that are very consistent and testable, but the only theory we could come up for this wouldn't be based in math, it'd be the equivalent to blaming it on magic, and no amount of advancement in science would ever come closer to explaining it.

[maxbond]

How do know the difference between a problem that cannot be solved with math, and a problem you haven't solved with math yet?

Let's say you throw a baseball into orbit. That's very strange, a profound mystery. You tell me that we must live in a simulation. I contend something strange happened which we don't understand, because we only have one datapoint, but that a satisfactory explanation does exist. How do you know I'm wrong?