Math is merely a different teleology, a top-down knowledge structure that begins with axioms. It is non-scientific by definition.

By contrast, science is bottom-up--a continuing process of experimentation and analysis. Although scientists have varying beliefs, scientific literature normally makes starting assumptions only insofar as they are helpful to the process--like the (unproven but very helpful) assumption that physical processes obey consistent physical laws that don't change between experiments, or mathematical axioms and their resulting knowledge/methods. But all knowledge obtained scientifically should be held lightly and remain subject to falsification by further experimentation.

There's nothing wrong with top-down knowledge structures built on a set of starting assumptions, as long as we don't "catch" worldviews like the cold without subjecting them to truth tests like correspondence to reality and internal consistency.

Math is an invented tool. It controls nothing.

I wouldn't say math was invented. One thing plus another thing has always been two things, even before we existed to give names to that concept. The names, symbols, etc were invented but the language of mathematics is just how we describe what has always existed.

One thing and another thing just exist. They don't perform abstract operations on one another. They may engage in physical interaction but that behavior is only modeled by mathematics. There is nothing to do a "plus" without man to account for it. It is not an inherent attribute of the universe.

The Pythagoreans believed the underlying substance of the universe was not water, air or fire but math. It is, I'd argue, the modern world view.

The key difference between hydrogen and helium, for instance, seems to be a matter of number.

So does Max Tegmark [0], who believes the multi-verse is literally made of math, but I wouldn't say that's the modern world view. Most believe that math is our best tool for understanding reality, but that reality maintains an independent existence.

[0] https://en.wikipedia.org/wiki/Our_Mathematical_Universe

Math, maybe, is invented.

But wouldn't you say that arithmetic, geometry and harmonics are intrinsic properties of every universe?

The discovery of these properties seems to produce almost magical effects in our world. As it would for every intelligent society discovering these properties.

Math is built of analogues to preexisting patterns. The symbols may be invented, but the concepts are discovered.

If math is invented, then why are some answers right and some answers wrong?

Same reason that while DnD is an invented game, some actions are allowed while others are not. To be coherent, a system (invented or not) must remain consistent within itself.

In math, a wrong answer isn't so much "wrong" as it is inconsistent with established mathematical properties/rules.

So it sounds like some aspects are not invented.

As a knowledge structure (axioms and theorems), math is absolutely invented.

The fact that it often corresponds to our experience of reality is a consequence of thousands of years of refinement with the goal of making it describe reality as closely as possible while remaining internally consistent.

But that doesn't make it any less invented... just a very helpful tool for modeling reality.

It seems you are confusing the mathematical language with the concepts themselves.

You’re stretching my thinking — thanks for that. It can be hard to delineate the difference between the properties of reality itself and a knowledge structure, built by people, that undeniably corresponds very closely to reality and is internally consistent — the two tests for truth.

I think we can both agree that reality (the physical universe) is well-ordered, self-consistent, and eminently logical in its operation. (Side note: my own belief is that it exhibits these qualities because it reflects the character of its Creator.)

And yes, it obeys certain concepts with absolute constancy - which we have worked to discover and which our mathematical language describes.

But I still maintain that the math and physics knowledge we have is at best limited and at worst an incomplete set of poor approximations. Because they cannot (and I maintain they won’t ever) account for everything we observe, or answer every question we have about the universe, and because its axioms have led to all sorts of abstract structures that have no relation at all to anything ever observed, I still think it’s fair to call math “invented”.

That being said, the real concepts we attempt to grasp in what we observe of the universe are clearly vastly superior to our comparatively small efforts to understand and model them.

Because we invented it specifically to establish a system in which some answers were right (those which could be proven given a set of axioms and a set of legal reasoning techniques) and some were wrong. Why would it being invented affect whether it could have right and wrong answers?

Languages are "invented" too, but we can still use them to approximately describe reality.

Things are true in math if we can follow the rules to derive the truth from axioms. That knowledge may then describe or predict something which should hold true in reality, which is tested via experiments.