All math is just a system of ideas, specifically rules that people made up and follow because it's useful.
I'm so used to thinking this way that I don't understand what all the fuss is about, mathematical objects being "real". Ideas are real but they're not real in the way that rocks are.
Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But this just creates another mystery: what is the relationship between the material and the immaterial realm? What governs that? (Calling one or more of the immaterial entities "God" doesn't really make it any less mysterious.)
If we add entities to our model of reality to answer questions and all it does is create more and more esoteric questions, we should take some advice from Occam's Shovel: when you're in a hole, stop digging.
unless you're a mathematician
then maths is really THE absolute best description available of language and nature.
but non-mathematical minds will simply wonder and be amazed at how "maths explains the world", a clear indication that somebody is not thinking like a mathematician.
> Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But this just creates another mystery: what is the relationship between the material and the immaterial realm?
the relationship between the material and the immaterial pattern beholden by some mind can only be governed by the brain (hardware) wherein said mind stores its knowledge. is that conscious agency "God"? the answer depends on your personally held theological beliefs. I call that agent "me" and understand that "me" is variable, replaceable by "you" or "them" or whomever...
oh, and I love (this kind of figurative) digging. but I use my hands no shovels.
> unless you're a mathematician
As a young math researcher, my mentor definitely did not believe that Math was the absolute descriptor of the universe.
You can definitely imagine a scenario where the world does not operate perfectly mathematically correct though Math still exists - as an abstract separate entity.
You can do this such that everytime you recognize a new quirk in the world, then you can invent some new math/logical framework to match/approximate the current understanding. I don't know if this is the reality of this world, but when you look at things like complexity theory you have to wonder "okay... maybe we designed a useful system rather than discovering a true law of reality"
At one point, many people would have said that quantum field randomness is non-mathe
I am a published PhD in mathematics.
You're doing the exact thing that makes up what the fuss is about: arguing over what is "real" without defining what "real" means.
Let's all take a minute to ask ourselves what we mean by "real" every time we use that word. It may be that everyone's talking about a different thing.
Praised be therefore William of Ockham.
entia non sunt muliplicanda praeter necessitatem.
Thou shalt not multiply entities beyond necessity.
https://en.wikipedia.org/wiki/William_of_Ockham
Ideas are real in the way rocks are if we are concerned with their informational being. They are real informationally - ideas and math participate in forming the world. Nowadays, LLMs, Search and other apps probably affect the world even more than any common rock. Which is more real?
I don't know what is meant by the informational being of a rock.
one way to think about rock is to acknowledge it as an informational entity. an entity which is likely more passive then lets say a human or an app, yet by simply being part of the environment, it changes what can be done in the environment. if it wasn't there and if it didn't had a certain shape, the opportunities of other actors in the environment would surely be different. after all rock can be used as a tool and even as a computer. if its still not intuitive, think about Aeolian Harp which is a passive statue, yet a musical instrument, or think how you could encode a perceptron or a simple neural net into a stone (through which a water or air would flow for example). now, even if any ordinary rock doesn't exactly encode neural net, it should be more clear that it still affects information flow. does it help?
The real question is whether 1 + 1 = 2 is true independent of us recognizing it. If the answer is no, then math really is just a system of ideas, and you’ve slipped into psychologism, where truth depends on minds.
But take one thing and then another: you have two things. That’s true whether or not anyone notices. Some mathematics is a human system of ideas, but some of it isn’t. Arithmetic reflects real patterns in the world. Logic, too, is not merely invention, it formalizes cause and effect. Numbers, in the Pythagorean sense, aren’t just marks on paper or symbols of order; they are the order inherent in reality, the ratios and structures through which the world exists at all.
At bottom, this debate is about the logos: what makes the universe intelligible at all, and why it isn’t simply chaos. When people say “math is real,” they mean it in the Platonic sense, not that numbers are rocks, but that they belong to the intelligible structure underlying reality.
God enters the picture not as a bolt-on explanation, but as the consequence of taking mathematical order seriously. If numbers and geometry are woven into reality itself, then the question isn’t whether math is real, it’s why the universe is structured so that it can be read mathematically at all. Call that intelligible ground the logos, or call it God; either way, it’s not an extra mystery but the recognition that reason and order are built into the world.
Calling math “just useful” misses the point. Why is the universe so cooperative with our inventions in the first place? The deeper issue is the logos: that the world is intelligible rather than chaos. That’s what people mean when they say math is real, not that numbers are physical things, but that the order they reveal is woven into reality itself.
> But take one thing and then another: you have two things. That’s true whether or not anyone notices.
You cannot justify this statement without equally justifying my position.
Say you conceive of a counterfactual world without any humans in it. You know that within this world there could be a rock and another rock, you understand that this would be two rocks, and so you are reassured that one and one is two, even though no one is watching within this counterfactual world.
All of this happened in your mind. All along, you were the observer of the supposedly unobserved world you conceived of.
You are the unavoidable human observer of any counterfactual world you conceive of. You intend the world to have no human observers, but your intention fails. It is impossible. The properties of a truly unobserved world are unknowable to you.
This is why the Enlightenment left Platonism behind centuries ago. We can't say what the world would be without us, because any attempt is not only constructed within the mind, but also contemplated and observed through the mind. You can't escape projecting your systems of ideas onto everything you think about.
Once this is taken into account, Platonism has no explanatory power and is nothing more than superfluous metaphysical mystification.
> But take one thing and then another: you have two things.
This isn't true in general, because for example you can take two equal volumes of a material and put them together, you will have less than two times the volume because of gravity. The mathematical statement that 1+1=2 follows by definition, and it's useful in applications only when the conditions are met that make it accurate, or accurate enough for the given purposes.
Mathematics is useful because the physical world exhibits regularities in its structure. Talking about logos or God adds an air of mystery to that but I don't know what more it adds