[wolfkill]

As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.

[empath75]

The roots of mathematics in the west are fairly inextricably tied up with the development of religion via Pythagoras and especially Plato. Plato (or at least Platonists) taught, for example that God literally was One -- as in the number 1. And that all of reality is the result of successive emanations from 1 -- to the dyad (2), then the rest of the numbers, on through geometry and so on. Those beliefs influenced the philosophical development of all the major monotheistic religions.

[yters]

Math was one of Plato's main methods of showing there was a reality beyond the physical world that we could access with our minds.

[User23]

It logically follows that any faith that believes God to be a unitary creator is going to attribute math to Him.

Your absolutely correct observation about gaps notwithstanding, the driving question for me here is this: why does math work so well? I personally exclude any explanation that doesn't involve the Logos in some form as incoherent, but I don't have a specific answer and probably never will.

[placebo]

I'm also very interested in this question. My current understanding is that mathematics only works well because the mind is only capable of conceiving a mathematical reality, i.e math is basically the end result of an evolved mind, a tool that divides experience to concepts (including objects, properties, relationships) which at first approximation don't change with time (a lion will remain a lion, a lion will remain dangerous). Later, higher level observations that are constant are also observed (e.g location that linearly changes with time is a constant speed, every triangle on a plain has 180 degrees etc.) - my point is that the mind is geared to find relationships that are constant (in every level of abstraction), and once we find such a constant we call it "truth" (or if we're more honest, we at least admit it's a good model). So I think the bigger question is not why mathematics works (it works because reality, including thought itself, can be seen through the filter of concepts that appear to be self consistent), but rather why reality lends itself to being categorized in the first place into "things" that have internal integrity and consistency.

[Retra]

Math works so well because we consistently abandon any math that doesn't work well.

[hyperpallium]

And where the math of reality seems ugly or awkward or contrived, we invent notation to make it look neat and simple.

The reason why math education takes so many years is to learn all the complexity, conventions and abuse of notation. As in speech and image interpretation, the adept cannot see the complexity.

You can make anything simple by inventing a language to state it in. Use custom entities instead of multiplying them.

[wolfkill]

I'm not convinced this does logically follow. There is a view point that God is the source of math only in the sense that God created humanity with the limited capacity for understanding the world around them and one way this capacity has manifested is through the development of Mathematics.

Why does math work so well? Well math is pretty great but I don't think it is magical. There have been thousands of years of slow mathematical advances to get us to where we are now.

[aphextron]

>why does math work so well?

This question really really bothers me. Why can I completely describe gravitational attraction (at certain distances) by just solving for f=g(m1*m2)/r^2? It's truly disturbing when you start appreciating this for the first time.

[Koshkin]

It must have been just as disturbing for the ancients to see how one could count the sheep using a sack full of pebbles. (We, modern people, are too used to the wonders given to us by the - quite abstract, in fact - notion of a number and never question our faith in the applicability of arithmetical operations to the real world.)

[Retra]

You can hear a band play music from a radio, even though there is no band inside your radio. How? Because electrons in a wire will slosh back and forth in near synchronous response to electrons in a different wire far away. We live in an interactive world where the fact that correlations can occur in matter interactions means that communication is possible.

And the ability to count sheep by counting pebbles is just a generalization of the same principles. One antenna can move in sync with another, without literally being the 'same' antenna. This is indirection or abstraction, depending on how you want to slice it.

The point being, there is no question of why arithmetical operations apply to the real world. The real world permits an infinite variety of valid and useful abstractions. I'd wager it is impossible to imagine a reality where this weren't the case.

[taoistextremist]

What kind of gaps do you mean? As someone who studies mathematics, I feel like this is a vague criticism I've seen some make without any concrete justification.

[wolfkill]

I work in applied mathematics and specifically in CFD. This may make me not a "true mathematician" to some of the mathematical community. In fluid dynamics nearly everything is an approximate solution to an imperfect model. In fact, there are whole branches of mathematics dealing with trying to figure out exactly how imperfect models are. "Perfect math" has limited applicability, and only perfectly reflects reality in contrived situations. For example, linear algebra works amazingly well in the contrived environment of a computer, but if you want to perfectly model the electron flow that is involved in that computation one must necessarily use an imperfect approximation.

[taoistextremist]

That's a problem with the model, though, not math itself. People who attribute divinity to mathematics aren't considering these types of things as its the application of math into another field, not an intrinsic truth within the field of mathematics.

[wolfkill]

I'm not convinced that such an intrinsic truth exists apart from application.

[taoistextremist]

That's a different take on mathematics than many people I've met who study it. For me, mathematics is an extension of philosophy, geared towards finding intrinsic truth in a quantitative domain, and it just happens to have applications.

[paganel]

Not the OP, and he/she mentioned "physical observations" so maybe he/she was only referencing hard sciences like Chemistry or, indeed, Physics, but I am of the same opinion to him/her when it comes to the gap between mathematics and social (for a lack of better word) sciences, which social sciences (and the underlying social component behind them, i.e., us, humans) play a very important role in, well, how the Universe runs, or is seen as running.

In other words, mathematics is very bad at modeling and explaining human behavior, be it in economics, history or even political science (even though one of the best political scientists that ever was, Hobbes, wrote his most famous book by trying to imitate Euclid's "Elements"). This is starting to become particularly important now because we try to build some "AI" functionalities that should imitate humans (and even surpass them) based mostly on mathematics (and some underlying data), but it is my opinion that because of this "gap" between how humans are and what mathematics can tell us about how humans are and behave, it is my opinion I say that those "AI" functionalities will never "become" human enough. Stanislaw Lem's "The Cyberiad" does a much better job compared to me at showing this gap between humans and "machines built on mathematics".

[taoistextremist]

In my opinion this is less of a gap and more of a misapplication of what mathematics is. Mathematics isn't a tool for describing human behavior, though social sciences may use results of mathematics (and I would argue to much greater accuracy than they'd otherwise have) and the fact that mathematics can't describe human behavior is not due to gaps (results of mathematics are consistent with reality, as far as I'm concerned) but because we aren't answering questions in the domain of mathematics.

The physical observations, though, I'm still waiting on an answer from OP about that. It's fairly weasely to say something like that with no example.

[paganel]

> but because we aren't answering questions in the domain of mathematics.

And then one can ask “what is the domain of mathematics?” or even “does mathematics have a domain?”, questions which lead us into a “philosophy of science” discussion with no end in sight.

I’ve felt for quite some time that the fact that mathematics can model/answer some aspects related to physical reality is just a happy coincidence at best, which we shouldn’t insist too much upon, for fear of then risking to miss the forest because of some trees that absorb our view, like “isn’t this mathematical equation perfectly describing how galaxies interact billions of light-years away?” might obstruct from us the very dire truth that there is no math to describe what will be my cat’s movings around the room in the next 5 minutes (and it’s not for lack of trying, just look at the billions of dollars invested by hedge-funds into mathematics so that they could “model”/predict the future; I don’t think they’re scientifically anywhere close to that).

[taoistextremist]

> And then one can ask “what is the domain of mathematics?” or even “does mathematics have a domain?”, questions which lead us into a “philosophy of science” discussion with no end in sight.

I think these are useful conversations even if we can't foresee them ending. It's what's helped us move physics beyond stuff like Newtonian mechanics where we expect things to line up with these nice equations, and apply math in a more appropriate fashion to our observations. i.e. We treat math as something we apply to our observations, and reconsider models as we run into problems, as opposed to demanding our observations line up with our initial model.

[Torwald]

> Can you elaborate on how Hobbes tried to imitate Euclid's "Elements?"

Please!

[Torwald]

Can you elaborate on how Hobbes tried to imitate Euclid's "Elements?"

[Koshkin]

So, are the natural numbers human? (Kronecker would famously disagree: Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.)

[pvg]

I don't think Erdős seriously, let alone literally, attributed the proofs in question to god in the sense you seem to be interpreting it in.

[wolfkill]

Fair point!