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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

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 9y ago
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 9y ago
  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 9y ago
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 9y ago
  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.
- aphextron 9y ago
  >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 9y ago
    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 9y ago
      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.
- Retra 9y ago
  Math works so well because we consistently abandon any math that doesn't work well.
  - hyperpallium 9y ago
    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 9y ago
  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.
taoistextremist 9y ago
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.
- paganel 9y ago
  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 9y ago
    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.
Koshkin 9y ago
So, are the natural numbers human? (Kronecker would famously disagree: Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.)
pvg 9y ago
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 9y ago
  Fair point!

empath75 9y ago

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 9y ago
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 9y ago

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 9y ago
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.
aphextron 9y ago
>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 9y ago
  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 9y ago
    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.
Retra 9y ago
Math works so well because we consistently abandon any math that doesn't work well.
- hyperpallium 9y ago
  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 9y ago
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.

taoistextremist 9y ago

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.

paganel 9y ago
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 9y ago
  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.

Koshkin 9y ago

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

pvg 9y ago

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 9y ago
Fair point!