Return to Answer

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. We are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree. Maybe I've seen so many infinite sums, products, and quotients that I've become desensitized to their wonder.

At the same time, it seems to me that any entity capable of creating the fabric of mathematics itself, would be more wondrous than the infinite quotient that started off this post. So either the quotient exists "just because," or the Demiurge exists "just because." Either way, it comes down to the axiom(s) you're will to accept.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. We are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree. Maybe I've seen so many infinite sums, products, and quotients that I've become desensitized to their wonder.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. We are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree. Maybe I've seen so many infinite sums, products, and quotients that I've become desensitized to their wonder.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. We are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree. Maybe I've seen so many infinite sums, products, and quotients that I've become desensitized to their wonder.

At the same time, it seems to me that any entity capable of creating the fabric of mathematics itself, would be more wondrous than the infinite quotient that started off this post. So either the quotient exists "just because," or the Demiurge exists "just because." Either way, it comes down to the axiom(s) you're will to accept.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. But we are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series

It depends on what axioms you are willing to accept.

First, it's curious you picked this particular expression as a basis for the question. There are oodles of infinite expressions leading to pi. See this mathworld.wolfram.com page or this page from Britannica.com. And those are just expressions for pi. There are infinite expressions for other fundamental quantities such as √2 and e. There are other, oft-cited examples of beauty in mathematics, such as the [Mandelbrot set][4], [fractals][5], and "[the most beautiful equation][6]" e^πi + 1 = 0. So I am curious why you plucked that particular equation for this post?

Second, what would such a proof look like? Maybe something like this:

1. The infinite expression for pi is both beautiful and complex and resolves to a fundamental quantity (pi).
2. Anything so beautiful and complex (yet resolving to a fundamental quantity) must be intentionally designed.
3. Therefore, the existence of the expression proves the existence of the Demiurge.

So, I'm sure you see where I'm going. If you are willing to accept #2 as an axiom (or you can prove it from other axioms) then you have a proof.

Whether anyone else accepts the proof will be up to them. You may get both kinds of responses on this site. You may ask, "What else could be responsible?" And you may get various answers from "no one knows" to "we haven't figured it all out yet" to "math is inherently beautiful" and "God made the integers, all the rest is the work of man." ([Leopold Kronecker][7]). Or "You look at something like that and wonder. What on Earth is pi doing there?"

Personally, I have to ask "Why are there so many infinite expressions leading to pi?" In my mind, that speaks to some attribute of pi or of recursive or [infinite processes][8] that I don't have the mathematical background to understand, rather than proof of a creator. We are lousy with infinite series for pi and other constants. Seems to me that a designer wouldn't have needed as many. But that's just what seems reasonable to me. Others will disagree. Maybe I've seen so many infinite sums, products, and quotients that I've become desensitized to their wonder.

[4]: https://en.wikipedia.org/wiki/Mandelbrot_set#:~:text=The%20Mandelbrot%20set%20(%2F%CB%88m,aesthetic%20appeal%20and%20fractal%20structures. [5]: https://science.howstuffworks.com/math-concepts/fractals.htm [6]: https://www.wabash.edu/magazine/2002/WinterSpring2002/mostbeautiful.html [7]: http://scihi.org/leopold-kronecker/ [8]: https://en.wikipedia.org/wiki/Fourier_series