One esteemed poster wrote in 2011:
Intuition says “Invention”. But how do we account for fractals such as the Mandelbrot set ? The set continues on into infinity, so no human can hold it in his head at once.
… no one, not even Benoit Mandelbrot himself […] had any real preconception of the set’s extraordinary richness. The Mandelbrot set was certainly no invention of any human mind. The set is just objectively there in the mathematics itself. If it has meaning to assign an actual existence to the Mandelbrot set, then that existence is not within our mind, for no one can fully comprehend the set’s endless variety and unlimited complication.
An alien civilization would come up with the same Mandelbrot set that we do, yet they probably wouldn’t create the plays of Shakespeare. [1] So the latter was created and the former discovered.
Unfortunately, I find the idea of a discovered mathematics to be imponderable as well. If math is discovered, then it has an existence independent of the human mind. Math has no mass: is it measurable? I find this topic rather confusing. Penrose tentatively posits a Platonic world of mathematics, which is a reasonable model though it’s metaphysically unsettling. Reverend Berkeley would have probably said that the Mandelbrot set is situated in the mind of God.The Reality of Fractals | Syntopia
So I say math was discovered and endorse this view…
Thudlow_Boink:
I think mathematical truths do exist, but they do not exist “in nature.”
I think some people are reluctant to saying that mathematics is discovered because of their philosophical commitment to materialism: the belief that only the material world can be said to exist or be discoverable.
…but I confess I struggle with the idea of non-material things existing outside of somebody’s mind. A good starting point for myself might involve a taxonomy of stuff that exists, eg., things made of matter, ideas of one person, shared ideas, viral ideas. Then work in math (various types?) and logic.