Is mathematics the language of the Universe?

[Measure_for_Measure]

@Smurfie

This is another face of the old Math debate…Do Mathematicians ‘discover’ new things or ‘invent’ new things.

Precisely.

@John_Mace

The question is: did the universe “invent” math in order to exist (pardon the anthropomorphizing), or did humans invent math in order to understand the universe? I’m not sure how you would prove this, but it seems intuitively obvious to me that it’s the latter.

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.

@Roger Penrose

… 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.
[1] Idea lifted from here: The Reality of Fractals | Syntopia