Math-invention or discovery?

Originally Posted by Arainach

Basic Algebra and Calculus may be things we invented to explain the universe, but I'd love to hear how things such as non-euclidian geometry, imaginary numbers, and most of modern theoretical mathematics fit into the known Universe.

One way that complex numbers are used is in a physical system where there is dampening. A normal wave going through a medium will satisfy the wave equation. In the case where there is dampening on that wave the energy lost is determined by complex numbers. Hell any level of physics 300+ has you using complex numbers ALL the time.

As for non Euclidian geometry off the top of my head I'd say you can use that for orbits, specifically those of comets which either follow elleptical or parabolic orbits.

I'm sure some current mathematics don't have a physical meaning yet, but this is has always been the case. Number Theory was invented in the mid 1500s in Europe and can be traced back even further than that through the Greeks and other civilizations. Now? It's the basis for cryptology and computer encryption.

The question at hand is a very good one. On one hand you can say that Calculus was invented as the result of algebraic derivations, but on the other because it describes the behavior of practically any physical system humans only discovered the way in which the universe expresses itself.

I'd say that it can actually be both. For instance if some substance... say xyz hadn't been discovered yet, and some chemist synthesizes some in a lab through artificial processes. Now a week later archaeologists unearth a centuries old xyz deposit.

Did the scientist invent the xyz or did he discover it?

One way of thinking is that he did invent it because he came up with a substance that was thought to not yet have existed.

However how can you invent what already exists?

I think of math as human ingenuity discovering what the universe has already known.

Jam it back in, in the dark.