Start from this cool comparison of Mathematics and Physics by Richard Feynman. Physicists are always about the special case. Mathematicians are always about the general case. Physicists do reverse engineer the world; recreating the technologies, available in the Universe. Physicists even think beyond the Universe…
Continue with these ruminations about Mathematics by Stephen Wolfram – was mathematics invented or discovered. He thinks that the math is already there, we just need to get to those spaces.
Here are details on the Computing Theory of Everything, by Stephen Wolfram. Like Galileo Galilei invented the telescope to observe and discover the far space, Wolfram invented and invents tools to discover the math, all those spaces. It is not combinatoric mess, as the spaces could be shaped nicely, depending on the laws within. Look at this amazing Rule 30, look at this annoying Rule 184.
Think of forthcoming Quantum Computing, which is closer to what Feynman foresaw about machinery without mathematics (watch first video, from 6:00 to 7:30). Why we need an infinite computational power, based on mathematics & logic, to figure out what happens in the tiny place in space? Pretty modern supercomputer needs few hours to simulate 10^11 individual atoms, which is ~10^11 times smaller than the number of atoms in only 1 gram of iron (Fe)…
But about simulating the new worlds, at the level of individual atom. We could build a simulation, and it will go with mathematics. We just need to squeeze the computational power from the physical universe.
Are mathematics and physics converging?
PS. Everything above physics in understood. Chemistry deals at bigger sizes. And so on upwards to huge sizes… till the edge of the Universe, where we still don’t understand. But maybe the Math will help here?