I keep on thinking that everything around us is basically just information. Be it DNA, atoms, or spacetime itself. And math is the set of rules that explain the interaction, flow and existence of this information. We did not uncover all the rules yet. Does this make sense?
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> can math be though of as a set of rules that describe everything that exist?
Not really, if nothing else because of the fact that maths also describes things that *don’t* exist.
Maths is the creative exploration of patterns and rules.
It has useful applications to the real world (which seems to run on maths) but is far broader. It is about playing around with rules to see what patterns emerge.
Not really ELI5, but you should check out Max Tegmark’s, Our Mathematical Universe.
In it he argues that the universe is mathematical structure and everything within is mathematics. It’s a very interesting book.
We define math. We have tried our best to alter, replace or throw out the definitions we made over time in an attempt to define math into something without contradictions, and with as much generality as possible (meaning that math does not only apply in certain scenarios, it applies as widely as possible).
In doing so, we have created something that is, quote: “unreasonably effective at describing the natural world.” Physics seeks to find the set of rules that describes everything that exists. It uses math as the language to write these rules. But that doesn’t mean math is the set of rules. I think that’s the best analogy I’ve heard. Math is a language. It’s a very precise language, unlike most others. And we can write statements in that language. Those statements may be true or false just like any other language. The rules of the universe may or may not be withing humans’ grasp, but the most effective language we have to write those rules is math.
Maths is sort of just studying sets of rules in general. Some sets of rules are useful for describing the real world, others aren’t. The “useful” ones, when applied, are basically the foundations of what we call theoretical physics.
This is an important distinction: Physics is science, maths isn’t. Physics studies the real world and lets you predict what happens and you can build experiments around statements in physics (experimentation is one of the key defining features of science). Maths is “just” one of the tools physicists use to describe the world.
Also, it’s important to note that this is a matter of _describing_ the real world. Some descriptions are better than others. E.g. Newton’s description of motion is less sophisticated than Einstein’s. This doesn’t mean that Newton’s is “wrong” or useless, just that it’s not accurate in extreme circumstances. Einstein’s way of describing motion (relativity) is much more sophisticated and can handle star-sized objects moving at nearly the speed of light, but it’s much more cumbersome, and not meaningfully more accurate, for describing day-to-day stuff on Earth.
I would say what you are describing is essentially number theory. This is a part of math which deals with sets and what that means. If you have ever heard of the real numbers or the complex number, those can be thought of as number sets, for example. But the great thing about sets, is that most things in this universe can be described using sets, including knowledge and stuff in our mind. It is a very interesting field of study that can provide a solid foundation for understanding our universe.
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