– what does it mean for a theory to be “proven” mathematically?
In: Mathematics
Unlike most things in our world, math is bound by its own rules. We call these basic rules axioms. This is different from most sciences, where we develop theories that describe what we have observed. These theories can change as the evidence changes. But in math, axioms don’t change. We decided on the basic rules and we can use them to solve problems.
A mathematical proof is a logical argument that uses these axioms to show that something else is true. These proofs can follow different approaches, but they all boil down to using the rules we have established to demonstrate something.
If you are familiar with the Pythagorean Theorem (a^2 + b^2 = c^2 for right triangle lengths), [here](https://www.cut-the-knot.org/pythagoras/index.shtml) are some proofs of it
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