– what does it mean for a theory to be “proven” mathematically?
In: Mathematics
Depends on what you mean by “theory” (as in, what a scientist means, or what is commonly called a theory). And what you mean “mathematically” (like, that the result of an equation is proof?). This is a really vague question.
In physical sciences, you cannot really prove anything mathematically, you prove with data that your math describes reality. Of course that data will be likely analysed with maths too, especially statistics. But at the end of the day the data is the proof, not the math. So you don’t really prove theories mathematically, but math is involved.
Math itself doesn’t have “theories” as such (unless you mean theorems, which is a term), but here the proof is one of logic. What you’re proving is that the result you’re proposing is a direct consequence of applying the rules of math to some initial statement. I.e. You propose some initial assumption, apply previously proven math to it and show that either your result has to be true or (because some things can’t be proven true directly) there is a contradiction in maths itself if your initial statement isn’t true/false (depending what you’re proving). If you can show that “if A is true then B is true” or “if A is true/false then math breaks”, you have proven something in math.
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