# How does math work [closed]

I'm currently learning about probability theory, and a sudden question popped into my mind: how does math work. To me it seems that math consists of a bunch of symbols, such as $x$, $y$, $\theta$, $1$, $2$ etc., and a bunch of rules for manipulating those symbols, such as the production rule and summation rule. Using those components as building blocks, people are creating more rules that can either make our life easier or reveal more insights into a problem, like the Bayes theorem for example.

But this way of thinking definitely cannot model all the components of math. For instance, how could I incorporate the definitions like variance, expectation and Gaussian distribution etc. into this framework, and how to account for the proofs which play a huge role in math.

So, my question is, is there any conceptual framework that can formally and comprehensively model how math works? Thanks!

## closed as unclear what you're asking by Jack M, GNUSupporter 8964民主女神 地下教會, José Carlos Santos, B. Mehta, ShaileshMay 4 '18 at 2:56

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• Study abstract algebra and the Peano axioms. That would be my suggestion. Others might have better ones. – Clarinetist May 3 '18 at 20:11
• Mathematics grew out of the necessity of measuring things and their relationships. In that sense, it is the science of measurement. – John Wayland Bales May 3 '18 at 20:16
• Formalism was a (meta-)mathematical philosophy which asked a bit of the same questions. Can we use symbols to capture and express all of mathematics? – mathreadler May 3 '18 at 20:17
• IMHO, since I am not a mathematician myself, you gave a possible description of how math works on the first paragraph, and I cannot see why the second paragraph would invalidate the first one. Of course, the development from building blocks is usually guided to a final result that the mathematician have already in mind, which is informed by their intuition and imagination. – toliveira May 3 '18 at 20:18
• Formalism and axiomatic system seem quite interesting. I'll take a look! – NoSegfault May 3 '18 at 20:24