Math and science are built upon axioms. Very simply, an axiom is something that is always true and assumed to be true. An example is the reflexive property in algebra. A number is always equal to itself. Axioms are the building blocks, from which new truths are discovered. A proof is an inferential argument for a mathematical statement, using other previously established statements. That means a proof can be traced back to the original, assumed truths, those axioms that are the foundation of mathematics.
This is how we accumulate knowledge about the physical world over generations. The proofs based on those building blocks are eventually incorporated into the building blocks of math. The theorems and proofs multiply, slowly building up the stock of things that are known to be true. Calculus was built upon algebra and physics was built upon calculus and so on. It why a student can quickly go from zero to trying to discover new truths about the world. They inherit a supply of things assumed to be true.
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