>>12782134Computing an answer is the activity of using established quantities / objects and relationships between those quantities / objects to come to a conclusion. Calculations can (and often do) rely on results given by proofs, and oftentimes they can help give intuition for new proofs.
Writing a mathematical proof is establishing new relationships among quantities / objects. You start with definitions, a collection of axioms, which are elementary statements about the definitions you consider true without proof, and a system of deduction which allows you prove things true.
