Proof

We know things in mathematics by proving them by applying accepted rules of inference to our premises to reach a conclusion.

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Certainty

Unlike science, mathematical proof is one of the few cases where we can ever be certain that something is true.

Mathematics

Proof is essential to all branches of mathematics. By proving things, mathematicians have built up all the knowledge about arithmetic, geometry, logic, sets, probability, ... that we have been relying on thoughout this course

Security

Proof is expected in some fields, like cryptography and safety-critical systems, where you need to be really sure that your algorithm does what you think it does.