Proof and evidence are related but distinct concepts in the fields of law, science, and mathematics.

Evidence refers to information or data that is presented in support of a claim or argument. Evidence can be circumstantial, testimonial, or physical, and its strength and reliability depend on a variety of factors, including the credibility of the source and the consistency of the information. Evidence is used to build a case or support a hypothesis, but it is not conclusive on its own.

Proof, on the other hand, is a higher standard of evidence that demonstrates the truth or validity of a claim with certainty. Proof can be mathematical, logical, or scientific, and it requires a rigorous process of testing and validation. In a mathematical proof, for example, a set of premises and reasoning are used to deduce a conclusion that is considered to be incontrovertibly true. In a legal context, proof beyond a reasonable doubt is the standard of evidence required to convict someone of a crime.

TL;DR - evidence is information that supports a claim, while proof is the highest standard of evidence that establishes the truth of a claim beyond a reasonable doubt.