1. The problem asks to explain the difference between a theorem and a proof. 2. A theorem is a statement that expresses a mathematical truth or fact. It is a claim that has been established based on previously known facts or axioms. 3. A proof is a logical sequence of statements and reasoning that demonstrates why the theorem is true. It provides the justification and evidence supporting the theorem. 4. Therefore, the correct understanding is: A theorem is a statement of mathematical truth, while a proof is the series of statements that support the theorem's claim. Final answer: A theorem is a statement of mathematical truth, while a proof is the series of statements that support the theorem's claim.