In

**mathematics**, a**proof**is a deductive argument for a**mathematical**statement. In the argument, other previously established statements, such as theorems,**can**be used. In principle, a**proof can**be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.Herein, what is the definition of formal proof?

A

**formal proof**or derivation is a finite sequence of sentences (called well-formed formulas in the case of a**formal**language) each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a**formal**system.What is a proof in geometry?

A

**geometric proof**involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a**geometric**statement.Why is proof in mathematics important?

All mathematicians in the study considered

**proofs**valuable for students because they offer students new methods,**important**concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.