Expert mathematicians may not be able to explain how they find a proof of a difficult mathematical statement, but once a correct proof is found, it can be, with sufficient work, be formalized (most mathematicians don't do this part). This formal proof can be mechanicaly checked, without any creativity, step-by-step according to the axioms and inference rules of a mathematical logic.
Up to the limits of the Goedels incompletness theorem.
Dependenting on the used notation the formal proof can be very long. For example, Principia Mathematica took about 300 pages to prove that 1 + 1 = 2.
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Expert mathematicians may not be able to explain how they find a proof of a difficult mathematical statement, but once a correct proof is found, it can be, with sufficient work, be formalized (most mathematicians don't do this part). This formal proof can be mechanicaly checked, without any creativity, step-by-step according to the axioms and inference rules of a mathematical logic.
Up to the limits of the Goedels incompletness theorem.
Dependenting on the used notation the formal proof can be very long. For example, Principia Mathematica took about 300 pages to prove that 1 + 1 = 2.
https://commonplacefacts.com/2022/07/27/principia-mathematic...