Addition and multiplication (i.e. arithmetic) over the integers are all that are necessary to express first order logic and allowed Gödel to express his incompl

Addition and multiplication (i.e. arithmetic) over the integers are all that are necessary to express first order logic and allowed Gödel to express his incompleteness theorems at such a fundamental level. The logical power of arithmetic is likely why many seemingly simple questions about arithmetic can have very complicated answers or no definitive answers at all.