Input (grade 13): GÃ del's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems for mathematics.
Output (grade 10): GÃ del's incompleteness theorems is the name given to two theorems, proved by Kurt GÃ del in 1931. They are about limitations in all but the most trivial formal systems for arithmetic of mathematical interest.