Gödel’s Incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic.

The first incompleteness theorem: No consistent formal system capable of modelling basic arithmetic can be used to prove all truths about arithmetic.

In other words, no matter how complex a system of mathematics is, there will always be some statements about numbers that cannot be proved or disproved within the system.