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The idea that mathematics could contain inherent contradictions acquired much speculation and criticism as it put into question the fundamental system by which we interpret the world. In searching for mathematical proofs that are consistent and hold no contradictions, Hilbert tried different methods one of which involved using models, but this proved logically incomplete, "for even if all the observed facts are in agreement with the axioms, the possibility is open that a hitherto unobserved …

…this distinction between mathematics and meta-mathematics because one construct merely provides the tools for the other to operate with. However, there seems to be a limitless number of statements that can be said about mathematics, and it appears that the information content associated with meta-mathematics is unlimited. Meta-mathematics is used throughout the field of math as well as philosophy. The working assumption of meta-mathematics is that mathematical content can be captured in a formal system.