Metamathematics

Metamathematicsmathematics usedstudy mathematics. It was originally differentiated from ordinary mathematics in19th centuryfocus on what was then calledfoundations problemmathematics.

Important branches include proof theory, model theory,mathematical logic. The original meaningDavid Hilbertclosestproof theory.

Many issues regardingfoundationsmathematics (thereno longer necessarily consideredbe any one "problem") andphilosophymathematics touch on or use ideas from metamathematics. The working assumptionmetamathematicsthat mathematical content can be captured informal system.

Onother hand, quasi-empiricismmathematics,cognitive sciencemathematics,ethno-cultural studiesmathematics, which focus on scientific method, quasi-empirical methods or other empirical methods usedstudy mathematicsmathematical practice by which such ideas become accepted,non-mathematical waysstudy mathematics.