Home > Metamathematics
Metamathematics is mathematics used to study mathematics.It was originally differentiated from ordinary mathematics in the 19th century to focus on what was then called the foundations problem in mathematics.
Important branches include proof theory and model theory. The original meaning of David Hilbert is closest to proof theory (see Hilbert's program).
These would nowadays be considered part of Mathematical logic, which (according to Googlefight ) is much more widely used than the obsolescent(?) term metamathematics [though still used by the Library of Congress and the books Metamathematics of Fuzzy Logic (2002) & Gödel, Escher, Bach].
Many issues regarding the foundations of mathematics (there is no longer necessarily considered to be any one "problem") and the philosophy of mathematics touch on or use ideas from metamathematics. The working assumption of metamathematics is that mathematical content can be captured in a formal system.
On the other hand, quasi-empiricism in mathematics, the cognitive science of mathematics, and ethno-cultural studies of mathematicsEthno-cultural studies of mathematics is one term used to describe the study of informal mathematics — historically the predominant form of mathematics at most times and in most cultures. Another term used is folk mathematics which is ambiguous; the folk, which focus on scientific methodThe scientific method is a sequence or collection of processes that are considered characteristic of scientific investigation and the acquisition of new scientific knowledge based upon physical evidence. Science deals with assertions about the way the wor, quasi-empirical methodsQuasi-empirical methods are applied in science and in mathematics. The term empirical methods' refers to experiment, disclosure of apparatus for reproduction of experiments, and other ways in which science is validated by scientists. These are studied ext or other empirical methods used to study mathematics and mathematical practiceThe term mathematical practice arose in the philosophy of mathematics to distinguish actual practices of working mathematicians (choices of theorems to prove, informal notations to persuade themselves and others that various steps in the final proof are f by which such ideas become accepted, are non-mathematical ways to study mathematics.
Mathematical logic
LogicIn ordinary language, logic is the reasoning used to reach a conclusion from a set of assumptions. More formally, logic is the study of inference—the process whereby new assertions are produced from already established ones. As such, of particular concern
