Abstract: This paper discusses the way metamathematics were developed within the Hillbert school, and attempts to do so with broader context.
I. Introduction:
By mathematical logic there are two things that can be meant:
It can be taken to mean the characterization of the subject matter, meaning mathematical logic refers to the study of the principles of mathematical reasoning.
Alternatively, it can characterize the methods of the discipline, meaning mathematical logic refers to the general study of the principles of reasoning, using specifically mathematical methods and techniques.
The term metamathematics in the title of the paper to refer to the overlap of these statements, or the mathematical study of the principles of mathematical reasoning.
The phrase "and proof theory" points to a specific metamathematical approach.