Please write a short manuscript about the “Methods and Thinking used in Mathematics”. The manuscript should have two chapters. Chapter one is “Methods of Mathematical Proofs”. And chapter two is “Methods of Mathematics”. Wikipedia might be helpul with the chapters https://en.wikipedia.org/wiki/Mathematical_proof and https://en.wikipedia.org/wiki/List_of_mathematics-based_methods.
To the secound Wikipedia-List: Please keep it limited to pure mathematics this will shortn the wikipedia list by more than 90%. Do not write about any form of applied mathematics (no voting systems, no quantum theory, no epidemiology or similar). We only need pure mathematics here – no application. Try to find the basic thinking and basic strategies used in mathematics and descibe them very short in a few sentences. This manuscript should have 20 references in vancouver style.
Dont go too much in details. This manuscript should give an overview.
Please only describe the skeletal structure, the basic structure and the framework of the thinking and methods in pure mathematics.
Do not develop any own ideas or hypotheses. Only review the literature and descibe what has been written before.