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# How Mathematicians Develop a Branch of Pure Mathematics

DOI link for How Mathematicians Develop a Branch of Pure Mathematics

How Mathematicians Develop a Branch of Pure Mathematics book

# How Mathematicians Develop a Branch of Pure Mathematics

DOI link for How Mathematicians Develop a Branch of Pure Mathematics

How Mathematicians Develop a Branch of Pure Mathematics book

## ABSTRACT

The axiomatic method is the framework within which all the “If—then” statements of mathematics are formed. The process of arriving at such a statement involves not only the hypothesis and the conclusion of the “If—then” statement itself; but also the laws of logic and the use of previously proved theorems, definitions, and, ultimately, certain basic statements called variously axioms, postulates, assumptions. An individual’s code of ethics is an example of a set of basic assumptions. It forms for him a set of axioms from which he derives the theorems determining his conduct. The property of consistency is a “must” property for any set of axioms. From the point of view of a pure mathematician, however, an independent set of axioms possesses a nicety not found in a set of axioms lacking this property. In a sense, it makes a mathematician “start from scratch” when he has an independent axiom set.