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Quote by Saunders Mac Lane

“The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of sets but functions between sets. This can be done by using the language of categories and universal constructions.”

Quote by Saunders Mac Lane

Book:Mathematics, form and function

Work

Mathematics, form and function

This book delves into the fundamental concepts of mathematics, examining how mathematical structures and functions are used to understand and solve problems across various disciplines. more

Author

Saunders Mac Lane

Mathematician born on August 4, 1909, in the United States, and died on April 14, 2005. He made significant contributions to algebraic topology and category theory. more

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Book:Mathematics, form and function

Source: Mathematics, form and function

“. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.”

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