Mathematics, Form and Function

Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane.

Throughout his book, and especially in chapter I.11, Mac Lane informally discusses how mathematics is grounded in more ordinary concrete and abstract human activities.

For a bullet list that can be compared and contrasted with this table, see section 3 of Where Mathematics Comes From.

Mac Lane (1986) cites a related monograph by Lars Gårding (1977).

Mac Lane cofounded category theory with Samuel Eilenberg, which enables a unified treatment of mathematical structures and of the relations among them, at the cost of breaking away from their cognitive grounding.