Introduction to mathematicals thinking: The formation of concepts in modern mathematics - Waismann, Fredrich (New York Harper & Brothers, 1959)
This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic and progresses to the problems of the real-number continuum and concepts of the calculus.
Keywords: Mathematical theory; Mathematics philosophy; Mathematics