"What is the book that changed your life? (not novels or religious texts)"
I think it's a wonderful way to connect in a less superficial way and learn a little more about each other. It's also a wonderful way to discover new books worth reading.
This is one of them (the full list is here):
An unabridged, unaltered printing of the Second Edition (1920), with original format, all footnotes and index: The Series of Natural Numbers - Definition of Number - Finitude and Mathematical Induction - The Definition of Order - Kinds of Relations - Similarity of Relations - Rational, Real, and Complex Numbers - Infinite Cardinal Numbers - Infinite Series and Ordinals - Limits and Continuity - Limits and Continuity of Functions - Selections and the Multiplicative Axiom - The Axiom of Infinity and Logical Types - Incompatibility and the Theory of Deductions - Propositional Functions - Descriptions - Classes - Mathematics and Logic - Index