This book considers the manifold possible approaches past and present to our understanding of
the natural numbers. They are treated as epistemic objects: mathematical objects that have been
subject to epistemological inquiry and attention throughout their history and whose conception
has evolved accordingly. Although they are the simplest and most common mathematical objects
as this book reveals they have a very complex nature whose study illuminates subtle features
of the functioning of our thought. Using jointly history mathematics and philosophy to grasp
the essence of numbers the reader is led through their various interpretations presenting the
ways they have been involved in major theoretical projects from Thales onward. Some pertain
primarily to philosophy (as in the works of Plato Aristotle Kant Wittgenstein...) others to
general mathematics (Euclid's Elements Cartesian algebraic geometry Cantorian infinities set
theory...). Also serving as an introduction to the works and thought of major mathematicians
and philosophers from Plato and Aristotle to Cantor Dedekind Frege Husserl and Weyl this
book will be of interest to a wide variety of readers from scholars with a general interest in
the philosophy or mathematics to philosophers and mathematicians themselves.
