My book which first appeared with Cambridge University Press in 2003.
Preface:
1 Introduction: a role for history
Part I. Human and Artificial Mathematicians:
2 Communicating with automated theorem provers
3 Automated conjecture formation
4 The role of analogy in mathematics
Part II. Plausibility, Uncertainty and Probability:
5 Bayesianism in Mathematics
6 Uncertainty in mathematics and science
Part III. The Growth of Mathematics:
7 Lakatos’s philosophy of mathematics
8 Beyond the methodology of mathematical research programmes
9 The importance of mathematical conceptualisation
Part IV. The Interpretation of Mathematics:
10 Higher dimensional algebra