The Growth of Mathematical Knowledge

Front Matter....Pages i-xli
On Mathematical Explanation....Pages 103-119
Mathematics and the Reelaboration of Truths....Pages 121-132
Penrose and Platonism....Pages 133-141
On the Mathematics of Spilt Milk....Pages 143-152
Knowledge of Functions in the Growth of Mathematical Knowledge....Pages 1-15
Huygens and the Pendulum: From Device to Mathematical Relation....Pages 17-39
An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics....Pages 41-57
The Mathematization of Chance in the Middle of the 17th Century....Pages 59-75
Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider....Pages 77-80
The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge....Pages 81-91
Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations: A Study in the Interaction of Mathematics and Physics....Pages 93-101
The Growth of Mathematical Knowledge: An Open World View....Pages 153-176
Controversies about Numbers and Functions....Pages 177-198
Epistemology, Ontology and the Continuum....Pages 199-219
Tacit Knowledge and Mathematical Progress....Pages 221-230
The Quadrature of Parabolic Segments 1635 – 1658: A Response to Herbert Breger....Pages 231-256
Mathematical Progress: Ariadne’s Thread....Pages 257-268
Voir-Dire in the Case of Mathematical Progress....Pages 269-280
The Nature of Progress in Mathematics: The Significance of Analogy....Pages 281-293
Analogy and the Growth of Mathematical Knowledge....Pages 295-314
Evolution of the Modes of Systematization of Mathematical Knowledge....Pages 315-329
Geometry: the First Universal Language of Mathematics....Pages 331-340
Mathematical Progress....Pages 341-352
Some Remarks on Mathematical Progress from a Structuralist’s Perspective....Pages 353-362
Scientific Progress and Changes in Hierarchies of Scientific Disciplines....Pages 363-376
On the Progress of Mathematics....Pages 377-386
Attractors of Mathematical Progress — the Complex Dynamics of Mathematical Research....Pages 387-406
On Some Determinants of Mathematical Progress....Pages 407-416
Back Matter....Pages 417-428