Acknowledgments. Introduction. Notes on Contributors. Part I: The Question of Empiricism. The Role of Scientific Theory and Empirical Fact in the Growth of Mathematical Knowledge. 1. Knowledge of Functions in the Growth of Mathematical Knowledge; J. Hintikka. Huygens and the Pendulum: From Device to Mathematical Relation; M.S. Mahoney. 2. An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics; D. Gillies. The Mathematization of Chance in the Middle of the 17th Century; I. Schneider. Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider; M. Liston. 3. The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge; E. Grosholz. Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations; C. Fraser. 4. On Mathematical Explanation; P. Mancosu. Mathematics and the Reelaboration of Truths; F. de Gandt. 5. Penrose and Platonism; M. Steiner. On the Mathematics of Spilt Milk; M. Wilson. Part II: The Question of Formalism. The Role of Abstraction, Analysis, and Axiomatization in the Growth of Mathematical Knowledge. 1. The Growth of Mathematical Knowledge: An Open World View; C. Cellucci. Controversies about Numbers and Functions; D. Laugwitz. Epistemology, Ontology, and the Continuum; C. Posy. 2. Tacit Knowledge and Mathematical Progress; H. Breger. The Quadrature of Parabolic Segments 1635-1658: A Response to Herbert Breger; M.M. Muntersbjorn. Mathematical Progress: Ariadne's Thread; M. Liston. Voir-Dire in the Case of Mathematical Progress; C. Mclarty. 3. The Nature of Progress in Mathematics: The Significance of Analogy; H. Sinaceur. Analogy and the Growth of Mathematical Knowledge; E. Knobloch. 4. Evolution of the Modes of Systematization of Mathematical Knowledge; A. Barabashev. Geometry, the First Universal Language of Mathematics; I. Bashmakova, G.S. Smirnova. Part II: The Question of Progress. Criteria for and Characterizations of Progress in Mathematical Knowledge. 1. Mathematical Progress; P. Maddy. Some Remarks on Mathematical Progress from a Structuralist's Perspective; M.D. Resnik. 2. Scientific Progress and Changes in Hierarchies of Scientific Disciplines; V. Peckhaus. On the Progress of Mathematics; S. Demidov. Attractors of Mathematical Progress: The Complex Dynamics of Mathematical Research; K. Mainzer. On Some Determinants of Mathematical Progress; C. Thiel.