CONTENTS 



Preface 



5 



Introduction 9 



I. THE SCIENTIST AND SCIENCE. 

 I. The Selection of Facts . . . .15 

 11. The Future of Mathematics ... 25 



III. Mathematical Discovery .... 46 



IV. Chance 64 



II. MATHEMATICAL REASONING. 

 I. The Relativity of Space 

 II. Mathematical Definitions and Education 



III. Mathematics and Logic 



IV. The New Logics 



V. The Last Efforts of the Logisticians 



93 

 117 



143 

 160 



177 



in. THE NEW MECHANICS. 



I. Mechanics and Radium 199 



II. Mechanics and Optics 213 



III. The New Mechanics and Astronomy . . 235 



IV. ASTRONOMICAL SCIENCE. 



I. The Milky Way and the Theory of Gases . 253 



II. French Geodesy 270 



General Conclusions 284 



