Contents -- 16. GEORG FRIEDRICH BERNHARD RIEMANN (1826-1866) -- A. On the hypotheses which lie at the foundation of geometry -- 17. HERMANN VON HELMHOLTZ (1821-1894) -- A. The origin and meaning of geometrical axioms -- B. The facts in perception -- C. Numbering and measuring from an epistemological viewpoint -- 18. JULIUS WILHELM RICHARD DEDEKIND (1831-1916) -- A. On the introduction of new functions in mathematics -- B. From the Tenth Supplement to Dirichlet's Lectures on the theory of numbers -- C. Continuity and irrational numbers -- D. From On the theory of algebraic integers -- E. Was sind und was sollen die Zahlen? -- F. From the Eleventh Supplement to Dirichlet's Lectures on the theory of numbers -- G. Letter to Heinrich Weber (24 January 1888) -- H. Felix Bernstein on Dedekind and Cantor -- I. From the Nachlass -- 19. GEORG CANTOR (1845-1918) -- A. On a property of the set of real algebraic numbers -- B. The early correspondence between Cantor and Dedekind -- C. Foundations of a general theory of manifolds: a mathematico-philosophical investigation into the theory of the infinite -- D. On an elementary question in the theory of manifolds -- E. Cantor's late correspondence with Dedekind and Hilbert -- 20. LEOPOLD KRONECKER (1823-1891) -- A. Hilbert and Kronecker -- B. Extract from Hilbert's Göttingen lectures -- C. Two footnotes -- D. On the concept of number -- 21. CHRISTIAN FELIX KLEIN (1849-1925) -- A. Klein on the schools of mathematics -- B. On the mathematical character of space-intuition and the relation of pure mathematics to the applied sciences -- C. The arithmetizing of mathematics -- 22. JULES HENRI POINCARÉ (1854-1912) -- A. On the nature of mathematical reasoning -- B. On the foundations of geometry -- C. Intuition and logic in mathematics -- D. Mathematics and logic: I -- E. Mathematics and logic: II.

F. Mathematics and logic: III -- G. On transfinite numbers -- 23. THE FRENCH ANALYSTS -- A. Some remarks on the principles of the theory of sets -- B. Five letters on set theory -- 24. DAVID HILBERT (1862-1943) -- A. On the concept of number -- B. From Mathematical problems -- C. Axiomatic thought -- D. The new grounding of mathematics First report -- E. The logical foundations of mathematics -- F. The grounding of elementary number theory -- G. Logic and the knowledge of nature -- 25. LUITZEN EGBERTUS JEAN BROUWER (1881-1966) -- A. Mathematics, science, and language -- B. The structure of the continuum -- C. Historical background, principles, and methods of intuitionism -- 26. ERNST ZERMELO (1871-1953) -- A. On boundary numbers and domains of sets: new investigations in the foundations of set theory -- 27. GODFREY HAROLD HARDY (1877-1947) -- A. Sir George Stokes and the concept of uniform convergence -- B. Mathematical proof -- 28. NICOLAUS BOURBAKI -- A. The architecture of mathematics -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Y -- Z.