## From Kant to Hilbert Volume 1: A Source Book in the Foundations of MathematicsImmanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics—algebra, geometry, number theory, analysis, logic and set theory—with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics. |

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### Contents

1 | |

11 | |

2 COLIN MACLAURIN 16981746 | 93 |

3 JEAN LEROND DALEMBERT 17171783 | 123 |

4 IMMANUEL KANT 17241804 | 132 |

5 JOHANN HEINRICH LAMBERT 17281777 | 152 |

6 BERNARD BOLZANO 17811848 | 168 |

7 CARL FRIEDRICH GAUSS 17771855 | 293 |

10 WILLIAM ROWAN HAMILTON 18051865 | 362 |

11 GEORGE BOOLE 18151864 | 442 |

12 JAMES JOSEPH SYLVESTER 18141897 | 510 |

13 WILLIAM KINGDON CLIFFORD 18451879 | 523 |

14 ARTHUR CAYLEY 18211895 | 542 |

15 CHARLES SANDERS PEIRCE 18391914 | 574 |

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xxiii | |

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### Common terms and phrases

abstract admit algebra angles appear applied Aristotle arithmetic axioms Benjamin Peirce Berkeley’s Bolzano Boole calculus called complex numbers conceive concept consequence considered curve definition demonstration denote determined differential differential calculus equal equation Euclid example existence expression finite ﬂuxions function Gauss geometry George Boole given Hamilton idea imaginary increments inference infinitely small infinitesimals integer interpretation intuition judgements Kant laws Leibniz letters logic logic of relatives magnitude mathematicians mathematics means method Morgan motion multiplication nature negative Newton non-Euclidean geometry notation number as small object operations particular Peirce philosophy philosophy of mathematics plane polygon positive possible precisely predicate principles priori proof proposition proved pure quantity quaternions ratio reason reference regard relation represent result rules scientific selections sense space supposed syllogism symbols synthetic propositions theorem theory things thought tion triangle true truth velocity William Rowan Hamilton words Xs are Ys