## From Kant to Hilbert Volume 1 : A Source Book in the Foundations of Mathematics: A Source Book in the Foundations of Mathematics, Volume 1 (Google eBook)Immanuel 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

4 | |

11 | |

GODFREY HAROLD HARDY | 27 |

COLIN MACLAURIN 16981746 | 93 |

JEAN LeROND DALEMBERT 17171783 | 123 |

IMMANUEL KANT 17241804 | 132 |

JOHANN HEINRICH LAMBERT 17281777 | 152 |

B Mathematical proof 1243 | 158 |

AUGUSTUS DE MORGAN 18061871 | 331 |

WILLIAM ROWAN HAMILTON 18051865 | 362 |

GEORGE BOOLE 18151864 | 442 |

A The mathematical analysis of logic being an essay | 451 |

JAMES JOSEPH SYLVESTER 18141897 | 510 |

WILLIAM KINGDON CLIFFORD 18451879 | 523 |

ARTHUR CAYLEY 18211895 | 542 |

CHARLES SANDERS PEIRCE 18391914 | 574 |

BERNARD BOLZANO 17811848 | 168 |

E Was sind und was sollen die Zahlen? 787 | 170 |

GEORG CANTOR 18451918 838 | 249 |

CARL FRIEDRICH GAUSS 17771855 | 293 |

DUNCAN GREGORY 18131844 | 314 |

### Common terms and phrases

admit algebra analysis angles appear applied Archimedes arithmetic axioms Benjamin Peirce Berkeley Berkeley's body Bolzano Boole calculus called conceive concept consequence considered curve Dedekind definition demonstration denote derived determined differential differential calculus doctrine equal equation Euclid example existence expression finite quantities fluxions foundations foundations of mathematics function Gauss geometry given Hamilton imaginary increments inference infinite number infinitely small infinitesimals infinity intuition judgements Kant kind latter laws Leibniz limit logic magnitude mathematicians mathematics means metaphysics method method of fluxions mind Morgan motion multiplication nature negative Newton non-Euclidean geometry object operations Parallel Postulate particular Peirce philosophy philosophy of mathematics plane polygon possible precisely predicate principles priori proof proposition proved pure quaternions ratio reason regard relation represented scientific sense simple space straight line subtangent supposed syllogism symbols synthetic propositions theorem theory things thought tion treatise triangle true truth velocities words