## The World of Mathematics, Volume 3Vol. 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and mathematics as an art. Specific contributions by Jacob Bernoulli, George Bernard Shaw, Bertrand Russell, Hans Hahn, Ernst Mach, Hermann Weyl, George Boole, Alfred Tarski, and many others. Informative commentary by noted mathematics scholar James R. Newman precedes each essay. Numerous figures. |

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There is a picture somewhere in this book which I copied before ( not sure) , and I am still willing to get that picture because this is a kind of cool.

### Contents

Commentary | 1416 |

Foundations of Vital Statistics | 1421 |

First Life Insurance Tables | 1437 |

Commentary | 1448 |

The Law of Large Numbers | 1452 |

Commentary | 1456 |

Sampling and Standard Error | 1459 |

On the Average and Scatter | 1487 |

Commentary | 1767 |

The Essence of Mathematics | 1773 |

Commentary | 1784 |

The Economy of Science | 1787 |

Commentary | 1796 |

Measurement | 1797 |

Numerical Laws and the Use of Mathematics in Science | 1814 |

Commentary | 1830 |

Mathematics of a Lady Tasting Tea | 1512 |

Commentary | 1522 |

The Vice of Gambling and the Virtue of Insurance | 1524 |

The Supreme Art of Abstraction Group Theory | 1533 |

Commentary | 1534 |

The Group Concept | 1538 |

The Theory of Groups | 1558 |

Mathematics of Infinity | 1575 |

Mathematics and the Metaphysicians | 1576 |

Commentary | 1591 |

Infinity | 1593 |

Mathematical Truth and the Structure of Mathematics | 1613 |

Commentary | 1614 |

On the Nature of Mathematical Truth | 1619 |

Geometry and Empirical Science | 1635 |

The Axiomatic Method | 1647 |

Goedels Proof | 1668 |

A Mathematical Science | 1696 |

Mathematics and the World | 1708 |

Mathematical Postulates and Human Understanding | 1723 |

The Mathematical Way of Thinking | 1755 |

Commentary | 1756 |

The Study That Knows Nothing of Observation | 1758 |

The Mathematical Way of Thinking | 1832 |

Mathematics and Logic | 1851 |

Commentary | 1852 |

Mathematical Analysis of Logic | 1856 |

History of Symbolic Logic | 1859 |

Symbolic Notation Haddocks Eyes and the DogWalking Ordinance | 1878 |

Symbolic Logic | 1901 |

The Unreasonableness of Mathematics | 1933 |

Commentary | 1934 |

Paradox Lost and Paradox Regained | 1936 |

The Crisis in Intuition | 1956 |

How to Solve It | 1977 |

Commentary | 1978 |

How to Solve It | 1980 |

The Vocabulary of Mathematics | 1993 |

Commentary | 1994 |

New Names for Old | 1996 |

Mathematics as an Art | 2011 |

Commentary | 2012 |

Mathematics as an Art | 2015 |

2023 | |

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### Common terms and phrases

algebra arithmetic assertion assumptions average axiomatic axiomatic method axioms Bertrand Russell calculation called cardinal number concept consistency construction contains counting curve deduction deﬁned deﬁnition derived difﬁculty equal equation Ernest Nagel errors euclidean euclidean geometry example experience experimental expression fact false ﬁeld ﬁgure ﬁnd ﬁnite number ﬁrst ﬁve ﬁxed formal formula geometry given Goedel number googol googolplex Hans Hahn ideas implication inﬁnite inﬁnite sets integer intuition Leibniz logic mathe mathematical logic mathematical propositions mathematician matics meaning measure ment meta-mathematical method natural numbers non-Euclidean geometries notion objects observation obtained operation parallel axiom philosophy physical plane positive number possible postulates principle problem proof pure question real numbers reasoning relation result rule sample satisﬁed scientiﬁc sense sentence sentential calculus sentential function signiﬁcance space speciﬁc statement straight line symbols theorems theory things tion transformations true truth undeﬁned variables velocity words