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Mathematical Treasure: The Principia Mathematica of Russell and Whitehead

Frank J. Swetz (The Pennsylvania State University)

In the latter half of the nineteenth and the beginning of the twentieth centuries, the mathematics community was involved in a controversy surrounding the question, “What is mathematics?” Three schools of thought evolved, Logicism, Intuitionism, and Formalism. The Logicist movement, which holds that all mathematics can be reduced to logic, was founded by Gottlob Frege (1884-1925) but was best articulated by the British philosophers and mathematicians, Bertrand Russell (1872-1970) and Alfred North Whitehead (1861-1947) in their work Principia Mathematica. This three-volume text was compiled in the period 1910-1913. The title page for Volume I of the 1925 edition of Principia Mathematica is shown here:


In the Introduction the authors outlined their philosophy:

The logical argument establishing the cardinal number 1 is given on page 351, below. Note the density of logical symbolism.

This excerpt from page 362 establishes the proposition from which 1 + 1 = 2 can be proven:

The images above were obtained from the Rare Book Collection at Franklin and Marshall College, Lancaster, Pennsylvania.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Principia Mathematica of Russell and Whitehead," Convergence (February 2016)