Date of Award
Dr. D. M. Seward
Some of the most memorable events of the twentieth century took place as a result of conflict. Out of the numerous conflicts staged during this period, only one was resolved not on a common everyday piece of writing paper. The proponents of the conflict--E. V. Huntington, Oswald Veblen, Bertrand Russell, A. N. Whitehead, and David Hilbert--did not use weapons, but they used basic mathematical structure to wage the most extensive and critical investigation into the foundations of mathematics. As a result three schools of thought which are of special prominence and interest were brought to light. These are the postulational school, the logical school, and the formalist school.
The postulational school is led by Professors E. V. Huntington and Oswald Veblen. The specific aim of the school is to establish satisfactory sets of postulates for various branches of mathematics.
The logical school centers around Bertrand Russell and Professor A. N. Whitehead, and their three-volume treatise, Principia Mathematica. The members of this school are interested in the explicit formation of symbolic logic as a foundation for mathematics.
The formalist school is led by David Hilbert of the University of Gottingen, an eminent mathematician who near the beginning of the century would have been classed as a postulationist. The formalist are attempting to make mathematical proofs rigorous by formalizing the structure of mathematics.
Rhodes, Carolyn, "Comparison of Three Schools of Thought in the Foundations of Mathematics" (1971). Honors Theses. 423.