Famous Feuds In Mathematics

Introduction

A feud of sorts can also arise because of the very different viewpoints of two individuals. This was the case with]. Huxley made important contributions in zoology, geology, and anthropology but seemed to have a hole where his mathematics should be. Hence he could argue that "mathematics knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." It is, in short, "useless for scientific purposes" (Midonick 759). Mathematicians were outraged and felt that Huxley had to be challenged. They chose Sylvester as their champion.

Discussion

The battle between Sylvester and Huxley took place in a rarified space and centered on their two very different points of view. Their discussions and statements would have an effect on the teaching of both science and mathematics in Great Britain and the United States. All of the feuds so far have been between highways respected, well placed players.

In the case of Georg Cantor, we have a very different kind of battle, one in which there is a clear underdog (Midonick 759), but the underdog happens to have been one of the most inventive mathematicians in the field's history. This was both his glory and his difficulty. Cantor had been lucky enough to study with three of Germany's most illustrious mathematicians. He was unlucky, however, in that one of the three was Leopold Kronecker, a well-known but highway conservative professor of mathematics. Cantor's troubles started when he began to move out in several bold directions. Cantor had in fact opened a wild new world of mathematics.

The arguments back and forth, by Zermelo and Borel, as well as by their followers, spell out some of the more interesting aspects of the continuing history of set theory (chapter 7). Still, for a while it had seemed that everything was going to become explainable in terms of set theory, that set theory would become the foundation of all mathematics.

In 1901, however, Bertrand Russell-a well-known British philosopher-turned-mathematician-asked a simple question, yet it shook the foundations of set theory and all it stood for in the wider world of mathematics. For it had no answer and was therefore a paradox, or contradiction (Straub 36). This paradox and others like it had a variety of effects, especially on people interested in the foundations of mathematics, for it began to appear that the whole structure of their beloved discipline was shaky or perhaps was built on a weak foundation.

Clearly, the traditional view of mathematics as an exact, logical, and certain discipline had been badly eroded. Starting around the turn of the 20th century, a fairly large group of mathematicians became engaged in studies along this line, but they divided into several mutually antagonistic groups. These gradually formed into three main groups, or schools. The first school we talk about is logicism, whose main exponent was Bertrand Russell (Fellman F1eckenstein 55). Russell believed that pure mathematics could be built on a small group of fundamental logical concepts, and that all its propositions could be deduced from ...