CRISIS IN MATHEMATICS

New Zealand Listener, Volume 36, Issue 915, 22 February 1957, Page 11

CRISIS IN MATHEMATICS

"TF you were to write a paper with the heading ‘The Crisis in Mathematical Philosophy,’ and send it to any mathematical or philosophical journal, the Editor would know exactly what you were talking about. The crisis is quite public and it has been going on now for about 50 years. . . I’m trying to give you some idea of what the fuss is about." In these words the well-known mathematician W. W. Sawyer explains the scope of four talks which will start from 1YC on Wednesday, February 27, and later will be heard from other YC stations, Mr. Sawyer shows how mathematics developed in the 17th, 18th and 19th centuries, and how mathematical philosophy has now become a "burning question." The present upheaval is reflected in the existence of three major conflicting schools of thought-the intuitionists, the logicians and the formalists, and Mr. Sawyer explains the ideas behind these schools. Among the problems discussed is the arithmetic of infinities, one of the most controversial branches of mathematics, a problem which leads him to the views of the logicians and the intuitionists. His last talk is mainly about the formalists. Mr. Sawyer does not promise to solve any of the difficulties he raises. He would. like to have done so, but he concluded that after months of research he may well have reached a solution that nobody else would agree with. "There won’t be any summing up," he says, "because I’m dealing with questions to which I don’t know the answer." The talks are intended for listeners with some knowledge of mathematicsengineers, scientists, biologists and those interested in philosophy. In them Mr. Sawyer overcomes the major problem of the radio speaker on tmathematicsthe loss of the traditional blackboard and chalk.