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I The State of the Mathematical Sciences

OCR for page 43
This part of the report contains an overview of the mathematical sciences. It has been written in a form that we hope will be mean- ingful to nonmathematicians. In order to accomplish this, and to keep the report within reasonable size, it was necessary to sacrifice any attempt at completeness. It was also necessary to avoid details and the use of symbolism, without which a profound discussion of mathematical subjects may be impossible. Yet we hope that this Part, supplemented by our collection of essays,7 will communicate to the nonmathematical scientist and the educated layman a feeling for the intellectual atmosphere of mathematical sciences at the threshold of the last third of the twentieth century.