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The Rate of Growth of Mathematics During Four Centuries

Published online by Cambridge University Press:  03 November 2016

P. J. Wallis
P. J. Wallis*
Affiliation:
Department of Education, St. Thomas Street, University of Newcastle upon Tyne
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Extract

The exponential law of increase has been described by Professor D. J. de Solla Price as “the fundamental law of any analysis of science”, and considered to hold over long periods of time [1]. The same writer suggested that low-grade work doubled in about ten years, but that the period taken was about twice as long for very high quality activity. It is useful to remember that a doubling every fifteen years corresponds to a multiplication by about a million in three centuries, or an annual increase of nearly five per cent.

Type
Research Article
Information
The Mathematical Gazette , Volume 52 , Issue 380 , May 1968 , pp. 127 - 130
Copyright
Copyright © Mathematical Association 1968

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References

1. Little Science, Big Science, Columbia University Press, 1963.Google Scholar
2. “Quantitative Growth of the Mathematical Literature”, Science cliv no. 3757 pp. 1672-3, Dec. 30, 1966.Google Scholar
3. An unpublished note by the present writer. The error depends on the product of the length of the period considered and the growth rate, so smaller rates need longer periods to calculate with the same accuracy.Google Scholar
4. By the present writer, issued for private circulation by the Department of Education, the University of Newcastle upon Tyne, May 1967.Google Scholar
5. The line drawn, by eye and not by least-squares analysis, gives increases from 1 to 30 in three centuries, corresponding to a doubling period of 61 years and an annual increase of 1-1%.Google Scholar
6. The Biobibliography is in active preparation, but clearly still incomplete. There is evidence that the number of authors may be as many as five thousand, about twice those now listed. It is intended to be comprehensive, so the works cited range from first books on number to advanced treatises. Different treatment of anonymous authors, translators and editors would affect the figures graphed, but is unlikely to affect the slope of the line.Google Scholar
7. Pollard, A. W. and Redgrave, G. R., 1926.Google Scholar
8. Output figures at intervals of ten years are conveniently given in Edith Klotz, L. “A Subject Analysis of English Imprints &”, Huntington Library Quarterly 1.4 417-9, July 1938. My figure of 4-5 comes from a growth from 125 to 560 titles in the century.10.2307/3815838Google Scholar
9. It is considered that the new S.T.C, will have some ten per cent of new titles and 30% of new editions and issues (Bennett, H. S., English Books & Readers 1558 to 1603 &, 1965, p. viii).Google Scholar
10. English Book Trade 2nd ed. 1965, p. 445, gives a growth from under a hundred new books p.a. at the beginning of the century to 580 early in the next century. The former figure can be contrasted with the 560 for 1640 (note 8) to indicate its incompleteness. The factor of six can only be approximate, too, as the figures are taken from different works which could have varying degrees of incompleteness.Google Scholar
11. This Note has been prepared as part of the writer’s fuller study of mathematical bibliography, which has been aided by grants from the Marc Fitch Trust and University of Newcastle upon Tyne Research Fund, and which owes much to the unselfish aid of librarians all over the country ; the writer would particularly like to mention Mr. Paul Morgan of the Bodleian Library.Google Scholar