Adding It All upBibliography and Research Manual of the History of Mathematics by Kenneth O. MayReview by: S. A. JayawardeneIsis, Vol. 65, No. 4 (Dec., 1974), pp. 524-526Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/229344 .

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BOOK REVIEWS

Adding it all up Kenneth 0. May. Bibliography and Research Manual of the History of Mathematics. viii + 818 pp. Toronto: University of Toronto Press, 1973. $20.

Since 1868 four abstracting and indexing journals have tried to keep track of the literature of mathematics including that of the history of mathematics. They are:

1. Jahrbuch iuber die Fortschritte der Mathematik, 1868-1940 2. Revue Semestrielle des Publications Mathematiques, 1893-1932 3. Zentralblatt fur Mathematik und ihre Grenzgebiete, 1930- 4. Mathematical Reviews, 1940-

The literature of the history of mathematics is also recorded in the following:

5. "Critical Bibliography of the History and Philosophy of Science" in Isis, 1913- 6. Bulletin Signaletique, Histoire des Sciences, 1952-

Kenneth May has used the first five as the basis for a classified bibliography of published writings (up to 1965) on the history, biography, and bibliography of mathemat- ics. A number of bibliographies and indexes other than those mentioned above have also been used. Articles in standard reference works, however, have been excluded. The first part of the book (34 pp.) is a research manual dealing with information retrieval, personal information storage, historical analysis, and writing. The second part (650 pp.) is a bibliography divided into five chapters: biography; mathematical topics; epimathematical topics; historical classifications; information retrieval.

The first chapter begins with a list of biographical collections and biographical dictionaries excluding dictionaries of national biography. It is then followed by a list of biographies of mathematicians; critical studies of the work of a mathematician are included here. The second chapter lists historical studies of mathematical topics. The arrangement is by key word; generally a title is classified under the key word of smallest scope. (It would have been helpful if a list of key words, arranged under main headings, had been given.) The third chapter is devoted to epimathematical topics (external aspects of mathematics and related fields, e.g., abacus, accounting, golden section, mathematical instruments). In the fourth chapter the literature is classified under five main headings: General; Old Civilizations; Time Periods; Countries and Regions; Cities, Organizations, Universities. Under General are listed the general histories of mathematics published from 1615 to 1968. Histories of elementary mathematics, popular histories published since 1900, and textbooks for courses are listed separately. Next comes a classification of the literature into special cultural groups (African, American Indian, Arab, Japanese, Sumerian, etc.) and Time Periods (Prehistory, Antiquity, Middle Ages, Renaissance, XIth century, etc.). In the next section the literature of the history of mathematics in the modern world is classified under countries and regions. The chapter ends with a list of works relating to learned societies, universities, and other institutions.

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BOOK REVIEWS-ISIS, 65 * 4 * 229 (1974) 525

Chapter 5 is headed Information Retrieval. The main topics are bibliography, anthologies on the history of mathematics, source books, historiography of mathematics, historical methods, libraries, manuscripts, museums, reference materials. Of particular importance are the bibliographies of the history of mathematics and the bibliographies of mathematics. The section Reference Materials contains a list of useful general encyclope- dias and select lists of mathematical dictionaries, handbooks, and encyclopedias.

One feature of the bibliography which is irksome is the absence of the titles of the articles in periodicals. This reduces the value of the work as a reference tool; however, there are brief notes which give an idea of the content of some of the articles. The appendix contains a coded list of serials cited in the bibliography and of other mathematical serials that have come to the compiler's attention. The abbreviations of serial titles used by May do not conform to any standard, for the existing standard abbreviations were considered too long to be used by scholars in note-taking and by computers.

An important reference work which May seems to have ignored in compiling his bibliography is the Royal Society's Catalogue of Scientific Papers, 1800-1900,' in which mathematical papers and biographies of mathematicians are indexed in the first two volumes of the subject index. Many of the biographies listed therein are not found in May.

In the case of the Isis Critical Bibliography we do not know what criteria May followed in selecting items for inclusion. It is very likely that he had difficulties when he came to entries relating to eminent persons like Leonardo da Vinci, Copernicus, Galileo, Pascal, Leibniz, and Newton, whose interests were not restricted to mathematics. The number of comparable entries in May and in the Isis Cumulative Bibliography are:

May (post- 1913) Isis CB Leonardo da Vinci 46 275 Copernicus 24 178 Galileo 57 249 Pascal 78 132 Leibniz 110 142 Newton 219 332

For what they are worth here are the results of some test checks I have carried out. Among the items which I cannot find in May are:

Nineteen items on Newton which I can find in Russo.2 Several books on the history of mathematical topics mentioned by Russo. Many papers on the history of mathematics by Father Bosmans (listed in Isis,

1928, 12: 88-112). * Several biographical articles found in Revue dHistoire des Sciences (cf. Tables des

matieres, 1947-1967, in Tome 21, 1968). Primary sources reviewed in Zentralblatt and Mathematical Reviews. Bio-bibliography of Otto Neugebauer in Osiris, 1962 (noted in Isis CB 1963). Necrologies of Rene Dugas in Archives Internationales d'Histoire des Sciences, 1957,

and of Ugo Cassina in Revue dHistoire des Sciences, 1965 (Isis CB 1966).

' Royal Society of London, Catalogue of Scien- tific Papers, 1800-1900 (London, 1867-1902 and Cambridge, 1914-1925), 19 vols. and Subject Index (Cambridge, 1908-1914), 3 vols. in 4.

2Frangois Russo, Elements de bibliographie de I'histoire des sciences et des techniques(2nd ed., Paris: Hermann, 1969).

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526 BOOK REVIEWS-ISIS, 65 . 4 . 229 (1974)

A. C. Crombie's Robert Grosseteste and the Origins of Experimental Science (Oxford: Clarendon Press, 1953).

* Edward Rosen's annotated Copernicus bibliography in Three Copernican Treatises (2nd ed., New York: Dover, 1959).

* Several works by Ettore Bortolotti and by Kurt Vogel (listed in their published bibliographies but not recorded in Mathematical Reviews).

Users of May's Bibliography should bear in mind that it is based on abstracting journals and indexes whose coverage is not exhaustive. In any case it is only a "first approximation to a complete bibliography"; it has to be supplemented by the Royal Society's Catalogue of Scientific Papers, Subject Index, Volumes I and II, Isis Cumulative Bibliography, and Bulletin Signaletique, Histoire des Sciences. By omitting the titles of articles and by using very short abbreviations for titles of serials it has been possible to pack 31,000 entries under 3,700 headings into a book of manageable size. If conventional methods of citing had been followed, two volumes would have been necessary, and the work would have been too expensive for students.

Kenneth May has provided a key to the literature of the history of mathematics-in particular, to that published between 1868 and 1965 and recorded in the major abstracting journals of mathematics. Thanks to him it is now possible to find out what has been written on a given subject without having to visit libraries which stock these abstracting journals and examining some 250 volumes. The book is a welcome addition to the bibliographical guides of Loria, Sarton, and Russo which the historian of mathematics already has for his use.

S. A. JAYAWARDENE 42 West Park Avenue

Kew, Surrey TW9 4AL, England

* BIBLIOGRAPHICAL TOOLS

Wayne Somers. Early Scientific Books in the Schaffer Library, Union College. With an introductory essay by Brooke Hindle. (Union College Studies No. 1.) 70 pp., indices. Schenectady, N.Y.: Union College, 1971. $2 (paper).

The place of the library in an early American college and its use as a resource is analyzed by Brooke Hindle, with special reference to Union College, founded in 1795. Four years after its founding its library contained 799 books-"a respect- able size even at the moment of its first establishment."

The 307 books arranged by subject in Wayne Somers' checklist were published between 1533 and 1800. Somers' finding list of authors, editors, and translators shows most authors to be represented in one field. The two authors with the largest number of titles in the Union College

Library were Euclid and Benjamin Martin, mathematician and physicist, with ten titles each, followed by Priestley with nine and George Adams with six. The physical sciences are richly represented, the biologi- cal, scantily. An index of printers or pub- lishers, arranged primarily by cities and then chronologically, highlights the history of publishing and also makes it evident that the students at Union sought English-lan- guage books. London, for example, is the longest entry dating from 1570, Paris the second longest, from 1632.

Hindle's essay of eighteen pages, an en- gaging analysis, concludes that "science was conceived in the American college within a distinctly anti-intellectual framework." He believes that "the celebration of experi- mental science . . . tended to denigrate speculation and discarded concepts and theories. Students were not encouraged to look behind the existing structure of science or to study the process by which it had been created," as they would have had they consulted the library. "When science stu-

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