By Joseph W. Dauben

Bibliographic extravagance is a sin rather than a virtue, a real perversity. George Sarton

George Sarton liked to describe the history of science as a ``secret history'', and the history of mathematics as the secret within the secret, for while most scholars might know something of the history of science in general, few mathematicians, scientists, or even specialists in the history of science could be expected to know much about the history of mathematics. In part, this was because of the theoretical and often abstruse nature of mathematics, but also in part because so little had been done to make the history of mathematics accessible to those who might have need of it, or to others who might simply be interested in learning more about it. A major goal of this bibliography in the history of mathematics is, in fact, to furnish a reference work that will help to open the doors to this secreta secretorum, and to provide something of an Ariadne's thread through the labyrinth of this increasingly specialized and often difficult domain of human knowledge.

The History of Mathematics

Mathematics has a history that begins in pre-history. The earliest archaeological and anthropological evidence we possess makes it clear that even as homo sapiens began to speak, he began to count as well. Much before there was any way to express even the simplest numbers in written form, man was counting and calculating. By the time neolithic cultures had emerged along the rivers of the Tigris-Euphrates, Nile, Hwang Ho, and Indus, mathematics was already developed and in some cases to a high and sophisticated degree. This was especially true in Mesopotamia, where the Babylonians developed algebra to a considerable extent and devised a very powerful sexagesimal (base-sixty) arithmetic which was well suited to their complex but correspondingly effective mathematical astronomy. For the most part, however, ancient knowledge of arithmetic, algebra, and geometry was imperfect or only approximate and was reserved for the small numbers of royal scribes and priests who became adept at solving basic problems in accounting, surveying, and astronomy, often with mystical and religious overtones. The Egyptian Book of the Dead makes this quite clear in describing a Pharaoh who knows a mnemonic device, learned in the form of a rhymed chant, to remember how to count from one to ten on his fingers. His ability to do so is considered sufficient to establish that he is indeed a king with full knowledge of things reserved for the gods, thereby convincing the ferryman to transport him across the river of forgetfulness to the divine world of eternal life.

Centuries later, the Greeks of the archaic period began to ``demythologize'' their world (to borrow Henri Frankfort's phrase) and adopted both a more secular and objective perspective on nature than did their predecessors, the Egyptians or Babylonians. But they also succeeded in elevating mathematics to the idealized realm of perfect, eternal knowledge, whose truths were associated with the loftiest philosophical ideals. The Greeks, having learned their mathematics from the Egyptians and Babylonians, soon transformed it into a powerful epistemological tool. From Thales to Euclid numerous discoveries were made in geometry and arithmetic. Equally important, methods were developed to prove the validity of an assertion or mathematical theorem. This, of course, culminated in two major achievements---Aristotle's formal logic of the syllogism and Euclid's axiomatic geometry. By this time the practical importance and theoretical significance of mathematics was also clear not only to philosophers and mathematicians, but to shopkeepers, mariners, generals, and government administrators. Moreover, mathematics had found its first true historian (of whom any record survives)---Eudemos of Rhodes, a disciple of Aristotle who wrote a summary of Greek mathematics in the early 4th century (fl. 335 B.C.).

For the rest of antiquity the Greek advances remained the norm, and for over 900 years few advances were made. Despite nearly a millennium of the so-called Dark Ages, mathematics eventually experienced a second miracle, as George Sarton called it, that is, the interest of Arab scholars first in discovering and preserving the mathematics of the ancients and then in augmenting and transmitting that knowledge. In so doing, they transformed and invigorated much of the received mathematics. They also developed the Hindu-Arabic decimal system, a seminal discovery that eventually was transmitted to the Latin West.

Both the Arabic and Latin traditions were particularly strong, and much richer than is usually thought, largely because until recently little in the way of systematic research to produce viable texts and informative commentaries was available to historians of science. When Gustav Enestr\"om began publishing corrections in the 1890s in Bibliotheca Mathematica (item \xr31\\) to the monumental Geschichte der Mathematik (item \xr 74\\) of Moritz Cantor, the areas most often found wanting were those for ancient, Islamic, and medieval mathematics. Since 1900, these areas have received considerable attention, and recent research reflects strong interest now in each of these periods. Such activity is well represented in this bibliography, with substantial sections devoted to Egyptian, Babylonian, Greek, and medieval mathematics of the Indian, Islamic, Hebrew, and Western Latin cultures.

The most important stage in the advance of European mathematics coincided with the Italian and Northern Renaissance of the fourteenth and fifteenth centuries, when the progress of mathematics and the sciences generally was as rapid as the social and economic development of Western Europe. Beginning with 1600, this bibliography proceeds by roughly 100-year intervals (although a certain amount of overlap between centuries is unavoidable) as it surveys the development of mathematics from the Renaissance through the 17th, 18th, 19th, and 20th centuries.

In the last hundred years, mathematics has developed into a highly abstract and esoteric body of knowledge which, nevertheless, has extraordinary versatility in applications that permeate almost every aspect of life in any modern society. Its past history, as already indicated, is enormous, from its beginnings evident in the notched bones of caveman tally sticks to, more recently, the sublimities of group theory, abstract algebra, and the powerful applications of differential equations and high-speed computers. In fact, the last two major divisions of this bibliography investigate the history of mathematics by 22 subject areas, ranging from the philosophy and sociology of mathematics to mathematics in Africa and the Orient, as well as the subject of women in mathematics.

One way to bring order to this long, diverse, and complicated history of mathematics, however, is through the guidance of a good critical, annotated bibliography.

The Role and Significance of Bibliographies

The art of compiling bibliographies is nearly as old as the history of written documents themselves. It is of interest to historians of science that the first bibliographies of which any record is known were drawn up by the Roman physician Galen in the second century A.D. They are his De libris propriis liber, followed by a second version, the De ordine librorum suorum liber (which survives only in a fragment), both of which were intended to authenticate his own works and distinguish them from the many spurious writings attributed to him. Later bibliographies in antiquity and the early medieval period, like those of St. Jerome and the Venerable Bede, fall into the tradition of compiling lists of ecclesiastical authors and their works.

The first bibliography encompassing printed works rather than manuscript material was compiled in the 15th century by Johann Tri theim, whose Liber de scriptoribus ecclesiasticis (1494) continued in the tradition of Jerome and Bede. None of these works, however, whether of books or manuscripts, was actually called a bibliography---the words used most often were those like ``bibliotheca,'' ``catalogus,'' ``repertorium,'' ``inventarium,'' or ``index.'' The word ``bibliography'' was actually used first in France, it seems, by Gabriel Naud\'e, secretary and librarian to Cardinal Richelieu, for his Bibliographia politica.

Bibliography actually came into its own in France, although slowly. The word is absent from the first edition of the Dictionnaire de l'Acad\'emie Fran\c coise, and was still missing in 1751. Nor does it occur in Diderot and D'Alembert's Encyclop\'edie (although the term ``bibliographer'' does, but only in the sense of one skilled in the use of ancient manuscripts, e.g., a paleographer; there is no reference to catalogues or lists). In the fourth edition of the Acad\'emie's Dictionnaire, however, ``bibliography'' in the modern sense, finally appears.

It was the French Revolution, however, that marked the real turning point in the history of bibliography. In fact, the subject became a matter of considerable urgency and was the special subject of a ``Rapport sur la bibliographie'' issued on 22 Germinal of the Year II of the Revolution (April 11, 1794). Not only was this the first official document of a government on the subject of bibliography, submitted by Henri Gr\'egoire (1750--1831), the constitutional Bishop of Blois and a Deputy of the Convention, but it addressed directly the problem of cataloguing the mass of books confiscated from religious organizations and emigres, all of which subsequently became the property of the French nation. It was also in France that the subject was first institutionalized, at the Ecole des Chartes, where a professorship was established for bibliography in 1869. Courses were regularly offered, chiefly on the classification of archives and libraries.

As for bibliographies of interest to the history of mathematics, one of the first is attributed to Cornelius \`a Beughem, a book-seller and publisher who lived for a long period in Emmerich, Westphalia, and who produced a number of specialized bibliographies, including one in 1688 entitled Bibliographia mathematica et artificiosa novissima, which ran to nearly 500 pages and included the works of nearly 2000 writers.

Not until the 19th century, however, was any real impetus given to the systematic production of bibliographic resources. These were naturally stimulated by the progress of public education and the proliferation of universities, learned societies, and related institutions. Stabilization of the book trade, the growth of periodical presses, and the establishment of the first great public archives and libraries all provoked an obvious need for systematic bibliography. For the first time, rather than trying primarily to record, note, or save from oblivion the works of the past, the role of bibliography advanced to one of dissemination, calling to the attention of scholars and interested readers the most current advances in learning. Here, not surprisingly, leadership came first from Germany. The organization of universities and their emphasis upon careful scholarship made the creation of research libraries essential, and these in turn both depended upon and stimulated the subject of bibliography. If one surveys the major bibliographies produced in this period and, especially those of interest to the historian of mathematics, an instructive pattern emerges: 1830. I. Rogg. Bibliotheca Mathematica (T\"ubingen). 1839. J. O. Halliwell. Rara Mathematica (London). 1847. A. de Morgan. Arithmetical Books from the Invention of Printing (London). 1854. L. A. Sohncke. Bibliotheca Mathematica (Leipzig). 1863. J. C. Poggendorff, ed. Biographisch-literarisches Handw\"orterbuch (Leipzig). 1868--1887. B. Boncompagni. Bulletino di Bibliographia e Storia delle Scienze matematiche e fisiche (Rome). 1873--1928. P. Riccardi. Biblioteca matematica italiana (Modena). 1873. A. Erlecke. Bibliotheca Mathematica (Halle). 1884--1914. G. Enestr\"om, ed. Bibliotheca Mathematica (Stockholm).

Among these works, the most significant, even today, remains the seminal contribution of J. C. Poggendorff, an historian, biographer, and bibliographer. At age 27, he became editor of the Annalen der Physik und Chemie (founded in 1790) and, as a result, initiated a correspondence with the leading scientists of his day. This eventually prompted a project that was naturally suited to his historical interests (also expressed in his lectures and in a book on the history of physics), namely, the Biographisch-literarisches Handw\"orterbuch zur Geschichte der exakten Naturwissenschaften. In 1863 it consisted of only two volumes, comprised primarily of brief biographical information and bibliographic references for 8400 scientists up to 1858. By 1974, however, the continuation of this series had grown to 18 volumes.

Mention should also be made of Baldassarre Boncompagni, who even established his own private printing plant in order to ensure the high standards of his publications related to the history of science. Especially important is the Bullettino Boncompagni, which George Sarton once described as ``a very rich collection, a model of its kind.'' Another of those dedicated to bibliography and the history of mathematics before this century was Gustav Enestr\"om, who began his career as a librarian. Although little is known of his private life, one biographer has called him ``very original and eccentric.'' Perhaps no greater tribute could be made to Enestr\"om's contributions to the history of mathematics than one paid by George Sarton in 1922: ``Personal notes for living scholars have been thus far avoided in \jrIsis, but an exception must be made in favor of Gustav Enestr\"om, than whom no one has ever done more for the sound development of our studies.''

More recently, George Sarton's guides to the history of science set a new generation on a more interdisciplinary and historical course. Of special interest to users of this bibliography is Sarton's The Study of the History of Mathematics (item \xr48\\), published in 1937 and devoted, in part, to a discussion and critique of bibliographic resources on the subject. Sarton's work was followed a decade later, in 1946, by Gino Loria's Guida allo studio della storia delle matematiche (item \xr47\\). This too provided excellent critical discussion of the history of mathematics, with the advantage that it was able to profit from the appearance of Sarton's guide as well.

Shortly after the appearance of Loria's guide, George Sarton published Horus, a major effort on his part not only to provide a rationale for the purposes and meaning of the history of science (Part I of Horus), but a bibliographic summary as well, meant ``to provide a kind of vade mecum for students'' (Part II). ``The first part is meant to be read,'' Sarton wrote, ``the second to be used as a tool.'' In his introduction to Part II, Sarton asserted that ``nothing is more instructive than a good bibliography$\ldots$Every bibliography must begin with a bibliography, and it must end with a better bibliography.''

The most recent of all the bibliographic guides concerned with the history of mathematics, however, is Kenneth May's (item \xr17\\). Its aim was ``to assist mathematicians, users of mathematics, and historians in finding and communicating information required for research, applications, teaching, exposition and policy decisions.'' May's bibliography was inspired, in part, by the rampant growth of literature related to mathematics, which he estimated in 1966 as already consisting of half-a-million titles and growing at the rate of 15,000 new items annually. May was particularly concerned that ``this enormous collection is not indexed. No one knows its nature or contents. Preliminary studies suggest that there is a vast amount of duplication, and that the important information is contained in perhaps as little as 10\% of the titles.'' In order to reduce this problem and obtain what he called ``effective entry to this storehouse so as to find information, orientation, and enlightenment,'' May's bibliography offered 31,000 entries under 3700 topics, with an appendix listing about 3000 periodicals in which papers on mathematics and its history are published.

Bibliographies and Information Retrieval

Recently, some scholars have sensed an impending crisis in the domain of information retrieval. Within the past decade, most major libraries, universities, and publishers have begun to rely on computerized indexes and reference systems to facilitate data management. Some fear that soon we shall be so inundated with the printed word that even attempting to do basic research on a given subject will be a bibliographical nightmare. Automation may indeed help to solve some bibliographical problems, but it may also contribute to the problem by facilitating even more rapid production of the written word and of information in general.

Not all agree, however, and among the most persuasive of the dissenters is Yehoshua Bar-Hillel, who more than twenty years ago posed the question, ``Is information retrieval approaching a crisis?'' In Bar-Hillel's opinion, there is no crisis. Simply because the growth of mathematical information may seem to be pathologically out of control (to adopt a point of view made popular by Derek de Solla Price) does not mean that researchers will wallow in a hopeless miasma of printed material, making it impossible for anyone to keep abreast of the latest books, monographs, papers, and articles on a given subject. Bar-Hillel observes that:

Scientists did not spend on the average in 1961 more time on reading than they did 12 years ago, though printed scientific output has indeed almost doubled during this period. There must therefore have been a way out between the horns of the dilemma. What is it? Everybody knows it: Specialization.

Nonetheless, as research becomes increasingly focused, bibliographies become all the more important, especially for those who choose to move from their own areas of specialization into others that may be related, or even wholly new. Here bibliographies play a crucial role in helping to orient new readers to a field in which they may be less than proficient.

There is another service bibliographies perform, and this is related to facilitating research and helping to reduce duplication of efforts. Not long ago it was suggested that hundreds of thousands of dollars (estimates ranged from \$200,000 to \$250,000) had been wasted because a Russian paper on Boolean matrix algebra and relay contact networks was not known to American researchers. According to an article in \jrScience, the Russian paper had appeared in an ``important, readily available Soviet journal'' and ``simply reposed on a library shelf waiting to be noticed.'' This example had been noted as early as 1956, when William Locke wrote in \jrScientific American, ``groups of people in several companies in the United States did, in fact, work for five frustrating years on the very points cleared up by this paper before discovering it.'' The paper in question was written by A. G. Lunts (also transliterated as Lunc) in 1950: ``The Application of Boolean Matrix Algebra to the Analysis and Synthesis of Relay Contact Networks,'' but published in Russian. The waste of both time and money suggested by this example was even brought to the floor of Congress as an example of costly duplication and inefficiency of research efforts due to lack of proper information dissemination.

The thrust of Locke's article in \jrScientific American was simple: an inexpensive means of translating material from Russian to English should be made available so that such a waste of time and money could be avoided in the future. Ironically, as a letter published in the March issue of \jrScientific American noted, the Lunts paper should have been known already, since it had been abstracted in \jrMathematical Reviews. As R. P. Boas, Jr., also pointed out in a letter to \jrScience (Boas was then executive editor of \jrMathematical Reviews): ``If people are unable or unwilling to use the bibliographic aids that are already provided, there is little point in supplying them with even more in the form of translations and so on.'' E. H. Cutler posed an equally germane question. Because the article by Lunts had been annotated in \jrMathematical Reviews, he asked, ``Does not the case suggest more the need for the application of machines to the bibliographic problems of cross-referencing publications rather than the more fascinating application to the problem of translation?'' Locke agreed. On the same page of the March issue of \jrScientific American, he noted that ``My example does show the need for machines to keep the bibliographies of specialized fields up to date.''

Whether or not machines are used to store, catalogue, and retrieve bibliographic information, there are many ways in which bibliographies, whatever their form, are essential resources for serious research. Not only does a good bibliography eliminate the need to read everything on a given subject---clearly impossible with the overwhelming number of publications produced annually in mathematics, not to mention the burgeoning growth of literature in the history of mathematics---but it ought to provide a simple way of orienting the user to the most significant works in print on a particular topic.

Another and often unappreciated value of bibliographies is the extent to which they are historical and sociological resources in their own right. This, in fact, was the point made in 1952 by Victor Zoltowski in an article entitled ``Les cycles de la cr\'eation intellectuelle et artistique'' in \jrAnn\'ee sociologique, and quoted by Louise Malcl\`es to the effect that ``the gifts of bibliography are capable of leading to the discovery of cycles of intellectual and artistic creation.'' As Malcl\`es says, ``Just as the demographer inventories populations, and studies their movements, without knowing each citizen of the country in question, the bibliographer, without having read all books, follows their creation, their purport, and distribution.''

What sets this annotated bibliography apart is that all entries have been read critically and annotated by experts. This means that readers have at their disposal those works regarded as essential by specialists in a large number of different areas of the history of mathematics. From these, it is a far simpler task for researchers to compile increasingly detailed bibliographies of their own, with the knowledge that the most essential material on a given topic appears here as a starting point.

Insofar as trends or cycles of intellectual interest might be discerned from reading this bibliography, it may be of interest to contrast it briefly with the only other major bibliographic reference work to appear for the history of mathematics in the last decade, namely, Kenneth O.\ May's Bibliography and Research Manual of the History of Mathematics (item \xr17\\). As early as 1966 May had written a short article for \jrScience, in which he discussed the problems raised by the fact that the annual list of publications in mathematics was growing rapidly. May's solution was a project he did not complete until 1973---his Bibliography and Research Manual (and even then, it was not really finished, for he continued to update it until his death in 1977). May's Bibliography remains an important reference work for the history of mathematics in all periods and subjects. What sets it apart from this bibliography, however, is the fact that it lacks annotations and is now more than ten years out of date. The number of articles which have appeared in new journals like \jrHistoria Mathematica (founded in 1974), and the number of serious book-length biographies and special histories of specific branches of the history of mathematics (not to mention the stimulus given to all areas of the history of science by the monumental Dictionary of Scientific Biography, item \xr10\\), show the extent to which the history of mathematics has become professionalized in its own right as a subject for serious study in the last ten years.

Special Aspects of This Bibliography: Caveats and Comments

Ralph Waldo Emerson once quipped that consistency was the hobgoblin of small minds. Users of this bibliography should probably keep that in mind---along with George Sarton's equally sardonic statement that bibliography was ``a sin $\ldots$ a real perversity.'' By this he meant that some researchers elevate bibliography to the point where it appears to take precedence over everything else, including the subject matter. However, Sarton was very much aware of the need and crucial contribution that good bibliographies make to professionals and amateurs alike, for Sarton was a consummate if idiosyncratic bibliographer. But he disdained, above all, more lists of titles, however long, as ends in themselves. Such lists he termed ``bewildering'' (Sarton, item \xr48\\, p. 26). Bibliographies took on greater value when annotated, constructed in such a way that expert understanding might guide newcomers to a particular subject.

Each section of this bibliography reflects a considered judgment as to what works are absolutely essential on any given topic or period, accompanied with critical descriptions of those works. Emphasis has been given to the most useful and authoritative secondary sources and, when appropriate, to texts, manuscripts, correspondence, and other varieties of primary sources. Reviews of major items have also been included, especially when they warn readers of special quirks, problems, or prejudices in a given item, or provide substantive additional information relevant to a given subject. Older standard works that have established themselves as a continuing part of the history of mathematics are also, of course, included. The major European languages, especially French and German, are essential tools for the historian of mathematics, and no attempt has been made to minimize the frequency of their appearance in this bibliography. References in other languages, however, are included only when thought essential, but titles in Italian, Spanish, Russian, Chinese, and Japanese have been listed whenever appropriate. Where English translations or their equivalents exist, these have been noted. Finally, truly obscure studies, unless thought crucial, have been minimized in favor of more easily available sources, but not always.

Although most entries are annotated, some are not, if in the opinion of the reviewer the title accurately reflects the content of the reference. In other cases, where an item has appeared elsewhere in the bibliography with sufficient annotation, only a cross-reference has been given. However, if a work is important for differing reasons to more than one section, it has been repeated (again with cross-references), but with a separate annotation tailored specifically to the relevance of the work for the section in which it appears.

Ultimately, in editing this volume I have adopted as pragmatic a position as possible; the final consideration has always been to make this as useful a reference work as possible. Because of the large number of individual contributors, however, it has not always been possible to attain complete consistency in the format and amount of information supplied for each title. Although format guidelines were issued to all contributors, not everyone chose to follow them exactly or consistently. Where practicable, the editor has brought as much uniformity of format to references as possible, but there were limits to which additional information could be retrieved. In most cases what discrepancies remain are of little consequence; the one exception is in the case of different editions of a given work. Some contributors have tried to be as inclusive as possible, incidating the significance between editions, or at least noting the number of different editions of a given work and their dates. Some have preferred to supply the first, others only the most recent edition. Readers should therefore be aware that it is always wise to make their own bibliographic searches to discover which editions or versions of a work may be available to them, as well as the number and differences among various reprintings and editions of a given work. (Usually this can be done most easily by referring to the National Union Catalog of the Library of Congress.)

A major orthographic dilemma facing any bibliographer dealing with material in multiple languages is, of course, the different possible spellings and transliterations of a title or author's name. This is most acute for citations in Russian, Japanese, Chinese, and Arabic. One notable example in this bibliography is that of A. P. Youschkevitch, whose name variously appears in some references as Juschkewitsch, Ju\v skevi\v c, Juschkevic, Youskevich, or Youschkevitch. The practice that has been followed in all cases here is to present a given name as it is spelled on the title page of the work in question. Thus, one will find item \xr 355\\ listing ``Youschkevitch,'' with item \xr 467\\ as ``Juschkewitsch,'' one reflecting a French, the other a German translation. In the indexes at the end of the book, however, all are cross-referenced to the canonical spelling that has been otherwise adopted in this bibliography, namely, ``Youschkevitch.'' Other but less complicated cases of variant transliterations include ``Bashmakova,'' ``Kowalevskaya,'' and ``Lobachevsky.''

Similar variations occur in the case of Greek names. Here the practice has been followed of giving names in terms of transliterations of Greek spellings, e.g., Diophantos. However, in all citations, names are always given as they appear on title pages, which often follow earlier convention and use the Latinized version of Greek names, e.g., Diophantus.

With but two exceptions, all entries within a given section of the bibliography are arranged alphabetically. As explained in the introduction to the section on Babylonian mathematics, titles there are arranged in chronological order. This makes it possible to follow at a glance the changing currents of research, and for readers to follow sequentially the extent to which understanding of Babylonian mathematics has depended greatly upon the primary sources available at any given time. Thus, the more recent material on Babylonian mathematics tends to be more authoritative in terms of current knowledge, even though earlier works still remain important for their essential texts and other information they contain.

The 19th-century bibliography (pages 176--203) also departs from a strictly alphabetical arrangement, as certain topics within a particular subject area are grouped together and then annotated with a single common entry.


Why would anyone wish to undertake a project such as this one? My own reasons have been both professional and personal, but before saying more, I would like to dismiss one motive for undertaking bibliographic research that has been attributed to George Sarton. Marc De Mey, writing in the 1984 Sarton memorial volume of \jrIsis, interprets Sarton's penchant for bibliography in very psychological terms. What interested De Mey was that Sarton's interest in bibliography seems to have antedated his interest in the history of science. Based upon a letter that Sarton sent to the Chief Librarian of the University of Ghent, dated November 4, 1902, De Mey conjectures as follows: If, as in classical embryology, the order of formation is taken as an indication of primacy (here intellectual), it is obvious that Sarton's interest in bibliographies is more basic than his interest in science to which he, only several years later, applied this attitude in so masterly a fashion. Confronted with such a vigorous need, one feels compelled to take certain psychoanalytic claims seriously and search for the sources of this attitude in early childhood. It seems almost a textbook case. The lonely child George Sarton, losing his mother at a very early age, starves, in May Sarton's words, for the tenderness that vanished with her. Deep insecurity could derive from lesser causes. The collector's attitude is considered a classical response to such insecurity: if life, on the whole, is uncertain, establishing and controlling a well-organized and complete collection of items belonging to a specific domain provides solidity and certainty for one subrealm at least. That attitude is later enthusiastically extended to science as the most solid domain. This is one plausible suggestion, but there might be others. In any case, if one were to engage in a study of Sarton along the lines that Erik Erikson applied to Martin Luther, Sarton's bibliographical bias should play a pivotal role, since in its fervor it comes close to the ``obsessive compensation'' characteristic of many great achievements.

I doubt that any of the contributors to this annotated bibliography would wish to see it in terms of ``obsessive compensation''! In fact, this should remind us of Sarton's own phraseology, as well as his caveat, that bibliography was ``a sin$\ldots$a real perversity.'' Surely this puts the lie to De Mey's interesting if arcane speculation, because Sarton, in the best sense of this bibliography, saw such guides as practical sources of information.

Despite the valiant efforts of the copy editor, it has not always been possible to fill certain gaps. Sometimes publishers' names could not be found, or issue numbers of periodicals within a given volume could not be identified. From time to time the National Union Catalog of the Library of Congress was inaccurate, or its information incomplete. Although I have attempted to bring an overall uniformity to the format of the citations, and to check them all for completeness, I have also tried to resist letting this become a bibliographic obsession. On the other hand, what has been an uncompromised goal is to make certain that each citation provides the essential information necessary to retrieve it from libraries or book sellers with relative ease.

My own reasons, as just indicated, for undertaking this project have been to some degree personal, and to a larger extent professional. Kenneth May was both a friend and a moving force in my own interest in the history of mathematics. This bibliography, for me, honors the efforts he made, especially through Historia Mathematica, to promote the subject in the most professional and international way possible. But it was primarily because I felt a strong need for such a bibliography that I was ultimately persuaded to undertake this project.

Actually, when Robert Multhauf and Ellen Wells first approached me about editing a volume on the history of mathematics for their Bibliographies on the History of Science and Technology series, I was doubtful whether any single individual was capable of surveying the entire history of mathematics from antiquity to the present in any sort of authoritative way. I agreed, however, with their basic premise: authoritative, annotated bibliographies in the history of science would be of great utility to the scholarly community. With this in mind, it seemed reasonable to suggest that a collaborative effort might be the perfect solution, involving a dozen or so experts who might reasonably be expected to cull the best forty or fifty titles in a given area, and provide annotations within a few months. As the editor of Historia Mathematica I was in close contact with leading authorities on virtually every aspect of the history of mathematics. Given assurances that this would be fine, I wrote to several dozen colleagues and modestly proposed (with what in hindsight was too much optimism) that if all were willing to draw up basic lists of essential works in their special fields, a preliminary draft of the bibliography might be possible within six months, with a completed annotated version in print within a year.

My initial letter was answered with a variety of responses. The majority of those to whom I wrote, I am happy to say, responded positively, even enthusiastically. Most recognized a definite need for such a critical bibliography to serve the interests of the history of mathematics and, furthermore, they were willing to take on the job without remuneration, for the sake of the subject and its future. Most agreed that they could comply with my request for preliminary lists within six months. This would allow time to check all of the proposed bibliographies for duplication, cross-reference them as needed, and thereby prevent unnecessary duplication.

The present volume is the result of an extraordinary amount of effort. It could never have been accomplished by a single person, but required the combined efforts of all those contributors who worked together in the best cooperative spirit of scholarly colloboration. This would have pleased Kenneth May greatly, and it is both fitting---and a reflection of the magnanimity of the many scholars who have contributed to this bibliography---that all royalties accruing from its publication will be used to establish a fund in his memory. This fund, in the names of all contributors to this volume, is to be administered by the International Commission for the History of Mathematics, and will be designated specifically to help promote the history of mathematics internationally.

I especially want to acknowledge the continuing help and moral support of three individuals in particular: Robert Multhauf for his persistent encouragement along the way; David Rowe for his diligence in helping to complete and proofread the final version of the bibliography; and Rita Quintas for her care in seeing this volume through the last editorial stages of its production. Moreover, I am happy to express my indebtedness and gratitude to all of the contributors to this volume, not only for their care in producing each of the individual sections, but for their patience owing to the time it has taken to cement the myriad pieces into a coherent and useful whole.

The ultimate goal of this bibliography has been to make the secreta secretorum of the history of mathematics much less a secret history than it may seem to many at present. I am grateful to all who have given so generously of their time and energy in order to make this reference work possible.



1. The information contained in this section of the Introduction draws heavily from Archer Taylor, A History of Bibliographies of Bibliographies (New Brunswick, N.J.: \pb The Scarecrow Press\\, \yr1955\\); Louise N. Malcl\`es, Bibliography, trans.\ T. C. Hines (New York: \pb The Scarecrow Press\\, \yr 1961\\); Georg Schneider, Theory and History of Bibliography (New York: \pb Columbia University Press\\, \yr 1934\\), especially pp.\ \pg 3--24\\; John Thornton and R. I. J. Tully, Scientific Books, Libraries and Collectors (London: \pb Library Association\\, \yr1954\\); and Theodore Besterman, The Beginnings of Systematic Bibliography (London: \pb Humphrey Milford for Oxford University Press\\, \yr1935\\).

2. \au G. Naud\'e\\, Bibliographia Politica (Venice: \pb F. Baba\\, \yr1633\\); also issued in French as La bibliographie politique (Paris: \pb G. Pel\'e\\, \yr1642\\). Strictly speaking, however, the word ``bibliography'' was also used in 1645 by Lewis Jacob de Saint Charles, but in a different sense from that currently understood. Jacob used the word to signify the mechanical writing and transcription of books. See Philip H. Vitale, Bibliography, Historical and Bibliothecal (Chicago: \pb Loyola University Press\\, \yr1971\\), p. \pg 14\\.

3. Le Dictionnaire de l'Acad\'emie fran\c coise (Paris, \pb J. B. Coignard\\, \yr 1694\\; reprinted Lille: L. Danel, 1901; fourth edition, 1762).

4. \au Cornelius \`a Beughem\\, Bibliographia mathematica et artificiosa novissima (Amsterdam: \pb J. \`a Wa\v esberge\\, \yr1688\\).

5. \jrIsis \vl2\\ (\yr1914\\), \pg133\\.

6. \au W. Lorey\\, \ar Gustav Enestr\"om (1852--1923)\\, \jrIsis \vl8\\ (\yr1925\\), \pg314\\.

7. \au G. Sarton\\, \ar For Gustav Enestr\"om's 71st Anniversary\\, \jr Isis \vl5\\ (\yr1922\\), \pg421\\.

8. \au G. Sarton\\, Horus (Waltham, Mass.: \pb Chronica Botanica\\, \yr1952\\), p. \pg ix\\.

9. Ibid., p. \pg71\\.

10.\ \au K. O. May\\, item \xr17\\, p. \pg iii\\.

11.\ \au K. O. May\\, \ar Growth and Quality of the Mathematical Literature\\, \jrScience \vl154\\ (\yr1966\\), \pg1672--1673\\. See also his article with the same title in \jrIsis \vl59\\ (\yr1968\\), \pg363--371\\.

12.\ \au Y. Bar-Hillel\\, \ar Is Information Retrieval Approaching a Crisis?\\ Chapter 20 of Language and Information. Selected Essays on Their Theory and Application (Reading, Mass.: \pb Addison-Wesley\\, \yr1964\\), p. \pg365\\.

13.\ \au Ralph E. O'Dette\\, \ar Russian Translation\\, \jrScience \vl125\\ (March 29, \yr1957\\), \pg 579--585; especially p. 580\\. At the time, R. E. O'Dette was Program Director of the Foreign Science Information Program of the National Science Foundation.

14.\ \au William N. Locke\\, \ar Translation by Machine\\, \jrScientific American \vl194\\ (January \yr1956\\), \pg29--33, especially p. 29\\. Locke was working at MIT in the Department of Modern Languages when he wrote this article.

15.\ See \au A. G. Oettinger\\, \ar An Essay in Information Retrieval or the Birth of a Myth\\, \jrInformation and Control \vl8\\ (\yr1965\\), \pg 64--79\\. Oettinger argues that the deleterious effects of the so-called information explosion are greatly exaggerated, and that the incident involving the Lunts paper is really a ``comedy of errors'' occasioned by ``overzealous proponents in the area of information retrieval,'' as characterized by A. J. Lohwater in his review of Oettinger's essay in \jrMathematical Reviews \vl29\\ (\is6\\) (June \yr1965\\), \#6960.

16.\ \jrMathematical Reviews \vl11\\ (September \yr1950\\), \pg574\\.

17.\ \jrScience \vl125\\ (June 21, \yr1957\\), \pg1260\\.

18.\ \jrScientific American \vl194\\ (March \yr1956\\), \pg6\\.

19.\ \au Malcl\`es\\, ibid., p. \pg8\\.

20.\ See above, note 11.

21.\ \au Marc De Mey\\, \ar Sarton's Earliest Ambitions at the University of Ghent\\, \jrIsis \vl75\\ (\is276\\) (\yr1984\\), \pg42\\.