BIBLIOGRAPHY.

The following are a few of the general works on the history of mathematics in the nineteenth century, not already mentioned in the foot-notes. For a complete bibliography of recent works the reader should consult the Jahrbuch über die Fortschritte der Mathematik, the Bibliotheca Mathematica, or the Revue Semestrielle, mentioned below.

Abhandlungen zur Geschichte der Mathematik (Leipzig).

Ball, W. W. R., A short account of the history of mathematics (London, 1893).

Ball, W. W. R., History of the study of mathematics at Cambridge (London, 1889).

Ball, W. W. R., Primer of the history of mathematics (London, 1895).

Bibliotheca Mathematica, G. Eneström, Stockholm. Quarterly. Should be consulted for bibliography of current articles and works on history of mathematics.

Bulletin des Sciences Mathématiques (Paris, IIième Partie).

Cajori, F., History of Mathematics (New York, 1894).

Cayley, A., Inaugural address before the British Association, 1883. Nature, Vol. XXVIII, p. 491.

Dictionary of National Biography. London, not completed. Valuable on biographies of British mathematicians.

D’Ovidio, Enrico, Uno sguardo alle origini ed allo sviluppo della Matematica Pura (Torino, 1889).

Dupin, Ch., Coup d’œil sur quelques progrès des Sciences mathématiques, en France, 1830-35. Comptes Rendus, 1835.

Encyclopædia Britannica. Valuable biographical articles by Cayley, Chrystal, Clerke, and others.

Fink, K., Geschichte der Mathematik (Tübingen, 1890). Bibliography on p. 255.

Gerhardt, C. J., Geschichte der Mathematik in Deutschland (Munich, 1877).

Graf, J. H., Geschichte der Mathematik und der Naturwissenschaften in bernischen Landen (Bern, 1890). Also numerous biographical articles.

Günther, S., Vermischte Untersuchungen zur Geschichte der mathematischen Wissenschaften (Leipzig, 1876).

Günther, S., Ziele und Resultate der neueren mathematisch-historischen Forschung (Erlangen, 1876).

Hagen, J. G., Synopsis der höheren Mathematik. Two volumes (Berlin, 1891-93).

Hankel, H., Die Entwickelung der Mathematik in dem letzten Jahrhundert (Tübingen, 1884).

Hermite, Ch., Discours prononcé devant le président de la république le 5 août 1889 à l’inauguration de la nouvelle Sorbonne. Bulletin des Sciences mathématiques, 1890; also Nature, Vol. XLI, p. 597. (History of nineteenth-century mathematics in France.)

Hoefer, F., Histoire des mathématiques (Paris, 1879).

Isely, L., Essai sur l’histoire des mathématiques dans la Suisse française (Neuchâtel, 1884).

Jahrbuch über die Fortschritte der Mathematik (Berlin, annually, 1868 to date).

Marie, M., Histoire des sciences mathématiques et physiques. Vols. X, XI, XII (Paris, 1887-88).

Matthiessen, L., Grundzüge der antiken und modernen Algebra der litteralen Gleichungen (Leipzig, 1878).

Newcomb, S., Modern mathematical thought. Bulletin New York Mathematical Society, Vol. III, p. 95; Nature, Vol. XLIX, p. 325.

Poggendorff, J. C., Biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften. Two volumes (Leipzig, 1863), and two later supplementary volumes.

Quetelet, A., Sciences mathématiques et physiques chez les Belges au commencement du XIXe siècle (Brussels, 1866).

Revue semestrielle des publications mathématiques rédigée sous les auspices de la Société mathématique d’Amsterdam. 1893 to date. (Current periodical literature.)

Roberts, R. A., Modern mathematics. Proceedings of the Irish Academy, 1888.

Smith, H. J. S., On the present state and prospects of some branches of pure mathematics. Proceedings of London Mathematical Society, 1876; Nature, Vol. XV, p. 79.

Sylvester, J. J., Address before the British Association. Nature, Vol. I, pp. 237, 261.

Wolf, R., Handbuch der Mathematik. Two volumes (Zurich, 1872).

Zeitschrift für Mathematik und Physik. Historisch-literarische Abtheilung. Leipzig. The Abhandlungen zur Geschichte der Mathematik are supplements.

For a biographical table of mathematicians see Fink’s Geschichte der Mathematik, p. 240. For the names and positions of living mathematicians see the Jahrbuch der gelehrten Welt, published at Strassburg.

Since the above bibliography was prepared the nineteenth century has closed. With its termination there would naturally be expected a series of retrospective views of the development of a hundred years in all lines of human progress. This expectation was duly fulfilled, and numerous addresses and memoirs testify to the interest recently awakened in the subject. Among the contributions to the general history of modern mathematics may be cited the following:

Pierpont, J., St. Louis address, 1904. Bulletin of the American Mathematical Society (N. S.), Vol. IX, p. 136. An excellent survey of the century’s progress in pure mathematics.

Günther, S., Die Mathematik im neunzehnten Jahrhundert. Hoffmann’s Zeitschrift, Vol. XXXII, p. 227.

Adhémar, R. d’, L’œuvre mathématique du XIXe siècle. Revue des questions scientifiques, Louvain Vol. XX (2), p. 177 (1901).

Picard, E., Sur le développement, depuis un siècle, de quelques théories fondamentales dans l’analyse mathématique. Conférences faite à Clark University (Paris, 1900).

Lampe, E., Die reine Mathematik in den Jahren 1884-1899 (Berlin, 1900).

Among the contributions to the history of applied mathematics in general may be mentioned the following:

Woodward, R. S., Presidential address before the American Mathematical Society in December, 1899. Bulletin of the American Mathematical Society (N. S.), Vol. VI, p. 133. (German, in the Naturwiss. Rundschau, Vol. XV; Polish, in the Wiadomości Matematyczne, Warsaw, Vol. V (1901).). This considers the century’s progress in applied mathematics.

Mangoldt, H. von, Bilder aus der Entwickelung der reinen und angewandten Mathematik während des neunzehnten Jahrhunderts mit besonderer Berücksichtigung des Einflusses von Carl Friedrich Gauss. Festrede (Aachen, 1900).

Van t’ Hoff, J. H., Ueber die Entwickelung der exakten Naturwissenschaften im 19. Jahrhundert. Vortrag gehalten in Aachen, 1900. Naturwiss. Rundschau, Vol. XV, p. 557 (1900).

The following should be mentioned as among the latest contributions to the history of modern mathematics in particular countries:

Fiske, T. S., Presidential address before the American Mathematical Society in December, 1904. Bulletin of the American Mathematical Society (N. S.), Vol. IX, p. 238. This traces the development of mathematics in the United States.

Purser, J., The Irish school of mathematicians and physicists from the beginning of the nineteenth century. Nature, Vol. LXVI, p. 478 (1902).

Guimarães, R. Les mathématiques en Portugal au XIXe siècle. (Coïmbre, 1900).

A large number of articles upon the history of special branches of mathematics have recently appeared, not to mention the custom of inserting historical notes in the recent treatises upon the subjects themselves. Of the contributions to the history of particular branches, the following may be mentioned as types:

Miller, G. A., Reports on the progress in the theory of groups of a finite order. Bulletin of the American Mathematical Society (N. S.), Vol. V, p. 227; Vol. IX, p. 106. Supplemental report by Dickson, L. E., Vol. VI, p. 13, whose treatise on Linear Groups (1901) is a history in itself. Steinitz and Easton have also contributed to this subject.

Hancock, H., On the historical development of the Abelian functions to the time of Riemann. British Association Report for 1897.

Brocard, H., Notes de bibliographie des courbes géométriques. Bar-le-Duc, 2 vols., lithog., 1897, 1899.

Hagen, J. G., On the history of the extensions of the calculus. Bulletin of the American Mathematical Society (N. S.), Vol. VI, p. 381.

Hill, J. E., Bibliography of surfaces and twisted curves. Ib., Vol. III, p. 133 (1897).

Aubry, A., Historia del problema de las tangentes. El Progresso matematico, Vol. I (2), pp. 129, 164.

Compère, C., Le problème des brachistochrones. Essai historique. Mémoires de la Société d. Sciences, Liège, Vol. I (3), p. 128 (1899).

Stäckel, P., Beiträge zur Geschichte der Funktionentheorie im achtzehnten Jahrhundert. Bibliotheca Mathematica, Vol. II (3), p. 111 (1901).

Obenrauch, F. J., Geschichte der darstellenden und projektiven Geometrie mit besonderer Berücksichtigung ihrer Begründung in Frankreich und Deutschiand und ihrer wissenschaftlichen Pflege in Oesterreich (Brünn, 1897).

Muir, Th., The theory of alternants in the historical order of its development up to 1841. Proceedings of the Royal Society of Edinburgh, Vol. XXIII (2), p. 93 (1899). The theory of screw determinants and Pfaffians in the historical order of its development up to 1857. Ib., p. 181.

Papperwitz, E., Ueber die wissenschaftliche Bedeutung der darstellenden Geometrie und ihre Entwickelung bis zur systematischen Begründung durch Gaspard Monge. Rede (Freiberg i./S., 1901).

Mention should also be made of the fact that the Bibliotheca Mathematica, a journal devoted to the history of the mathematical sciences, began its third series in 1900. It remains under the able editorship of G. Eneström, and in its new series it appears in much enlarged form. It contains numerous articles on the history of modern mathematics, with a complete current bibliography of this field.

Besides direct contributions to the history of the subject, and historical and bibliographical notes, several important works have recently appeared which are historical in the best sense, although written from the mathematical standpoint. Of these there are three that deserve special mention:

Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. The publication of this monumental work was begun in 1898, and the several volumes are being carried on simultaneously. The first volume (Arithmetik and Algebra) was completed in 1904. This publication is under the patronage of the academies of sciences of Göttingen, Leipzig, Munich, and Vienna. A French translation, with numerous additions, is in progress.

Pascal, E., Repertorium der höheren Mathematik, translated from the Italian by A. Schepp. Two volumes (Leipzig, 1900, 1902). It contains an excellent bibliography, and is itself a history of modern mathematics.

Hagen, J. G., Synopsis der höheren Mathematik. This has been for some years in course of publication, and has now completed Vol. III.

In the line of biography of mathematicians, with lists of published works, Poggendorff’s Biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften has reached its fourth volume (Leipzig, 1903), this volume covering the period from 1883 to 1902. A new biographical table has been added to the English translation of Fink’s History of Mathematics (Chicago, 1900).