### Bibliography

Some cited works have appeared in several versions. Information about the first often has historical interest, even when reference to a later one is more appropriate. In such cases, both dates are given.

Du Bois-Reymond, Emil. [1872] 1874. On the limits of natural science. *Popular Science Monthly* 5: 17–32. (This American journal was founded in 1872; in altered form it is still published.) Translation by Joseph Fitzgerald of “Über die Grenzen des Naturerkennens,” a lecture presented to the meeting of the Society of German Natural Scientists and Physicians in Leipzig in 1872, and published there that year by Veit & Comp.

Du Bois-Reymond, Emil. 1880. Die sieben Welträthsel (The seven world-riddles). *Monatsberichten der Königlich Preussischen Akademie der Wissenschaften zu Berlin:* 1045–1072. Speech presented on 8 July to the Academy’s Leibniz Celebration. The title was added for later editions.

Ewald, William B., editor. 1996. *From Kant to Hilbert: A Source Book in the Foundations of Mathematics.* Two volumes. Oxford: Clarendon Press. Contains Hilbert [1930] 1996 and Kronecker [1887] 1996.

Franzén, Torkel. 2005. *Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse.* Wellesley: A K Peters.

Galilei, Galileo. [1623] 1960. *The Assayer.* Translated by Stillman Drake. *The Controversy on the Comets of 1618,* by Galileo Galilei et al., 163–336. Philadelphia: University of Pennsylvania Press. Originally published as *Il saggiatore* in Rome, by Giacomo Mascardi.

Gauss, Carl Friedrich. [1808] 1863. Theorematis arithmetici demonstratio nova (New proof of an arithmetical theorem). In Gauss 1863–1929, volume 2, 151–154. Presented to the Society on 15 January 1808 in handwritten form, this German paraphrase was published in *Göttingische gelehrte Anzeigen* on 12 May 1808.

Gauss, Carl Friedrich. [1808] 1929. Astronomische Antrittsvorlesung (Inaugural lecture). In Gauss 1863–1929, volume 12, 177–199.

Gauss, Carl Friedrich. 1863–1929. *Werke.* Twelve volumes. Edited and published by the Gesellschaft der Wissenschaften zu Göttingen (Society of Sciences in Göttingen). Contains items Gauss [1808] 1863 and [1808] 1929.

Hilbert, David. [1900] 1902. Mathematical problems. *Bulletin of the American Mathematical Society* 8 (1902), no. 10: 437–479. Translation by Mary Winston Newson of “Mathematische Probleme,” an address presented to the International Congress of Mathematicians (ICM) in Paris in 1900 and published in *Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse* 1900: 253–297. (*Editor’s note:* Like many items in this Bibliography, Mary Winston Newson's translation into English of Hilbert's address to the 1900 ICM in Paris is available online, including at the AMS website as a full-text pdf of Mathematical Problems: Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900 and at the website of David Joyce of Clark University as Hilbert's Address of 1900 and His 23 Mathematical Problems.)

Hilbert, David. [1922–1923] 1988. *Wissen und mathematisches Denken: Vorlesung* (*Science and Mathematical Thought: Lecture*). Prepared by Wilhelm Ackermann. Göttingen: Mathematisches Institut der Universität.

Hilbert, David. [1925] 1969. On the infinite. In Van Heijenoort 1969, 367–392. Translated by Stefan Bauer-Mengelberg. Originally published as “Über das Unendliche,” *Mathematische Annalen* 95: 161–190.

Hilbert, David. [1930] 1971. Radio address. Forty-five-rpm disk recording of Hilbert reading material excerpted from the original version of Hilbert [1930] 1996. Distributed with Reidemeister 1971.

Hilbert, David. [1930] 1996. Logic and the knowledge of nature. Translated by William B. Ewald. In Ewald 1996, volume 2, 1157–1165. Originally published as “Naturerkennen und Logik,” *Naturwissenschaften* 18: 959–963.

Homer. [1884] 1949. *Odyssey.* Translated by George Herbert Palmer. Cambridge, Massachusetts: Houghton Mifflin Company.

Jacobi, Carl Gustav Jacob. [1830] 1881. Letter to Adrien-Marie Legendre, 2 July. In *Gesammelte Werke,* volume 1, edited by Karl W. Borchardt, 453–455. Berlin: Georg Reimer.

Kant, Immanuel. [1786] 1903. *Metaphysische Anfangsgründe der Naturwissenschaft *(*Metaphysical Foundations of Natural Science*). In *Kant’s* *gesammelte Schriften,* edited by the Royal Prussian Academy of Sciences, volume 4, 465–566. Berlin: Georg Reimer.

Kronecker, Leopold. [1887] 1996. On the concept of number. Translated by William B. Ewald. In Ewald 1996, 947–955. Originally published as “Ueber den Zahlbegriff,” *Journal für die reine und angewandte Mathematik* 101: 337–355.

Minkowski, Hermann. [1908] 1923. Space and time. *The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity,* by H. A. Lorenz et al., with notes by A. Sommerfeld, 73–91. London: Methuen and Company. Translation by W. Perrett and G. B. Jeffrey of “Raum und Zeit,” an address presented to the Society of German Natural Scientists and Physicians in Cologne in 1908 and published in *Jahresbericht der Deutschen Mathematiker-Vereinigung* 10: 75–88.

*Naturwissenschaften.* 1922. Celebratory issue honoring David Hilbert on his sixtieth birthday. *Naturwissenschaften* 10 (issue 4, January 27).

Poincaré, Henri. [1906] 1909. The choice of facts. *Monist* 19: 231–239. Translated by George Bruce Halsted. Address presented at the University of Paris in 1906. There are many more recent versions.

Poincaré, Henri. 1909. *Science et méthode.* Paris: Ernest Flammarion.

Reid, Constance. 1970. *Hilbert. *With an appreciation of Hilbert’s mathematical work by Hermann Weyl. New York: Springer-Verlag New York.

Reid, Constance. 1999. Down the rabbit hole, or Abenteuer im Wunderland (Adventure in Wonderland).* Mitteilungen der Deutschen Mathematiker-Vereinigung* 7: 26–34*.*

Reidemeister, Kurt, editor. 1971. *Hilbert Gedenkband *(*Hilbert Memorial Volume*). Berlin: Springer Verlag. Contains Hilbert [1930] 1971. Reissued in 2012 but, at that time, without Hilbert [1930] 1971.

Rowe, David E. 2013. History quiz: Who linked Hegel’s philosophy with the history of mathematics? *Mathematical Intelligencer* 35: 38–41. While the title question may not be directly relevant to the present paper, Rowe’s background discussion certainly is.

Sartorius von Waltershausen, Wolfgang. 1856. *Gauss zum Gedächtniss.* Leipzig: S. Hirzel. An English translation, *Carl Friedrich Gauss, a Memorial,* by Helen Worthington Gauss, saw limited publication in 1967 by Colorado College in Colorado Springs.

Schiller, Friedrich. 1795. Archimedes und der Schüler. *Die Horen* 11: item 7. This journal was published by Schiller himself. It is accessible online. In English, the title means *The Horæ* (goddesses of the seasons). This poem is reprinted in many editions of Schiller’s works.

Steinhaus, Hugo. [1950] 1983. *Mathematical Snapshots. *With a preface by Morris Kline. Oxford: Oxford University Press.

Tolstoy, Lev Nikolayevich. 1899. *What is to be done? Life.* Translated by Isabel F. Hapgood. New York: Thomas Y. Crowell. A translation of a redacted version of the essay “What is to be done” was published in 1887. The material quoted in the present article, however, is from this revised, uncensored 1899 version. There are many more recent versions.

Van Heijenoort, Jean van. [1967] 1970. *From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931.* Cambridge, Massachusetts: Harvard University Press. Contains Hilbert [1925] 1969.

Vinnikov, Victor. 1999. We shall know: Hilbert’s apology. *Mathematical Intelligencer* 21: 42–46.

Wang Hao. 1988. *Reflections on Kurt Gödel.* Cambridge, Massachusetts: MIT Press.

### About the Author

James T. Smith received the A.B. from Harvard College in 1961 and Ph.D. from the University of Saskatchewan, Regina, in 1970, in foundations of geometry. Since then he has worked primarily at San Francisco State University, mostly teaching and writing, and in software development. He is now retired but fully occupied with history, especially the legacies of Mario Pieri and Alfred Tarski.