Abstract
This chapter embodies a form of “mathematical criticism” that is similar in spirit to that advocated by Imre Lakatos over forty years ago. In essence, it contends that mathematical texts (especially proofs) possess literary qualities which render them amenable to literary-critical scrutiny. The discussion focuses on several classic proofs from the eighteenth and nineteenth centuries that were given by influential mathematicians such as Leonhard Euler and Carl Friedrich Gauss. Various aspects of narrative structure manifest in these texts are examined, particularly the artful shifts in tense that occur at pivotal moments. Although it is often assumed that mathematical proofs exist only in a disembodied form of the present tense, the examples explored in this chapter show that temporal transitions frequently reveal underlying conceptual limitations and methodological uncertainties.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aigner, Martin, and Günter M. Ziegler (eds.). 2014. Proofs from The Book, 4th ed. Berlin, Heidelberg, New York: Springer-Verlag.
Alsina, Claudi and Roger B. Nelsen. 2010. Charming Proofs: A Journey into Elegant Mathematics. Washington DC: The Mathematical Association of America.
Basu, Soham, and Daniel J. Velleman. 2017. On Gauss’ First Proof of the Fundamental Theorem of Algebra. American Mathematical Monthly 124 (8): 688–94.
Bruner, Jerome. 1986. Actual Minds, Possible Worlds. Cambridge, MA: Harvard University Press.
Cain, Alan J. Cain. 2010. “Deus Ex Machina and the Aesthetic of Proof.” Mathematical Intelligencer 32 (3): 7–11.
Colyvan, Mark. 2008. “Mark Colyvan.” In Philosophy of Mathematics: 5 Questions, edited by Vincent F. Hendricks and Hannes Leitgeb, 75−85. Pennsylvania: Automatic Press.
Cornell, Gary, Joseph H. Silverman, and Glenn Stevens (eds.). 1997. Modular Forms and Fermat’s Last Theorem. New York: Springer-Verlag.
Currie, Mark. 2007. About Time: Narrative, Fiction, and the Philosophy of Time. Edinburgh: Edinburgh University Press.
Curtin, Deane W. Curtin, ed. 1982. The Aesthetic Dimension of Science. New York: Philosophical Library.
Day, Gary. 2008. Literary Criticism: A New History. Edinburgh: Edinburgh University Press.
Derrida, Jacque. 2016. Of Grammatology. Translated by Gayatri Chakravorty Spivak, 40th anniversary edition. Baltimore: John Hopkins University Press.
Doxiadis, Apostolos, and Barry Mazur (eds.). 2012. Circles Disturbed: The Interplay of Mathematics and Narrative. Princeton and Oxford: Princeton University Press.
Euler, Leonhard. 1744. De fractionibus Continuis Dissertation. In Commentarii Academiae Scientiarum Petropolitanae 9: 98–137.
Fletcher, Charles R., Sarah Lucas, and Corinne M. Baron. 2010. “Comprehension of Mathematical Proofs.” In Narrative Comprehension, Causality, and Coherence: Essays in Honor of Tom Trabasso, edited by Susan R. Goldman, Arthur C. Graesser and Paul Van Den Broek, 195−208. London and New Jersey: Lawrence Erlbaum Associates.
Gaither, Carl C., and Alma E. Cavazos-Gaither (eds.). 2003. Astronomically Speaking: A Dictionary of Quotations on Astronomy and Physics. Bristol and Philadelphia: Institute of Physics Publishing.
Gauss, Carl Friedrich. 1799. Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse. Helmstedt.
Genette, Gérard. 1983. Narrative Discourse: An Essay in Method. Translated by Jane E. Lewin. Ithaca, New York: Cornell University Press [based on ‘Discours du récit’, a portion of Figures III (1972)].
Goldbach, Christian. 1728. De terminis generalibus serierum In Commentarii academiae scientiarum imperialis Petropolitanae 3: 164–73.
Graves, Robert Percival. 1882. Life of Sir William Rowan Hamilton, vol. 1. Dublin: Hodges Figgis.
Hardy, G.H. 1967. A Mathematician’s Apology. Cambridge: Cambridge University Press.
Harris, Michael. 2012. “Do Androids Prove Theorems In Their Sleep?” In Circles Disturbed: The Interplay of Mathematics and Narrative, edited by Apostolos Doxiadis and Barry Mazur, 130−82. Princeton and Oxford: Princeton University Press.
———. 2017. Mathematics Without Apologies: Portrait of a Problematic Vocation. Princeton, NJ: Princeton University Press.
Havil, Julian. 2003. Gamma: Exploring Euler’s Constant. Princeton, NJ: Princeton University Press.
Healy, Lulu and Celia Hoyles. 2000. “A Study of Proof Conceptions in Algebra.” Journal for Research in Mathematical Education 31 (4): 396−428.
Lakatos, Imre. 1993. Proofs and Refutations: The Logic of Mathematical Discovery, reprint. Cambridge: Cambridge University Press.
Metzidakis, Stamos. 2012. Difference Unbound: The Rise of Pluralism in Literature and Criticism. Amsterdam: Rodopi.
Netz, Reviel. 2009. Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic. Cambridge: Cambridge University Press.
Ostrowski Alexander. 1920. “Über den ersten und vierten Gaussschen Beweis des Fundamentalsatzes der Algebra.” In Nachrichten der Gesellschaft der Wissenschaften Göttingen 2: 1–18. Reprinted in Carl Friedrich Gauss. 2011. Werke, vol. 10, part 2, various editors, 299−316. Cambridge: Cambridge University Press.
Paulos, John Allen. 1998. Once Upon a Number: The Hidden Mathematical Logic of Stories. New York: Basic Books.
Smale, Stephen. 1981. “The Fundamental Theorem of Algebra and Complexity Theory.” Bulletin of the American Mathematical Society 4: 1–36.
Takeuti, Gaisi. 1987. Proof Theory, 2nd ed. Amsterdam: North Holland.
Thomas, R.S.D. 2002. “Mathematics and Narrative.” Mathematical Intelligencer 24 (3): 43−46.
Tomalin, Marcus. 2009. “William Rowan Hamilton and the Poetry of Science.” Romanticism and Victorianism On the Net 54. http://www.erudit.org/revue/ravon/2009/v/n54/038763ar.
Trollope, Anthony. 1950. Barchester Towers. New York: Random House.
Velleman, Daniel J. 1994. How to Prove it: A Structured Approach. Cambridge: Cambridge University Press.
Waugh, Patricia (ed.). 2006. Literary Theory and Criticism: An Oxford Guide. Oxford: Oxford University Press.
Wellek, René. 1963. Concepts of Criticism. New Haven and London: Yale University Press.
Wiles, Andrew. 1995. “Modular Elliptic Curves and Fermat Last Theorem.” Annals of Mathematics 114: 443−551.
Wohlgemuth, Andrew. 1990. Introduction to Proof in Abstract Mathematics. Philadelphia: Saunders College Publishing.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s)
About this chapter
Cite this chapter
Tomalin, M. (2021). Mathematics, Narrative, and Temporality. In: Tubbs, R., Jenkins, A., Engelhardt, N. (eds) The Palgrave Handbook of Literature and Mathematics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-55478-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-55478-1_31
Published:
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-030-55477-4
Online ISBN: 978-3-030-55478-1
eBook Packages: Literature, Cultural and Media StudiesLiterature, Cultural and Media Studies (R0)