Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T01:27:34.165Z Has data issue: false hasContentIssue false

13 - Mathematics

from Part II - Disciplines

Published online by Cambridge University Press:  28 March 2008

By
Craig Fraser
Edited by
Roy Porter
Roy Porter
Affiliation:
Wellcome Institute for the History of Medicine, University College London
Get access

Summary

Considered broadly, mathematical activity in the eighteenth century was characterized by a strong emphasis on analysis and mechanics. The great advances occurred in the development of calculus-related parts of mathematics and in the detailed elaboration of the program of inertial mechanics founded during the Scientific Revolution. There were other mathematical developments of note – in the theory of equations, number theory, probability and statistics, and geometry – but none of them reached anything like the depth and scope attained in analysis and mechanics.

The close relationship between mathematics and mechanics had a basis that extended deep into Enlightenment thought. In the Preliminary Discourse to the famous French Encyclopédie, Jean d’ Alembert distinguished between “pure” mathematics (geometry, arithmetic, algebra, calculus) and “mixed” mathematics (mechanics, geometrical astronomy, optics, art of conjecturing). He classified mathematics more generally as a “science of nature” and separated it from logic, a “science of man.” An internalized and critical spirit of inquiry, associated with the invention of new mathematical structures (for example, non-commutative algebra, non-Euclidean geometry, logic, set theory), represents characteristics of modern mathematics that would emerge only in the next century.

Although there were several notable British mathematicians of the period–Abraham De Moivre, James Stirling, Brook Taylor, and Colin Maclaurin among them – the major lines of mathematical production occurred on the Continent, a trend that intensified as the century developed. Leadership was provided by a relatively small number of energetic figures: Jakob, Johann, and Daniel Bernoulli, Jakob Hermann, Leonhard Euler, Alexis Clairaut, Jean d’Alembert, Johann Heinrich Lambert, Joseph Louis Lagrange, Adrien Marie Legendre, and Pierre Simon Laplace.

Type
Chapter
Information
The Cambridge History of Science , pp. 305 - 327
Publisher: Cambridge University Press
Print publication year: 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bos, Henk J., “Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus,” Archive for History of Exact Sciences, (1974).CrossRefGoogle Scholar
Boyer, Carl, A History of the Calculus and Its Conceptual Development (New York: Dover Publications, Inc., 1959; originally published by Hafner Publishing Company in 1949 under the title “The Concepts of the Calculus, A Critical and Historical Discussion of the Derivative and the Integral”).Google Scholar
Demidov, Sergei, “Création et développement de la théorie des équations différentielles aux dérivées partielles dans les travaux de J. d’Alembert,” Revue d’Histoire des Sciences 35/1 (1982).Google Scholar
Engelsman, Steven, “D’Alembert et les Équations aux Dérivées Partielles,” Dix-Huitième Siècle, 16 (1984).CrossRefGoogle Scholar
Engelsman, Steven B., Families of Curves and the Origins of Partial Differentiation (Amsterdam: North-Holland, 1984).Google Scholar
Euler, , “De infinitis curvis eiusdem generis seu methodus inveniendi aequationes pro infinitis curvis eiusdem generis,” Commentarii Academiae Scientiarum Petropolitanae 7 1734–1735 (1740).Google Scholar
Euler, , “De la controverse entre Mrs. Leibniz et Bernoulli sur les logarithmes des nombres negatifs et imaginaires, Mémoires de l’académie des sciences de Berlin 5 (1749), (1751);Google Scholar
Euler, , Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solution problematis isoperimetrici lattisimo sensu accepti (Lausanne, 1744).Google Scholar
Fisch, Menachem, “‘The Emergency Which Has Arrived’: The Problematic History of Nineteenth-Century British Algebra – a Programmatic Outline,” British Journal for the History of Science, 27 (1994).CrossRefGoogle Scholar
Frängsmyr, T. et al. (eds.), The Quantifying Spirit in the 18th Century (Berkeley: University of California Press, 1990).Google Scholar
Fraser, Craig, “The Origins of Euler’s Variational Calculus,” Archive for History of Exact Sciences, 47 (1994)CrossRefGoogle Scholar
FraserCraig, , “D’Alembert’s Principle: The Original Formulation and Application in Jean D’Alembert’s Traité de Dynamique (1743),” Centaurus, 28 (1985).Google Scholar
Fraser, Craig, “The Calculus as Algebraic Analysis: Some Observations on Mathematical Analysis in the 18th Century,” Archive for History of Exact Sciences, 39 (1989).Google Scholar
Fraser, Craig, “Lagrange’s Analytical Mathematics, Its Cartesian Origins and Reception in Comte’s Positive Philosophy,” Studies in the History and Philosophy of Science, 21 (1990).CrossRefGoogle Scholar
Fraser, Craig, “Joseph Louis Lagrange’s Algebraic Vision of the Calculus,” Historia Mathematica, 14 (1987).CrossRefGoogle Scholar
Fraser, Craig, “J. L. Lagrange’s Changing Approach to the Foundations of the Calculus of Variations,” Archive for History of Exact Sciences, 32 (1985)CrossRefGoogle Scholar
Fraser, , “Isoperimetric Problems in the Variational Calculus of Euler and Lagrange,” Historia Mathematica, 19 (1992).CrossRefGoogle Scholar
Fraser, , “The Background to and Early Emergence of Euler’s Analysis,” in Otte, M. and Panza, M. (eds.), Analysis and Synthesis in Mathematics History and Philosophy, Boston Studies in the Philosophy of Science, vol. 196 (Dordrecht: Kluwer, 1997).Google Scholar
Fraser, , “The Calculus as Algebraic Analysis,” and Marco Panza, “Concept of Function, between Quantity and Form, in the 18th Century,” in Jahnke, H. Niels et al. (eds.), History of Mathematics and Education: Ideas and Experiences (Göttingen: Vandenhoeck & Ruprecht, 1996).Google Scholar
Funkhouser, H. Gray, “Historical Development of the Graphical Representation of Statistical Data,” Osiris, 3 (1937)CrossRefGoogle Scholar
Gillies, Donald (ed.), Revolutions in Mathematics (New York: Oxford University Press, 1992).Google Scholar
Goldstine, Herman H., A History of the Calculus of Variations from the 17th through the 19th Century (New York: Springer-Verlag, 1980)CrossRefGoogle Scholar
Grabiner, Judith V., “Is Mathematical Truth Time-Dependent?” American Mathematical Monthly, 81 (1974)Google Scholar
Grabiner, Judith V., The Origins of Cauchy’s Rigorous Calculus (Cambridge, MA: MIT Press, 1981)Google Scholar
Grattan-Guinness, Ivor, The Development of the Foundations of Mathematical Analysis from Euler to Riemann (Cambridge, MA: MIT Press, 1970)Google Scholar
Grimsley, R. G., Jean d’Alembert (1717–1783) (Oxford: Clarendon Press, 1963).Google Scholar
Guicciardini, Niccolò, The Development of Newtonian Calculus in Britain, 1700–1800 (Cambridge University Press, 1989).CrossRefGoogle Scholar
Hahn, Roger, The Anatomy of a Scientific Institution: The Paris Academy of Science, 1666–1803 (Berkeley: University of California Press, 1971).Google Scholar
Jahnke, H. Niels, Mathematik und Bildung in der Humboldtschen Reform, volume 8 of the series Studien zur Wissenschafts-, Sozial-und Bildungsgeschichte der Mathematik,” eds. Otte, Michael, Schneider, Ivo, and Steiner, Hans-Georg (Göttingen: Vandenhoeck & Ruprecht, 1990).Google Scholar
Katz, Victor J., “Calculus of the Trigonometric Functions,” Historia Mathematica, 14 (1987).CrossRefGoogle Scholar
Lagrange, , Traité de la résolution des équations numériques de tous les degrés (Paris, 1798).Google Scholar
Langer, Rudolph E., “Fourier Series, The Evolution and Genesis of a Theory,” American Mathematical Monthly, 54, pt. 2 (1947).Google Scholar
McRae, Robert, “Condillac: The Abridgement of All Knowledge in ‘The Same is the Same,’” in The Problem of the Unity of the Sciences: Bacon to Kant (Toronto: University of Toronto Press, 1961).Google Scholar
Novy, L., Origins of Modern Algebra (Leiden: Noordhoff International Publishing, 1973).Google Scholar
Ovaert, J. L., “La thèse de Lagrange et la transformation de l’analyse,” in Houzel, Christian et al. (eds.), Philosophie et Calcul de l’Infini (Paris: Francois Maspero, 1976)Google Scholar
Pycior, Helena, “George Peacock and the British Origins of Symbolical Algebra,” Historia Mathematica, 8 (1981)CrossRefGoogle Scholar
Richards, Joan L., “The Art and the Science of British Algebra: A Study in the Perception of Mathematical Truth,” Historia Mathematica, 7 (1980)CrossRefGoogle Scholar
Stigler, Stephen M., The History of Statistics: The Measurement of Uncertainty before 1900 (Cambridge, MA: Harvard University Press, 1986).Google Scholar
Taton, René, “Inventaire chronologique de l’oeuvre de Lagrange,” Revue d’Histoire des Sciences, 26 (1974).Google Scholar
Tilling, Laura, “Early Experimental Graphs,” British Journal for the History of Science, 8 (1975).CrossRefGoogle Scholar
Varignon, Pierre, “Nouvelle formation de spirales beaucoup plus différentes entr’elles que tout ce qu’on peut imaginer d’autres courbes quelconques à l’infini; avec les touchantes, les quadratures, les déroulemens, & les longueurs de quelques-unes de ces spirales qu’on donne seulement ici pour éxemples de cette formation générale,” Histoire de l’Académie royale des sciences avec les mémoires de mathématique et de physique tirés des registres de cette Académie 1704 (Paris, 1706).Google Scholar
Youschkevitch, A. P., “The Concept of the Function up to the Middle of the 19th Century,” Archive for History of Exact Sciences, 16 (1976)Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Mathematics
  • Edited by Roy Porter, Wellcome Institute for the History of Medicine, University College London
  • Book: The Cambridge History of Science
  • Online publication: 28 March 2008
  • Chapter DOI: https://doi.org/10.1017/CHOL9780521572439.014
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Mathematics
  • Edited by Roy Porter, Wellcome Institute for the History of Medicine, University College London
  • Book: The Cambridge History of Science
  • Online publication: 28 March 2008
  • Chapter DOI: https://doi.org/10.1017/CHOL9780521572439.014
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Mathematics
  • Edited by Roy Porter, Wellcome Institute for the History of Medicine, University College London
  • Book: The Cambridge History of Science
  • Online publication: 28 March 2008
  • Chapter DOI: https://doi.org/10.1017/CHOL9780521572439.014
Available formats
×