Cookies Policy

This site uses cookies. By continuing to browse the site you are agreeing to our use of cookies.

I accept this policy

Find out more here

Intuition in Mathematics: a Perceptive Experience

No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.

Brill’s MyBook program is exclusively available on BrillOnline Books and Journals. Students and scholars affiliated with an institution that has purchased a Brill E-Book on the BrillOnline platform automatically have access to the MyBook option for the title(s) acquired by the Library. Brill MyBook is a print-on-demand paperback copy which is sold at a favorably uniform low price.

Access this article

+ Tax (if applicable)
Add to Favorites
You must be logged in to use this functionality

image of Journal of Phenomenological Psychology

This study applied a method of assisted introspection to investigate the phenomenology of mathematical intuition arousal. The aim was to propose an essential structure for the intuitive experience of mathematics. To achieve an intersubjective comparison of different experiences, several contemporary mathematicians were interviewed in accordance with the elicitation interview method in order to collect pinpoint experiential descriptions. Data collection and analysis was then performed using steps similar to those outlined in the descriptive phenomenological method that led to a generic structure that accounts for the intuition surge in the experience of mathematics which was found to have four irreducible structural moments. The interdependence of these moments shows that a perceptualist view of intuition in mathematics, as defended by Chudnoff (Chudnoff, 2014), is relevant to the characterization of mathematical intuition. The philosophical consequences of this generic structure and its essential features are discussed in accordance with Husserl’s philosophy of ideal objects and theory of intuition.

Affiliations: 1: Centre for Philosophy of Science LisbonPortugal


Full text loading...


Data & Media loading...

1. Biemel W."Les phases décisives dans le développement de la philosophie de Husserl" Husserl: cahiers de Royaumont 1959Vol Vol. 3 Paris Minuit 32 62
2. Bitbol M., Petitmengin C."A defense of introspection from within" Constructivist foundations 2013Vol Vol. 8 3 269 279
3. Broomé R. Descriptive phenomenological psychological method: an example of a methodology section from doctoral dissertation 2011 San Francisco Saybrook University Ph. D dissertation
4. Cellucci C. Hersh R."Introduction to Filosofia e matematica" 18 Unconventional Essays on the Nature of Mathematics 2006 New York Springer
5. Chudnoff E."The nature of intuitive justification" Philosophical studies 2011aVol Vol. 153 2 313 333
6. Chudnoff E."What intuitions are like" Philosophy and Phenomenological Research 2011bVol Vol. 82 3 625 654
7. Chudnoff E. Osbeck L., Held B."Intuition in mathematics" Rational intuition. Philosophical roots, scientific investigations 2014 Cambridge Cambridge UP
8. Corfield D. Towards a philosophy of real mathematics 2004 Cambridge Cambridge UP
9. Depraz N. Comprendre la phénoménologie. Une pratique concrète 2012 2nd edition Paris Armand Colin
10. Depraz N. Première, deuxième, troisième personne 2014 Zeta Books Online Depraz N.
11. Dieudonné J."L’abstraction et l’intuition mathématique" Dialectica 1975Vol Vol 29 1 39 54
12. Finlay J."Recommendations regarding the language of introspection" Philosophy and phenomenological researchVol Vol. 9 2 212 236 19348
13. Frege G. On the foundations of geometry and formal theories of arithmetic 1971 New Heaven Yale UP
14. Giommi F., Barendregt H. Singh N."Vipassana, insight and intuition: seeing things as they are" Psychology of meditation 2014 Augusta, Georgia-USA Georgia Regents University chap. 7
15. Giorgi A. Psychology as a human science: a phenomenologically based approach 1970 New York Harper & Row
16. Giorgi A. Giorgi A."Sketch of a psychological phenomenological method" Phenomenology and psychological research 1985 Pittsburg Duquesne UP
17. Giorgi A. Poupart J."De la méthode phénoménologique utilisée comme mode de recherche qualitative en sciences humaines: théorie, pratique et évaluation" La recherche qualitative: enjeux épistémologiques et méthodologiques 1997 Montréal Gaétan Morin 341 364
18. Giorgi A. The descriptive phenomenological method in psychology: A modified Husserl approach 2009 Pittsburgh PA Duquesne UP
19. Gödel K. Collected works 1985Vol Vol. iii Oxford Oxford UP
20. Gowers T. Mathematics: a very short introduction 2002 New York Oxford UP
21. Grothendieck A. Récoltes et semailles. Réflexions et témoignages sur un passé de mathématicien 1986
22. Hadamard J. The psychology of invention in the mathematical field 1945 Dover New-York
23. Hersh R. What is mathematics, really? 1999 New York Oxford UP
24. Hersh R. de Moura C.A., Kubrusly C.S."Mathematical intuition: Poincaré, Pólya, Dewey" The Courant-Friedrichs-Lewy (CFL) condition 2013 New York Springer Science+Business Media
25. Husserl E. Finlay J. Logical investigations 1970 New York Humanities Press
26. Husserl E. Kersten F. Ideas pertaining to a pure phenomenology and to a phenomenological philosophy. Book I 1983 The Hague Kluwer AP
27. Kidd C. Osbeck L., Held B."Husserl’s phenomenological theory of intuition" Rational intuition. Philosophical roots, scientific investigations 2014 Cambridge Cambridge UP
28. Petitmengin C. Varela F., Shear J."The intuitive experience" The View from Within. First-person approaches to the study of consciousness. 1999 London Imprint Academic
29. Petitmengin C. L’expérience intuitive 2001 Paris L’Harmattan
30. Petitmengin C., Bitbol M."The validity of first-person descriptions as authenticity and coherence" Journal of Consciousness Studies 2009Vol Vol. 5 363 404
31. Petitmengin C., Lachaux J.-P."Microcognitive science: bridging experiential and neuronal microdynamics" Frontiers in human neuroscience 2013Vol Vol. 7 article 617
32. Poincaré H. La valeur de la science 1905–1970 Paris Flammarion
33. Poincaré H."L’invention mathématique" Science et Méthode 1908–1947 Paris Flammarion 43 63
34. Pólya G. Mathematics and plausible reasoning. Princeton 1954 Princeton UP
35. Pólya G. Mathematical discovery 1980 New York Woley
36. Rodin A."How mathematical concepts get their bodies" Topoi 2010Vol Vol. 29 53 60
37. Rota G.-C."The phenomenology of mathematical proof" Synthese 1997Vol Vol. 111 2 183 196
38. Sokolowski R. Introduction to phenomenology 2000 New York Cambridge UP
39. Van-Quynh A."A phenomenological approach of the intuitive aspect of mathematical practice" Teorema 2015aVol Vol. xxxiv 3 177 196
40. Van-Quynh A."Contexte de découverte en mathématiques: une étude phénoménologique de l’intuition" 2015a Submitted
41. Varela F., Thompson E., Rosch E. The Embodied Mind: Cognitive Science and Human Experience 1991 Cambridge MIT Press
42. Varela F."Neurophenomenology: a methodological remedy for the hard problem" Journal of consciousness studies 1996Vol Vol. 3 4 330 349
43. Vermersch P. L’entretien d’explicitation 1994 Paris ESF
44. Vermersch P."Introspection as practice" Journal of Consciousness Studies. 1999Vol Vol. 6 15 42
45. Vermersch P."Rétention, passivité, visée à vide, intention éveillante. Phénoménologie et pratique de l’explicitation" Explicite 2006Vol Vol. 65 17 30
46. Vermersch P. Depraz N."Le dessin de vécu dans la recherche en première personne. Pratique de l’auto-explicitation" Première, deuxième, troisième personne 2014 Zeta Books Online Depraz N.
47. Wolcott F.L."On contemplation in mathematics" Journal of Humanistic Mathematics 2013Vol Vol. 3 1 74 95
48. Zahavi D. Husserl’s phenomenology 2003 Stanford Stanford UP

Article metrics loading...



Can't access your account?
  • Tools

  • Add to Favorites
  • Printable version
  • Email this page
  • Subscribe to ToC alert
  • Get permissions
  • Recommend to your library

    You must fill out fields marked with: *

    Librarian details
    Your details
    Why are you recommending this title?
    Select reason:
    Journal of Phenomenological Psychology — Recommend this title to your library
  • Export citations
  • Key

  • Full access
  • Open Access
  • Partial/No accessInformation