The nature of progress in mathematics: the significance of analogy

Hourya Benis Sinaceur (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

Whereas logic was traditionally regarded as a critical tool for the foundation or for the theoretical clarification of concepts, it has become "an effective tool for mathematical research". In particular, model theory has transformed logic into an art of invention. Examples borrowed from Tarski's work are given, namely the definability of subsets of real numbers (1931), which led to the concept of semi-algebraic set, and the quantifier elimination, which is the source of remarkable transfer principles.

Mots clés: mathematical invention; analogy; generalization; analysis; model theory; interpretation

Domaines: Histoire, Philosophie et Sociologie des sciences

Hourya Benis Sinaceur. The nature of progress in mathematics: the significance of analogy. Emily Grosholz; Herbert Breger. The Growth of Mathematical Knowledge, 289, Kluwer Academic Publishers, pp.281-293, 2000, Synthese Library, 0-7923-6151-2. ⟨10.1007/978-94-015-9558-2_19⟩. ⟨halshs-02496875⟩