How Discrete Patterns Emerge from Algorithmic Fine-Tuning: A Visual Plea for Kroneckerian Finitism

Ivahn Smadja (1)

1 SPHERE (UMR_7219) - Sciences, Philosophie, Histoire

This paper sets out to adduce visual evidence for Kroneckerian finitism by making perspicuous some of the insights that buttress Kronecker's conception of arithmetization as a process aiming at disclosing the arithmetical essence enshrined in analytical formulas, by spotting discrete patterns through algorithmic fine-tuning. In the light of a fairly tractable case study, it is argued that Kronecker's main tenet in philosophy of mathematics is not so much an ontological as a methodological one, inasmuch as highly demanding requirements regarding mathematical understanding prevail over mere preemptive reductionism to whole numbers.

Mots clés: philosophy of mathematics; finitism; arithmetization; elliptic functions; Kronecker

Domaines: Histoire, Philosophie et Sociologie des sciences

Ivahn Smadja. How Discrete Patterns Emerge from Algorithmic Fine-Tuning: A Visual Plea for Kroneckerian Finitism. Topoi, 2009, 29 (1), pp.61-75. ⟨10.1007/s11245-009-9067-2⟩. ⟨halshs-00456365⟩