In his “Découverte d’un nouveau principe de mécanique” (1750) Euler offered, for the first time, a proof of the so-called Euler’s Theorem. In this paper I will focus on Euler’s original proof and I will show how a look at Euler’s practice as a mathematician can inform the philosophical debate about the notion of explanatory proofs in mathematics. In particular, I will show how one of the major accounts of mathematical explanation, the one proposed by Mark Steiner in his paper “Mathematical explanation” (1978), is not able to account for the explanatory character of Euler’s proof. This contradicts the original intuitions of the mathematician Euler, who attributed to his proof a particular explanatory character.
Learning from Euler. From mathematical practice to mathematical explanation / Molinini D.. - In: PHILOSOPHIA SCIENTIAE. - ISSN 1775-4283. - ELETTRONICO. - 16:1(2012), pp. 105-127. [10.4000/philosophiascientiae.721]
Learning from Euler. From mathematical practice to mathematical explanation
Molinini D.
2012
Abstract
In his “Découverte d’un nouveau principe de mécanique” (1750) Euler offered, for the first time, a proof of the so-called Euler’s Theorem. In this paper I will focus on Euler’s original proof and I will show how a look at Euler’s practice as a mathematician can inform the philosophical debate about the notion of explanatory proofs in mathematics. In particular, I will show how one of the major accounts of mathematical explanation, the one proposed by Mark Steiner in his paper “Mathematical explanation” (1978), is not able to account for the explanatory character of Euler’s proof. This contradicts the original intuitions of the mathematician Euler, who attributed to his proof a particular explanatory character.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.