Lagrange's Theory of Analytical Functions and his Ideal of Purity of Method

Giovanni Ferraro (1) , Marco Panza (2)

1 Dipartimento S.T.A.T.
2 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

We reconstruct essential features of Lagrange's theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange's notions of function and algebraic quantity, and concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem --- especially the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method --- the generality and internal organization of the discipline.

Mots clés: Lagrange; Algebraic Analysis; Theory of Analytical Functions; Remainder Theorem

Domaines: Histoire, Philosophie et Sociologie des sciences; Histoire et perspectives sur les mathématiques [math.HO]

Giovanni Ferraro, Marco Panza. Lagrange's Theory of Analytical Functions and his Ideal of Purity of Method. Archive for History of Exact Sciences, 2012, 66, pp.95-197. ⟨hal-00614606⟩