Article ID: CBB001220403

Lagrange's Theory of Analytical Functions and His Ideal of Purity of Method (2012)

unapi

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 we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem---especially on 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.

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Authors & Contributors
Grabiner, Judith V.
Krzanowski, W. J.
Halák, Jan
Bingham, N. H.
Welsh, Whitney Elizabeth
Verburgt, Lukas M.
Concepts
Mathematics
Philosophy of mathematics
Geometry
Algebra
Arithmetic
Mathematics and its relationship to science
Time Periods
18th century
19th century
17th century
20th century, early
20th century
Early modern
Places
France
England
Italy
Scotland
Netherlands
Germany
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