19/11/08 16:46:01.10 nN7QsxvT.net
>>613
つづき
(1) When was the statement of the monodromy theorem first fully
formulated (resp. : proven)?
(2) When did the normal form for elliptic curves
y^2 = x(x ? 1)(x ? λ),
which is by nowadays’ tradition called by many (erroneously?)
‘the Legendre normal form’ first appear?
(3) The old ‘Jacobi inversion theorem’ is today geometrically formulated through the geometry of the ‘Jacobian variety J(C)’
of an algebraic curve C of genus g: when did this formulation
clearly show up (and so clearly that, ever since, everybody was
talking only in terms of the Jacobian variety)?
The above questions not only deal with themes of research which
were central to Weierstras’ work on complex function theory, but indeed they single out philosophically the importance in mathematics of
clean formulations and rigorous arguments.
Ath his point it seems appropriate to cite Caratheodory, who wrote
so in the preface of his two volumes on ‘Funktionentheorie’ ([Car50]):
‘ The genius of B. Riemann (1826-1865) intervened not only to bring
the Cauchy theory to a certain completion, but also to create the foundations for the geometric theory of functions. At almost the same time,
K. Weierstras(1815-1897) took up again the above-mentioned idea of
Lagrange’s 1
, on the basis of which he was able to arithmetize Function
Theory and to develop a system that in point of rigor and beauty cannot
be excelled. The Weierstras tradition was carried on in an especially
pure form by A. Pringsheim (1850-1941), whose book (1925-1932) is
extremely instructive.’
つづく