franz lemmermeyer
2006-06-01 07:43:15 UTC
Zitatfledderei ist ein Stilmittel, dessen sich WM und EB gern bedienen.
kuerzlich
einen seiner aelteren Artikel (The battle for Cantorian set theory)
wieder
publizieren lassen, auf dessen Besprechung im Zentralblatt ich hiermit
ganz unbescheiden hinweisen darf; der Bequemlichkeit mancher Leser
wegen habe ich die entscheidenden Abschnitte unten gleich angehaengt.
Der angesprochene Artikel von Poincare ist uebrigens sowohl im
franzoesischen Original, als auch in einer englischen Uebersetzung
mit google leicht online zu finden.
franz
On the first page of the article, he mentions Poincar\'e's
famous characterization of `Cantor's theory of transfinite
numbers as a disease from which he was certain mathematics
would one day be cured', and refers to Poincar\'e [L'avenir
des math\'ematiques, ICM Rome 1908]. There Poincar\'e does
not talk about transfinite numbers at all, but about paradoxes
of set theory, and concludes: ``Whatever may be the remedy
adopted, we can promise ourselves the joy of the physician
called in to follow a beautiful pathological case.'' Thus
Poincar\'e did not want to cure mathematics from set theory,
but set theory from paradoxes. See also J.~Gray [Math. Intell.
13, No.1, 19-22 (1991); Zbl 0716.01027].
The author then goes on to claim that Kronecker `attacked Cantor
personally, calling him a ``scientific charlatan'', a
``renegade'', and a ``corrupter of the youth''', and refers
to [Schoenflies, Acta Math. 50 (1927), 1--23; JFM 53.0026.05].
Schoenflies, however, only wrote that Kronecker's attitude left
the impression that he regarded Cantor as a corrupter of the youth.
On p. 226, he repeats the well known claim that Kronecker, in a
lecture at the Berliner Naturforscher-Versammlung in 1886, called
Lindemann's proof of the transcendence of $\pi$ worthless since
irrational numbers do not exist. The earliest references he offers
for supporting this claim are [Weber, Math. Ann. 43 (1893), 1--25;
JFM 25.0033.03] and [Kneser, Jahresber. DMV 33 (1925), 210--228;
JFM 51.0025.03]; both articles, however, only give Kronecker's
equally famous statement that ``God made natural numbers; all else
is man's work''. For a more historical evaluation of Kronecker's
``rejection'' of irrational numbers, see H.M.~Edwards
[Essays in constructive mathematics; Zbl pre02138825], as well as
J.~Boniface and N.~Schappacher [Rev. Hist. Math. 7 (2001), 207-275;
Zbl 1014.01003]. Let me also remark that in his lectures on
number theory published by Hensel [JFM 32.0184.06], Kronecker gives
the Leibniz series for $\pi/4$ and writes that ``this definition of
the transcendental number $\pi$ is actually of a number theoretic
character''.
Kronecker bezeichnete ihn wie Dein Büchlein schreibt
"vor seinen Studenten als Verderber der Jugend". Poincare meinte (ich
zitiere aus Deinem Büchlein) "Zukünftige Generationen werden die
Mengenlehre als eine Krankheit betrachten von der man sich erholt hat".
J.W. Dauben, seines Zeichens ein "historian of mathematics", hat"vor seinen Studenten als Verderber der Jugend". Poincare meinte (ich
zitiere aus Deinem Büchlein) "Zukünftige Generationen werden die
Mengenlehre als eine Krankheit betrachten von der man sich erholt hat".
kuerzlich
einen seiner aelteren Artikel (The battle for Cantorian set theory)
wieder
publizieren lassen, auf dessen Besprechung im Zentralblatt ich hiermit
ganz unbescheiden hinweisen darf; der Bequemlichkeit mancher Leser
wegen habe ich die entscheidenden Abschnitte unten gleich angehaengt.
Der angesprochene Artikel von Poincare ist uebrigens sowohl im
franzoesischen Original, als auch in einer englischen Uebersetzung
mit google leicht online zu finden.
franz
On the first page of the article, he mentions Poincar\'e's
famous characterization of `Cantor's theory of transfinite
numbers as a disease from which he was certain mathematics
would one day be cured', and refers to Poincar\'e [L'avenir
des math\'ematiques, ICM Rome 1908]. There Poincar\'e does
not talk about transfinite numbers at all, but about paradoxes
of set theory, and concludes: ``Whatever may be the remedy
adopted, we can promise ourselves the joy of the physician
called in to follow a beautiful pathological case.'' Thus
Poincar\'e did not want to cure mathematics from set theory,
but set theory from paradoxes. See also J.~Gray [Math. Intell.
13, No.1, 19-22 (1991); Zbl 0716.01027].
The author then goes on to claim that Kronecker `attacked Cantor
personally, calling him a ``scientific charlatan'', a
``renegade'', and a ``corrupter of the youth''', and refers
to [Schoenflies, Acta Math. 50 (1927), 1--23; JFM 53.0026.05].
Schoenflies, however, only wrote that Kronecker's attitude left
the impression that he regarded Cantor as a corrupter of the youth.
On p. 226, he repeats the well known claim that Kronecker, in a
lecture at the Berliner Naturforscher-Versammlung in 1886, called
Lindemann's proof of the transcendence of $\pi$ worthless since
irrational numbers do not exist. The earliest references he offers
for supporting this claim are [Weber, Math. Ann. 43 (1893), 1--25;
JFM 25.0033.03] and [Kneser, Jahresber. DMV 33 (1925), 210--228;
JFM 51.0025.03]; both articles, however, only give Kronecker's
equally famous statement that ``God made natural numbers; all else
is man's work''. For a more historical evaluation of Kronecker's
``rejection'' of irrational numbers, see H.M.~Edwards
[Essays in constructive mathematics; Zbl pre02138825], as well as
J.~Boniface and N.~Schappacher [Rev. Hist. Math. 7 (2001), 207-275;
Zbl 1014.01003]. Let me also remark that in his lectures on
number theory published by Hensel [JFM 32.0184.06], Kronecker gives
the Leibniz series for $\pi/4$ and writes that ``this definition of
the transcendental number $\pi$ is actually of a number theoretic
character''.