Das Kalenderblatt 100819

18/08/2010 - 13:08 von WM | Report spam
Meine MathOverflow-Episode (19)

Die folgende Frage von Alekk tàuscht eine Superioritàt der
Mathematiker gegenüber den Physikern vor, die in Wirklichkeit nicht
besteht:

Examples where physical heuristics led to incorrect answers?
I have always been impressed by the number of results conjectured by
physicist, based on mathematically non-rigorous reasoning, then (much)
later proved correct by mathematicians. [...] I would be interested in
knowing examples of results conjectured by physicists and later proved
wrong by mathematicians.

Diese Unausgewogenheit habe ich korrigiert.

Why do you ask for wrong physicists only?
Being wrong happens to mathematicians as well. In 1833, the year of
his dead, Adrien Marie Legendre presented an overwiev of proofs of the
parallel axiom to the French Académie des Sciences. It included six
rigorous proofs, three of which using infinite angular areas. (Here
"rigorous" is to be understood in the meaning of his times as present
mathematicians use "rigorous" in the meaning of our times. But
obviously there can never be absolute rigour, neither then nor today.)
{{Allein diese Feststellung muss natürlich jeden von der Unfehlbarkeit
des gegenwàrtigen Instrumentariums überzeugten Matheologen
veràrgern.}}

Or take the first proof of the Cantor-Bernstein theorem bei E.
Schroeder in 1896. The proof was wrong, as Schroeder admitted in a
letter to A. Korselt (who had improved the proof). Korselt gives a
copy of Schroeder's reply in his paper [A. Korselt: "Über einen Beweis
des Äquivalenzsatzes", Math. Ann. 70 (1911) 294.]

Nevertheless, Korselt's corrected version was not accepted in 1902 by
the Annalen. Only 9 years later, he could publish his paper. But that
was not widely noticed, so the incorrect proof survived for a long
time.

Cantor wrote to Hilbert on June 28, 1899 that E. Schroeder in 1896
(and Cantor's student F. Bernstein about Easter 1897) had proved the
theorem. So Cantor never noticed Schroeder's error.

A. Fraenkel mentioned in 1923 (!) that Schroeder's proof was wrong.
[A. Fraenkel: "Einleitung in die Mengenlehre", Springer (1923) p. 58]

E. Zermelo considered Schroeder's proof correct even in 1932. Zermelo
remarks in Cantor's collected works as an editor's note: "... wurde
erst im Jahre 1896 von E. Schroeder und 1897 von F. Bernstein bewiesen
und seitdem gilt dieser 'Aequivalenzsatz' als einer der wichtigsten
Saetze der gesamten Mengenlehre." [E. Zermelo: "Georg Cantor,
Gesammelte Abhandlungen mathematischen und philosophischen Inhalts",
Springer (1932) p. 209]

This shows that wrong things can survive in mathematics for about 35
years. Or even longer? And should that be different now?

Last but not least take take Cantor. He devised transfinite set
theory, according to his own words, in order to apply it to physics,
chemistry, minearlogy, biology, anthropology, medicine and even social
sciences. [Letter from Cantor to Hilbert Sept. 20, 1912]

Physicists and other scientists have shown that he has been wrong in
all respects concerning non-mathematical sciences.

And finally we should remember the late V. I. Arnold: Mathematics is a
part of physics. Physics is an experimental science, a part of natural
science. Mathematics is the part of physics where experiments are
cheap. V.I. Arnold: "On teaching mathematics" (1997). Translated by
A.V. Goryunov http://pauli.uni-muenster.de/~munsteg/arnold.html

Gruß, WM
 

Lesen sie die antworten

#1 Carsten Schultz
18/08/2010 - 13:28 | Warnen spam
Am 18.08.10 13:08, schrieb WM:

Meine MathOverflow-Episode (19)

Die folgende Frage von Alekk tàuscht eine Superioritàt der
Mathematiker gegenüber den Physikern vor, die in Wirklichkeit nicht
besteht:




Nur für jemanden, der nicht lesen kann.

Examples where physical heuristics led to incorrect answers?
I have always been impressed by the number of results conjectured by
physicist, based on mathematically non-rigorous reasoning, then (much)
later proved correct by mathematicians. [...] I would be interested in
knowing examples of results conjectured by physicists and later proved
wrong by mathematicians.

Diese Unausgewogenheit habe ich korrigiert.



Das soll wohl heißen, dass Du etwas geantwortet hast, das nicht auf die
Frage passte. Du missbrauchst Mathoverflow, um Dich zu produzieren, und
beklagst Dich hier nun, dass man das nicht hingenommen hat.

Carsten Schultz (2:38, 33:47)
http://carsten.codimi.de/
PGP/GPG key on the pgp.net key servers,
fingerprint on my home page.

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