Talk:Leopold Kronecker

husserl
I believe Kronecker, along with Weierstrass, was Edmund Husserl's chief teacher in mathematics (as mentioned in the Husserl article). Is this fact worth mentioning here anywhere, or is it too off-topic? (I dont know what other well-known students Kronecker might have had.) —rodii 03:26, 1 February 2006 (UTC)


 * I am not sure that's really worth mentioning in this article unless Husserl himself made any significant mathematical contributions; in the Husserl article it would seem somewhat more relevant, but wouldn't serve much of a purpose here. Arundhati bakshi 20:32, 24 March 2006 (UTC)


 * It may have everything to do with Kronecker's and Husserl's attitude that objective infinite sets are fictions.96.248.101.32 (talk) 17:09, 10 April 2018 (UTC)DeMikeal Rice

Infobox
The following infobox has been removed from the article. Pls discuss reasons for or against inclusion to reach consensus.SuperGirl 23:08, 18 November 2006 (UTC)

Keep I find this info very useful as summarised in the infobox. It us now pretty much standard for scientific biographies. SureFire 04:05, 26 December 2006 (UTC)


 * What do you mean with "it is now pretty much standard". If I look at the first twenty articles in Category:German mathematicians, the first category of scientists, then there is only one with such an infobox. -- Jitse Niesen (talk) 13:25, 27 December 2006 (UTC)

Keep. It is much more informative. Consensus here is to reinstate. I have put it back. bunix 10:47, 13 January 2007 (UTC)

Flags in infobox
I think that infoboxes like the one in this article generally should not have flags because the flags do not contain any information and put an emphasis on information that is not important; also see Manual of Style (flags). This is even more pertinent where the flag will not be recognized by many people (I have no proof for this, but I feel I'm well justified in making this assumption). That's why I think the flags should be removed. Discuss.

To make the situation more complicated, Prussia became part of the German Empire during Kronecker's life, so perhaps his nationality changed at that time. -- Jitse Niesen (talk) 15:05, 16 December 2007 (UTC)

Solution of quintic
It might be desirable to clarify the statement "Kronecker solved the quintic equation" so that it does not appear to be in conflict with the Abel-Ruffini theorem, which is often remembered as saying that "the quintic is unsolvable". Abel's theorem says that the general quintic equation cannot be solved in terms of radicals, whereas Kronecker (according to Mathworld) did obtain a formula for the solution of a general quintic, but it is not in terms of radicals. 208.127.218.127 (talk) 06:22, 22 December 2008 (UTC)

Clarification
What is this supposed to be? "---Intermezo-- There are now also people who are like finitism Because we can't walk an infinite route. ---End intermezo---" — Preceding unsigned comment added by 95.209.254.196 (talk) 21:31, 1 November 2011 (UTC)

Representation Theory
I'm surprised that there's nothing about Kronecker's work in group theory here (or at least a reference to the relevant articles. Kronecker's work was fundamental to that area (see, for example, Fulton and Harris). Rwilsker (talk) 19:07, 31 March 2010 (UTC)

finitism?
Did Kronecker espouse finitism (as opposed to constructivism)? Does anyone have a source for this? Tkuvho (talk) 15:16, 18 April 2012 (UTC)


 * Yes he did. He could not conceive a clear constructivism since no one at the time had a clear idea of construction or algorithm, and standards of proof were so inexplicit that people could not well separate constructively unacceptable reductio proof from constructively valid modus tollens.   They had a clear idea of finiteness.  As sources, see Howard Stein, "Logos, logic, and logistike': Some philosophical remarks on the ninteenth century transformation of mathematics" in Aspray and Kitcher eds. _History and Philosophy of Modern Mathematic_, University of Minnesota Press, 1988, pp. 238--59.  Or Eric Temple Bell, _The Development of Mathematics_, McGraw-Hill, 1945, around p. 561.  Sean Walsh in yet unpublished work discusses archival sources of Kronecker's ideas that have just recently become available. Colin McLarty (talk) 13:25, 8 September 2013 (UTC)

Wife's death
Kronecker's wife's death is variously said to have been caused by a skiing accident and a climbing one. — Preceding unsigned comment added by 88.150.234.8 (talk) 11:25, 26 June 2014 (UTC)

Source for Kronecker quote re integers
While researching the Kronecker quote re integers, I found the German original in an obituary by Weber. The article already has a partial reference to Weber's obituary, but it appears to have an incorrect date (1893 instead of 1891-2), and the link is a redirect to the one I added in a footnote. The 1893 reference could probably be removed as redundant. --192.183.212.185 (talk) 01:35, 5 October 2014 (UTC)

Kronecker quote re the integers
The comments in the article about the Kronecker quote re the integers were removed in this edit:

'[Kronecker] was quoted by as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" (traditionally rendered: "God made natural numbers; all else is the work of man"; he says Zahlen, not natürlichen Zahlen, but Zahlen, like the English word "numbers", can be interpreted as meaning integers).'

For the record, "ganzen Zahlen" means "integers".

--192.183.212.185 (talk) 02:15, 5 October 2014 (UTC)

In colloquial English: "In the mind of God is accounted the whole of mathematics, but it is left to "our fellows" to understand." — Preceding unsigned comment added by 66.87.115.61 (talk) 03:16, 6 May 2016 (UTC)

Several more possible translations:

In God's mind is accounted the whole of mathematics, Together man's purpose is to fulfill the work of creation.

The whole of mathematics our Dear Lord God has made, Together man's purpose is to fulfill the work of creation. — Preceding unsigned comment added by 2602:304:B17C:4550:41E5:FA3D:FE38:66E2 (talk) 09:45, 7 May 2016 (UTC)

Its also a reference to Genesis, "In the beginning God created the heavens and the earth." And, God created man, and "Be fruitful and increase in number, fill the earth, ..." — Preceding unsigned comment added by 2602:304:B17C:4550:BC91:D150:F63C:2BBE (talk) 19:03, 6 May 2016 (UTC)

Also, "numbers" is a reference to the Biblical book of Numbers. I think the reference means, they were about to enter the promised land (as we understand it). — Preceding unsigned comment added by 2602:304:B17C:4550:BC91:D150:F63C:2BBE (talk) 19:09, 6 May 2016 (UTC)

There are at least four levels of interpretation: 1) literal, 2) deep meaning, 3) comparative meaning (via similar quotes), 4) secret or esoteric meaning. Usually, this is in the context of the author of quote. — Preceding unsigned comment added by 2602:304:B17C:4550:BC91:D150:F63C:2BBE (talk) 19:14, 6 May 2016 (UTC)

Kronecker was a German and a businessman, well educated, and familiar with biblical topics. — Preceding unsigned comment added by 2602:304:B17C:4550:BC91:D150:F63C:2BBE (talk) 19:19, 6 May 2016 (UTC)

Remember that these quotes are in the context of the 19th century German scientific community, and can be interpreted as a conversation among German intellectuals. They can be interpreted on several levels and reveal the thinking of the community at the time. The 19th century was really a time of understanding and constructing the tools that would make possible the amazing developments of the 20th century. Only a partial picture of what we see today was available then. What one might view, is an immense scaffolding that still had to be filled in by later learning in physics and mathematics. — Preceding unsigned comment added by 66.87.115.61 (talk) 03:30, 6 May 2016 (UTC)


 * Well the Mathematische Annalen is a better known publication than the Jahresbericht, so perhaps the Annalen reference should be retained. Tkuvho (talk) 07:04, 5 October 2014 (UTC)
 * I am not sure why Gray's citation is necessary. Weber is already a secondary source, since we quote him on Kronecker.  Gray is a tertiary source which is preferably avoided at wiki as far as I understand policy. Could someone comment? Tkuvho (talk) 07:08, 5 October 2014 (UTC)


 * Gray is being cited as a source for the English translation. The link in the Weber, H. (1893) reference is a redirect to Weber's obituary in the Jahresbericht dated 1891-1892 (See the Titelseite). --50.53.39.240 (talk) 14:43, 5 October 2014 (UTC)
 * Gray claims in footnote 87 that the source for the quote is a lecture of Kronecker's from 1886. Is this based on Weber? If so, is Weber based on a written record or on his own memory? What I find incongruous about this quote is precisely the fact that it mentions the integers rather than the natural numbers. Kronecker was almost as suspicious of negative numbers as he was of transcendental numbers. Tkuvho (talk) 14:51, 5 October 2014 (UTC)
 * Weber gives the 1886 date on page 19 (third paragraph from the bottom). --50.53.39.240 (talk) 15:06, 5 October 2014 (UTC)
 * Thanks. Is it possible to determine from what he writes whether there is a written set of notes, or whether he is reporting from memory? Tkuvho (talk) 15:23, 5 October 2014 (UTC)
 * That would be good to know. For reference, here is a transcription of Weber's sentence from page 19:
 * "Manche von Ihnen werden sich des Ausspruchs erinnern, den er in einem Vortrag bei der Berliner Naturforscher-Versammlung im Jahre 1886 that: 'Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk'."
 * NB: That is my transcription. --50.53.39.240 (talk) 15:42, 5 October 2014 (UTC)
 * Even Gray being cited as a source for the translation is problematic. The translation is very old. Kronecker's statement is gender-neutral. The translation was at the time of the translation, but is not anymore. Someone should make a new translation and publish it, so that it can be cited in Wikipedia. 85.212.146.242 (talk) 20:44, 24 January 2022 (UTC)