Talk:John von Neumann

Subdivision of mathematical works

I notice recently that the Wikipedia article has many of the section headings changed and content moved around, primarily by User:Guillermind81. I believe this is a bit questionable but I wanted to have a discussion on it rather than change things willy nilly. The main reason is that much of von Neumann's work particularly on the applied side is hard to break up into sections like physics or applied math or defense work. For example, his work on quantum logic originated in trying to create a basis for physics theories, but taken on its own it's more closer to the field of pure mathematics in logic or algebra. The 2020 Mathematics Subject Classification classifies it under mathematical logic and quantum theory, with the lattice portions also coming under algebra. Another example is his defense work, much of it was involving around fluid mechanics, computing, or solving various physics and engineering problems where he made fundamental contributions, which would come under the aforementioned sections rather than be one on their own. In this sense perhaps it would be better for the section to be renamed to consulting and keep the technical work to other sections and only focus on consulting in the business sense. A final example I can quickly give is on weather systems and meteorology, which again are heavily related to von Neumann's various works on fluid mechanics. His work here on for example establishing numerical meteorology programs mostly occurred while he was a consultant to the US government. Any comments on this would be appreciated. STEMster42 (talk) 14:25, 6 March 2022 (UTC)

Hi,

I appreciate your comments and apologize for not opening up for discussion earlier. For the most part, I agree with your assessment of von Neumann's work. I'm no expert on mathematical subject classification but I do know that von Neumman was more of a mathematician than anything else. My only reason to change section headings was that you ended up with a long, long section under mathematics and the rest basically got lost, and I felt this could be an obstacle for non-experts who want to become familiar with von Neumman's work. I had no other agenda other than making the article more accessible, but I am ok with your suggested scheme should the other editors agree with it. Thanks. Guillermind81 (talk) 14:48, 14 March 2022 (UTC)

Hi again,

Looking at how it (the article) was before you made your changes, I'll try split it into 'Mathematics', 'Physics' and 'Economics'. Effectively it would remove the applied mathematics section and place its items into the aforementioned three. If you wouldn't mind checking it afterwards to see if you're okay with the changes, that would be great, especially since it would likely make the 'Mathematics' section a bit longer than it is currently. As a side note, are there any opinions on the suitability of the subsection 'Weather systems and global warming' in the 'Computer Science' section? It is strange to me because they don't have much to do with computer science beyond the fact they involve computers, it would likely be something closer to applied mathematics or physics, so perhaps we should keep an applied mathematics section? Or we could move it to the physics section. Additionally, some of the content in the 'Computer Science' section could just as easily belong to a section named something like 'Theoretical Biology' or the such, things like cellular automata and the universal constructor are of the field of artificial life, which is a mix between CS and Theoretical Bio so I can understand if opinions are that it stays in the same place. Cheers. STEMster42 (talk) 14:55, 28 March 2022 (UTC)

I'll be happy to go over your changes. I think we should wait to see how those sections look before we work on the "Computer Science" section (to make sure they "flow"). Thanks. Guillermind81 (talk) 16:25, 28 March 2022 (UTC)

Eugene Wigner's quote on JvN w/ regards to topology and number theory

In the article the following appears, ""Eugene Wigner wrote that "Nobody knows all science, not even von Neumann did. But as for mathematics, he contributed to every part of it except number theory and topology. That is, I think, something unique."[235]"". The source is correct, however I dispute the validity of the quote itself. Wigner gave several similar statements in various places (see [0] for example) about it but the problem with this specific version of it is that it is factually wrong (which is strange because he was friends with JvN).

Von Neumann early in his career did indeed publish a couple papers on various topics in number theory, for example his paper "Zur Prüferschen Theorie der idealen Zahlen" [1], which if I correctly remember deals with a part of the ideal theory of Ernst Kummer which later kinda died out as a research field. Searching this paper on Google shows that it appears in several number theory textbooks which should make it pretty obvious it belongs to number theory. Another one, "Ein System algebraisch unabhängiger Zahlen" [2], likewise with the previous example, a Google search for the paper title in either German or English shows that it once again belongs to number theory. There is at least one other paper he wrote on geometric number theory but it is pretty clear von Neumann did indeed publish on number theory.

The second subject, topology, is a bit more tricky. While in the second paragraph of the article it does say JvN contributed to topology as one of the many mathematics fields, I'm not sure I necessarily agree, as he didn't publish much *specifically* on topology. His work did require extensive knowledge of general topology (for example [3]), but the only paper which I would characterize as belonging specifically to topology is "On Complete Topological Spaces"[4]. JvN never published in algebraic topology or differential topology & manifolds, and only on a small section of general topology.

Overall, while you could argue that JvN didn't contribute to topology, he clearly did to number theory, and thus Wigner's quote is wrong. Additionally I believe that topology should be removed from the part of the second paragraph of the article that lists mathematics fields JvN contributed to. Are there any objects to any of this?

[0]: https://link.springer.com/book/10.1007/978-3-662-07791-7

[1]: https://zbmath.org/?q=an%3A52.0151.02

[2]: https://zbmath.org/?q=an%3A54.0096.02

[3]: https://www.jstor.org/stable/1968692

[4]: https://www.jstor.org/stable/1989693

STEMster42 (talk) 15:32, 28 March 2022 (UTC)

Notes & References

The 'Notes' part of the article seems to mix short and long references. Given that a number of sources are repeatedly cited across many pages, I believe the shortened footnote style [0] would be the best option for the article. If someone could move many of the sources given in the 'Notes' section into the 'References' section and then give shortened references in the format of [0] in the 'Notes' section that would be great. It would also be nice if the named references could be cleaned up as many of the current names aren't very clear to what they refer to.

[0]: https://wiki.alquds.edu/?query=Help:Shortened_footnotes

STEMster42 (talk) 15:42, 28 March 2022 (UTC)

Recognition and Legacy

Currently there exists two sections 'Recognition' and 'Legacy' which in my view broadly refer to the same thing. Under recognition there exists 'cognitive abilities' and 'eidetic memory' while under legacy exists 'mastery of mathematics' and 'honors and awards'. Surely how your mastery of mathematics is known and the honors and awards you receive are a part of your recognition? Previously, and I'll page User:Guillermind81 again because he made some of these changes, mastery of mathematics was under the 'Mathematics' section and 'Honors' was a separate section with the others being the same. My suggestion would be to merge the mastery of mathematics and honors and awards subsections into the recognition section and perhaps rename it 'recognition and legacy' or something like that. A boundary between the two is difficult because while the legacy of a person generally refers to them being known *after death*, recognition could refer to them both while living and after they die. If there is a legacy section it should strictly be for legacy after death, although in my view it would be easier just to have it all under one section.

EDIT: I would also like to add I plan to have a section on his personality, and potentially a subsection on his mathematical personality, however I am unsure of how it could differ/relate to the section on his mastery of mathematics. Perhaps mathematical personality would refer to *how* he did his mathematics while mastery of mathematics would focus on the end product of his mathematical abilities? If anyone has any pointers it would be helpful thanks. STEMster42 (talk) 16:35, 28 March 2022 (UTC)

Career and Private Life

I was reading the Career and Private Life section, and was confused when it said, "On New Year's Day 1930, von Neumann married Marietta Kövesi," and, "In 1930, before marrying Marietta, von Neumann was baptized into the Catholic Church." Was he baptized and married on the same day? If so, it should specify that, maybe something like, "In 1930, just before... ." If not, What's going on? Thanks. Bobby Neir (talk) 14:03, 28 September 2022 (UTC)

Interesting question. The first quote is accurate to the source of it. For the source of the second quote, Bochner's biography page 446, it only states that he was baptized in 1930, and doesn't connect it to his marriage to Marietta which is mentioned only on page 445 (it says he married her before coming to Princeton in 1930), so the phrasing isn't entirely accurate for the second one. For a review of other sources:

Bhattacharya's recent biography says he was married on New Year's day 1930. Dyson's "Turing's Cathedral" says they married in 1929 without being more specific. Dyson also says they arrived in Princeton in February 1930. Israel and Gasca's "The World as a Mathematical Game" says they married before leaving for Princeton in 1930, adding "On this occasion von Neumann converted to Catholicism." (page 15). Poundstone's "Prisoner's Dilemma": "This religious confusion would follow von Neumann through a life that would include a nominal conversion to Catholicism at the time of his first marriage and essentially agnostic beliefs for most of his adult life" (page 11). It also adds on page 17 that "His financée, daughter of a Budapest doctor, agreed to marry him in December. Mariette was Catholic. Von Neumann accepted his wife's faith for the marriage." Ulam's and Halmos' obituaries both mentions their marriage being in 1930. Hargittai's "The Martians of Science" says: "Just before leaving for Princeton, von Neumann went to Budapest and married Mariette Kövesi at the very end of 1929. She was Catholic and the von Neumann family had converted to Catholicism in 1929" (page 81).

Unfortunately from this it isn't exactly clear when exactly he converted and when he married because the sources conflict but it's pretty safe to say it was between December 1929 and January 1930. It's also possible it was on the same day. STEMster42 (talk) STEMster42 (talk) 18:37, 8 October 2022 (UTC)

John Patterson Mayberry

Since there was a recent edit regarding John Patterson Mayberry I thought I would a small comment in case in comes up again in the future. Although on his Mathematics Genealogy Project page[0] his adviser is listed as von Neumann there is reason to doubt this claim. His thesis title is listed as "Abelian Branched Coverings of Knots". To check this, we can look at an obituary of his[1] which says his thesis was on topology (knot theory). We can also look at papers that reference the thesis, for example[2] which on reference 19 states it as his 1955 Princeton PhD thesis. Thus we can be satisfied that this is accurate. However, looking at von Neumann's publications[3] there is nothing on low-dimensional topology or knot theory. Von Neumann himself admitted that he did not feel comfortable with it (evidence given on the main article under the "Mastery of mathematics" heading) so it would be very surprising that he would advise a PhD thesis on it, especially when Princeton at the time already had world leaders in topology, in particular Norman Steenrod, who would be far more suitable for this role. Also to note by the 1950s he was far more involved in military consulting as you can see under the "Consultancies" heading rather than academic work. This also reflects in his publication list which has significantly dried up by this time.

[0]: https://www.genealogy.math.ndsu.nodak.edu/id.php?id=115078

[1]: https://www.dignitymemorial.com/obituaries/st-catharines-on/john-mayberry-6115813

[2]: https://www.ams.org/journals/tran/1982-271-01/S0002-9947-1982-0648083-1/

[3]: https://www.worldscientific.com/doi/epdf/10.1142/9789812831088_bmatter STEMster42 (talk) 19:33, 8 October 2022 (UTC)

Lead is way too long

It does not adequately summarize the body of the article. Thenightaway (talk) 13:14, 29 November 2022 (UTC)