User:Dioskorides/sandbox 2

Bernhard Thibaut _______________________________________________________________________________________________________________

I see significant improvement. There are still a few left and one unreliable source that need to be fixed. The main blocking point from my point of view is in the prose, which is at time difficult to understand or redundant. One example:

In later years, Gauss held the emerging field of topology in very high esteem and expected great future developments for it, but since there is so few written, but unpublished material by Gauss on these matters, his influence was made mainly through occasional remarks and oral communications to his colleagues and students Mobius, Listing, and Riemann.

could be rewritten, without losing information, as

Gauss' influence in later years to the emerging field of topology, which he held in high esteem, was through occasional remarks and oral communications to Mobius, Listing, and Riemann.

The word count is above 11,000 but could be significantly reduced by simplifying the prose and removing unnecessary details.

@Dioskorides: I can leave the review on hold if you want to work on these items. Best, Broc (talk) 15:54, 30 June 2024

Another User has already substituted the text in that way you have proposed.

It might be a problem that both main authors User:Dioskorides and User:עשו are not native speakers of English language, so there might be stylistic mistakes. This article has an average daily number of page views of more than 1200. I rely upon this community of interested readers, possibly most well acquainted with English language, that they will correct the mistakes.

You wrote: "The chapter "Non-Euclidean geometries" is especially hard to understand." Since your re-review I was busy with shortening and clarifying the text at various chapters. I think there is a certain reason for obscure wording: we have to follow the sources, and a complex and obscure wording in WP only reflects the complex and obscure wording of the sources. I don't know why they have written in this way, but this sometimes overdetailed, often enthousiatic and - horribile est dictu - not comprehensible argumentation gives the pattern for a similar style of the WP text.

My text is based on Bühler (1981) as "new" author and Klein (1979 [1926]) as the one of the first authors who dealt with that matter. Klein tells the facts: 1. Gauss thought about the limits of Euclidean geometry and alternatives in some notices, 2. Gauss did not publish on it, 3. Gauss gave some hints in letters to colleagues, 4. Gauss asked them for strongest secrecy. 5. Sartorius (1856) was the first one who told about Gauss's thought about the basics of geometry, 6. The unpublished notices and the letters were published in Collected Works, Vol. 8 (1900). I put all these facts except no. 4 into the text.

Klein created a great biographical problem with only one sentence/statement/judgement (p. 57, in my translation): "Apart from this priority, Gauss has the greatest merit to the non-Euclidean geometry by the weight of his authority by which he helped this immediately strongly attacked creation of mind to common attention and finally to victory". This enthousiastic judgement has been taken, with other wording, by a lot of authors like a proved fact. I don't write in this way, following Bühler, who argues in a more distant way. Why? Take the table of contents of vol. 8 of the Collected Works, there you find "Grundlagen der Geometrie" on pp. 159–270. But there are only eight (!) numbers with together about thirty (!) pages with Gauss's notices on geometry, mostly less of any explanations, far from being something like a publication text or only a preprint; it is a collection of ideas, not more, and the eight parts are partly composed of some disseminated material found in the Nachlaß by the editors. And the few statements in the letters are often nebulous and obscure. We can read there fragments out of 17 letters to six correspondents, but mostly no (!) mathematicians, they did not made use of the Gauss informations, they all were not busy with geometry, except the private scholar Taurinus, whom Gauss wrote a comprehensible outline of his ideas of a non-Euclidean geometry in 1824. But Gauss forbed (!) Taurinus to make any use of this stuff or to cite him. So I don't see how Gauss put "the weight of his authority" on it. Gauss did not only avoid influence by publication, he definitely cared for not being brought in connection personally to this subject. One might say, he hid his ideas (ideas, because one can't name them "results"). And I can't see how Gauss could give his "authority" before publication of vol. 8 in 1900. And I would like to know, which of Gauss's ideas on this subject were new in the year 1900? What has he given to the mathematical community, which was not known until the publication of 1900? If we have a theorem or proof or sth. else fulfilling this criterium, we may add this to the chapter definitely, with source. But we don't need enthousiastic wording without substance. (By the way: Klein opinion of "priority" in the sentence above is the same as Gauss' opinion (as I have decribed in "The scholar"), and far from his contemporaries' or today's opinion.)

I have deleted one sentence which you can read in similar way in Bühler (1981, p. 100).

So I am very interested, what "is especially hard to understand" in the "Non-Euclidean geometries". And you wrote "especially": which other chapters or section are not well to understand? And: "There is a lot of redundant prose.": Where do you find still redundant prose? Please tell me, perhaps I can improve it. Greetings.

Non-Euclidean geometries Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory.

Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean. His friend Farkas Wolfgang Bolyai with whom Gauss had sworn "brotherhood and the banner of truth" as a student, had tried in vain for many years to prove the parallel postulate from Euclid's other axioms of geometry.

Bolyai's son, János Bolyai, discovered non-Euclidean geometry in 1829; his work was published in 1832. After seeing it, Gauss wrote to Farkas Bolyai: "To praise it would amount to praising myself. For the entire content of the work ... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." This unproved statement put a strain on his relationship with Bolyai who thought that Gauss was stealing his idea.[61]

Letters from Gauss years before 1829 reveal him obscurely discussing the problem of parallel lines. Waldo Dunnington, a biographer of Gauss, argues in Gauss, Titan of Science (1955) that Gauss was in fact in full possession of non-Euclidean geometry long before it was published by Bolyai, but that he refused to publish any of it because of his fear of controversy.[62][63]

"Gauss himself was only interested in the geometrical aspects of the physical space, but did not care about the philosophical aspects of an enlarged geometry." --