Talk:Carl Friedrich Gauss

References needed

I think the present version is lacking some references.

1. In sub-chapter "Further Investigations" we read in the third section: „…his two papers on biquadratic residues … are considered second in importance …“ Who considers? Such an arbitrary statement needs reference.

2. The same case in the third section of sub-chapter "Analysis": „Perhaps the most remarkables…“

3. Both the first two sections of "Analysis" are completely lacking references. Dioskorides (talk) 18:51, 31 January 2024 (UTC)

1. I remember I Read this statement somewhere, but I do not remember where. Anyway, relative importance is in the eye of the observer, so this is not such an important sentence. Most sources mention his article on biquadratic residues, so it is definitely one of his most important publications in number theory.

2. For the unique aspects of Gauss's tesselation in Gauss's work I can only give my private research on the topic, this Mathoverflow post - https://mathoverflow.net/questions/370190/how-did-gauss-characterize-the-metrical-relations-in-the-uniform-4-4-4-tiling. In particular, it is shown here that the drawing and Gauss's statements next to it can be derived with the help of Poincare disk model, so definitely Gauss had a significant anticipation of later ideas. This tessellation is also mentioned in John Stillwell's book "Mathematics and its history", but without the derivation of Gauss's statements.

3. Can you tell in more details which parts of the first two sections of "Analysis" deserve references? עשו (talk) 19:41, 31 January 2024 (UTC)

Thank you for your rapid answer. I have just completed some references and add some ideas.

1. We could reduce this sentence to "In his two important papers on biquadratic residues (published in 1828 and 1832) Gauss introduces..."

2. We can delete "Perhaps the most..."

I have read your interesting post on Mathoverflow, but unfortunately we can't take it as a reference, only if it were published in a journal — there is a specuial journal on Gauss resaerch in Göttingen, the Mitteilungen der Gauss Gesellschaft — or anywhere else. We can take the www.mathoverflow link in the Weblink section.I think we can preserve this sentence by omitting "Perhaps the moast remarkable of...", without further reference.

3. Please, see my remarks in the next chapter. Dioskorides (talk) 23:48, 1 February 2024 (UTC)

I have changed the two sentences 1. and 2. in this way. --Dioskorides (talk) 10:22, 18 February 2024 (UTC)

Where can we find it?

The article provides a large overview of Gauss’s own writings, and the text often refers to it (e.g. "Gauss (1809)". But in some remarks it is not clear tio which of Gauss’s writings it may concern.

1. Sub-chapter "Analysis", first section: "One of Gauss’s first independent discoveries…" Where published?

2. Sub-chapter "Analysis", second section: "…works which culminates with his discovery in 1808 of the very general Jacobi triple product identity…" Where can I find it?

3. Sub-chapter "Analysis", fifth section: "In 1822 Gauss published his prize winning essay on conformal mappings…" Title? Where published?

And: "In addition, in unpublished fragments from the years 1834-1839…" Which ones? The Collected Works contain all the unpublished things, which of them are concerned?

4. Sub-chapter "Numerical analysis", first section: "In 1815, he published an article on numeric integration…" Title? Where? Dioskorides (talk) 18:52, 31 January 2024 (UTC)

1. It is published in the Schlesinger's essay mentioned in the list of sources, where it is claimed that Gauss discovered the elementary properties of the AGM already in 1794. The exact year cannot be determined, but since already in Gauss's notebooks from the years 1797-1799 he arrived at more advanced results (not only "elementary" results) on diverse topics such as the lemniscate elliptic functions, Landen's transformation, it is quite probable that the dating to 1794 is accurate. Anyway, it was indeed one of his first independent discoveries.

2. For the claim in this sentence just look at the references in Rajan Roy's book.

3. (i) His prize winning essay (1822) is entitled "General solution to the task of depicting the parts of a given surface on another given surface in such a way that the image becomes similar to the smallest parts of what is depicted" (original german: Allgemeine Auflösung der Aufgabe die Theile einer gegebenen Fläche auf einer andern gegebnen Fläche so abzubilden, dass die Abbildung dem Abgebildeten in den kleinstenTheiIen ähnlich wird). You can find it in volume 4 of his collected works.

(ii) These unpublished fragments are in p.311-320 of volume 10-1 of his collected works. It is true that these fragments have not been discussed in depth anywhere (at least as far as I could find) except in Schlesinger's essay, but neverthless thay do represent a significant part of his work.

4. Gauss's article on numerical integration is entitled "Methodus nova integralium valores per approximationem inveniendi" and can be found in volume 3 of of his collected work.

Glad to help. עשו (talk) 19:26, 31 January 2024 (UTC)

1. I have just referenced with Schlesinger. I hope the page numbers are roughly correct.

2. OK, I have forund it.

3(i) I have inserted the missing title. It is an interesting point, that he wrote this article in German and not in Latin, as usual. Gauss claimed to have written in very short time, too short, and that perhaps could be the reason.

3(ii) I think the text dealing with conformal mapping could be better placed into the geodetic chapter, perhaps following or nearby to the sentence "Gauss developed the universal transverse Mercator projection of the ellipsoidal shaped earth (what he named conform projection) for representing geodetical data in plane charts."

4. OK, it is yet in the article.

In my opinion, we now have enough references. Many thanks to you for your valuable and detailed contributions to the mathematical chapter. I think this article will have some chance to become a "Good Article". Greetings --Dioskorides (talk) 00:13, 2 February 2024 (UTC)

Gauss and practical astronomy

The first five sections of the present text deal with Gauss‘ research on the orbits of minor planets, esp. Ceres and Pallas, and his masterpiece „Theoria motus..“. This is standard in Gauss biographies. As it is stated in the text, Gauss' most relevant astronomical activities were finished in 1818, when the new observatory had just gone ready for working. In the following time he mainly cared for geodesy and geophysics, as this were quite usual tasks for astronomers in this time.

But we should not forget that Gauss cared for practical astronomy, too, after 1818. He made a lot of observations and published them rapidly, otherwise the observations would be of low value for other astronomers. In the Collected Work Volume VI we can find the great number of these short communications. But those were standard results, comparable to those of other observatories, not spectacular ones. This may be the reason why biographers tend to ignore them.

Thus I am glad to see, that the last section covers the practical part of astronomical acticity. But I have some objections, the wording seems too "sensational" for me.

1.	"As early as 1799 he did some important work, recorded in entry 97 of his diary, on determining the lunar parallax in any place on Earth by reducing it to a collection of useful formulas, which improved the accuracy of the method of determining geographical location by observing the position of the Moon."

The diary note from 8 April 1799 is: „Formulas novas exactas pro parallaxi eruimus.“ That’s all, and that should not be overinterpreted in that way that he had produced complete new knowledge. His formulae novae were transformations of formulas yet in use by others (Bohnenberger, Lexell), so Gauss decided to keep them for his personal use only and not to publish them, for he presumed them already been published anywhere.

2.	"Later on, he attached importance to revising the values of fundamental astronomical constants, and thereby worked on diverse topics such as the precession and nutation constants, the obliquity of the ecliptic, the proper motion of the Solar System, constructing better stellar aberration tables, as well as the evaluation of the effect of atmospheric refraction on apparent star positions."

What does it mean:"attended importance" and "worked on"? Which results, where published resp. which unpublished papers? Gauss attended, of course, importance to it in his correspondance with Bessel on these subjects. It is widely seen by astronomical historians, that it was Bessel who finally gave the best values for the mentioned astronomical constants in his Fundamenta Astronomiae in 1818. And this corresponds with Brendel‘s view.

So I want to propose a modified text in this way:

"Even early in 1799, Gauss dealt with determination of longitude by use oft he lunar parallax, for which he developed more convient formulas than those were in common use. After his appointment as director of the Göttingen observatory he attached importance to the fundamental astronomical constants in correspondance with Bessel. Gauss himself provided tables for nutation and aberration, the solar coordinates, and refraction." Dioskorides (talk) 10:20, 18 February 2024 (UTC)

I have modified it following the previous proposal. --Dioskorides (talk) 21:26, 28 February 2024 (UTC)

Anyone else notice the signature has got a lil integral? 73.202.158.240 (talk) 05:06, 14 March 2024 (UTC)

Gauss in MacTutor

MacTutor is a useful encyclopedia of biographies. Some months ago, I have removed the MacTutor Gauss article from the external link collection. Why? I found a lot of errors, here there are:

• the school anecdote: is given as a proved fact
• Gauss discovered Bode's law: Bode's law, the Titius–Bode law, was discovered in 1772.
• "Gauss's teacher there was Kästner": right, but misleading, he was not the only one, e.g. Heyne, Lichtenberg.
• "Bolyai [was his] only known friend": In the Wikipedia article I have given other names.
• "They [Bolyai and G.] met in 1799": right, but this was their last meeting, they met first in 1796
• "left Göttingen in 1798 without a diploma": misleading, as if he had finally broken off his studies
• "returned to Brunswick where he received a degree in 1799": definitely no! Which degree? The stories is correctly told in the next sentences, the doctor diploma from Helmstedt University.
• "began corresponding with Bessel, whom he did not meet until 1825": Gauss and Bessel met in 1807, 1810, 1825, and 1842.
• "he went on making observations until the age of 70." Right, but longer, thus misleading. His last observation was with 74.
• "Berlin University" must be replaced by "Prussian Academy", these were different institutions.
• "Minna and her family were keen to move there": I would like to read a reliable proof for this.
• "In 1837, Weber was forced to leave Göttingen": no, he was dismissed, but went on working with Gauss very intensively. He left Göttingen voluntarily in 1842.

Errare humanum est, and nobody is perfect, but this is too much. And worse, there are 67 references at all, but I cannot find one single inline-reference, so we can't see, whether this errors are MacTutor-made or yet in the sources. We could not produce a WP-lemma in this way, and thus the MacTutor text cannot be a reference for it. And in addition, I think it's not useful for readers, if they find facts different in the external links than in the Wikipedia text. Dioskorides (talk) 21:38, 10 April 2024 (UTC)

Ambigeous Referencing

Referencing to Gauss' writings is a special problem. For example this paper:

• 1841: "Intensitas vis magneticae terrestris ad mensuram absolutam revocata". Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores. 8: 3–44. Original (from 1832)

He wrote this in 1832, and presented it to the Royal Academy at its session on 15 December 1832, see the subtitle of the publication Commentatio auctore Carolo Friderica Gauss in concessu Societatis MDCCCXXXII Dec. XV recitata This first publication is part of the series with full title Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores Volumen VIII ad a. MDCCCXXXII - XXXVII; it's edited Gottingae MDCCCXLI. So we have a text of 1832, published in 1841 in the issue of a series for the years 1832–1837.

If we refer to it in the text in the form ...Gauss (18xy), what could "xy" be: Gauss (1832), Gauss (1832-1837), (Gauss 1837), or Gauss (1841)? When I prepared the text, I have seen a certain text with different years in the different sources several times. This may cause confusion.

In the "Selected Writings" chapter I give at first the year of editorial publication, with a link to the digitalized Collected Works. We usually refer to the written text, and it is often necessary to make clear, when his contemporaries could get notice of it. But if we write: "Gauss developed his ideas on magnetism in 18xy", we should take the earliest year for xy, otherwise it were wrong. So, when necessary, I gave the early year in brackets at the of the source, and, in addition, a link to the original per, too, so anyone can check the dates. Dioskorides (talk) 15:47, 12 April 2024 (UTC)