27 votes
Accepted

Autistic Assistant of Gauss used to check Primality

The human computer was the computational prodigy Johann Martin Zacharias Dase (June 23, 1824 - September 11, 1861), who was born in Hamburg, Germany and also died there. He reportedly attended school ...
njuffa's user avatar
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10 votes

Gauss on philosophers

The quote is not accurate but Gauss actually wrote something similar to Schumacher in the letter of 1 November 1844 cited here, where he complains about concepts and definitions given in math books by ...
user6530's user avatar
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10 votes

Non-Euclidean geometry: motivations to develop it at the times of Gauss?

The motivation of discoverers of non-Euclidean geometry (Gauss, Lobachevski and Bolyai) was their attempts to prove the Fifth postulate of Euclid (to deduce it from the other axioms, or to replace by ...
Alexandre Eremenko's user avatar
9 votes
Accepted

What topological ideas did Gauss introduce to his student Möbius?

While you already accepted an answer, it seems not superfluous to add another one, in particular since you are implicitly asking for a better translation/understanding of the passage you quoted. ...
Peter Heinig's user avatar
8 votes

What was the "libration of Pallas" that Gauss studied, when Pallas is not a moon of Jupiter?

"Libration" loosely refers to longitudinal oscillations due to orbital resonances. The tidal lock and the trojans, the only situations that Wikipedia mentions, are just special cases. The existence of ...
Conifold's user avatar
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7 votes
Accepted

What was Gauss's method for solving the "trinomial equation"?

I think I can shed some sort of light on the other methods in use for solving trinomials (and general polynomials) from Lambert (1758) to Langrange (1770) and Euler (1776), as well as the (more ...
Sam Gallagher's user avatar
7 votes
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is there an online archive of all of Gauss' works?

The published version of Gauss's collected works, which contains 12 volumes (together with two other volumes that contain treatises by later mathematicians about different aspects of Gauss's work), ...
user2554's user avatar
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6 votes

Gauss's anticipation of quaternions and their relation to congruences

I asked a mathematician who is an expert to abstract algebra and he showed me that Gauss's congruence was actually correct. To prove Gauss congruence let's introduce the following notation: $$x = a+bi,...
user2554's user avatar
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6 votes
Accepted

What is the purpose of Gauss in his letter to János Bolyai when he mentioned "howling Boeotians"?

Gauss was probably afraid of attacks of some mathematicians and philosophers: the idea looked too radical for that time. The history shows that Gauss was right. When non-Euclidean geometry was ...
Alexandre Eremenko's user avatar
6 votes

Do you know about this anecdote or its source where the mother reads out the letter to Gauss and made him Gauss, the mathematician?

The following is taken from the book Walter K. Buhler, "Gauss: a biographical study." Springer Verlag, 1981. Only a very few characteristic and interesting facts are known from the childhood ...
Moishe Kohan's user avatar
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6 votes
Accepted

What was the influence of Gauss on the understanding of the importance of non-Euclidean geometry?

There was not much of an influence. Gauss chose to keep his thoughts out of public view to avoid controversy ("uproar of the Boeotians", as he put it poetically) and only shared them with a ...
Conifold's user avatar
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6 votes
Accepted

How did Gauss determine the number of primes?

For what it's worth: As Goldshtein writes, “Evidently Gauss considered the tabulation of primes as some sort of pastime and amused himself by compiling extensive tables on how the primes distribute ...
akhmeteli's user avatar
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5 votes

Did Gauss know Jacobi's four squares theorem?

I just wanted to summarize several useful facts about Gauss's notation and methodology which i infered from Gauss's original writings after a lot of effort (this doesn't constitute an answer to the ...
user2554's user avatar
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5 votes
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A question on Gauss' "Vicimus GEGAN"

zy_: There are two parts to Biermann's hypothesis on the meaning of "Vicimus GEGAN": i) GEGAN should be read in inverse order as standing for (vicimus) N[exum medii] A[rithmetico-] G[eometricum] ...
José Hdz. Stgo.'s user avatar
5 votes
Accepted

Were Gauss's 1846 remarks on the distinction between right and left related to orientability of surfaces?

The short answer to the title question is likely yes. There are two separate issues discussed in the OP, one is more philosophical on Gauss's disagreements with Kant's apriorism about space, and the ...
Conifold's user avatar
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5 votes

Do you know about this anecdote or its source where the mother reads out the letter to Gauss and made him Gauss, the mathematician?

This story has often been associated with Thomas Edison but is, in fact, a made-up anecdote. The origin of this story is because of the fact that Edison spent only a few months in a formal classroom ...
Big Brother's user avatar
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5 votes

In orbital determination of celestial bodies, why did the case of parabolic or nearly-parabolic orbits require separate development?

The core of the matter is that many of the calculations related to elliptical orbital motion depend on measures and quantities that are referred in some way to an entire cycle around the orbit. For a ...
terry-s's user avatar
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5 votes

Entry 97 in Gauss's diary and the status of "lunar parallax" in the late 18th century

Lunar parallax is a composite problem. Two parts of it are related by the 'horizontal parallax', $\pi$ in the source you cited and linked. It is evaluated in one part of the problem and applied in the ...
terry-s's user avatar
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4 votes
Accepted

Was Gauss aware of the non-euclidean implications of his work on modular forms?

The best source on this is Klein's Lectures on mathematics in XIX century, vol. I. It has a whole chapter on Gauss, with main focus on elliptic integrals and modular forms. Klein can be trusted ...
Alexandre Eremenko's user avatar
4 votes

Meaning of passages by Gauss on the "convergence of expansions (in infinite series) of the (elliptical) equation of the center"?

The "midpoint equation" is another name for the "equation of the centre", related to kepler's equation. What Gauss wanted to determine in this investigation is the asymptotic ...
user2554's user avatar
  • 4,409
4 votes

Where in Gauss's nachlass apears his sketch of a geometric proof for the biquadratic reciprocity law?

Fortunately (and surprisingly) i found the answer very quickly - at the website of Springer they allow the readers to see the first 2 pages of each chapter, and to see the complete list of references ...
user2554's user avatar
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4 votes

Question about Hermite's 1858 solution to the quintic equation using elliptic modular functions and it's relation to Gauss' and Jacobi's work

In general, transformation of elliptic integrals (or differentials) is finding algebraic solutions $F(x,y)=0$ of a differential equation $$\frac{dx}{\sqrt{f(x)}}=\frac{dy}{\sqrt{g(y)}},$$ where $f,g$ ...
Alexandre Eremenko's user avatar
4 votes
Accepted

Who discovered the thin lens equation $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$?

Darrigol's History of Optics names Barrow (1669) and Huygens (1653) as giving semi-verbal case by case variants of the lens formula before Halley, with Molyneux being the first to publish in 1692. ...
Conifold's user avatar
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4 votes
Accepted

A quote attributed to Gauss

The statement attributed to Gauss apparently first appeared in a biography of Gauss by the geologist Wolfgang Sartorius von Waltershausen, published shortly after Gauss's death: W. Sartorius v. ...
njuffa's user avatar
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4 votes

Implications of several unpublished "binomial congruences" of Gauss

I have seen papers and books on Gauss and Jacobi sums discuss such results, e.g., see https://core.ac.uk/download/pdf/82122545.pdf. The book "Gauss and Jacobi sums" by Berndt, Evans, and ...
KCd's user avatar
  • 5,597
3 votes

Several questions about Gauss's mathematical conception of braids

I found a useful reference that might help answering this question (this doesn't constitute an answer to the questions in post). The reference is from p. 46-47 of the book "From Riemann to ...
user2554's user avatar
  • 4,409
3 votes

What were Gauss's results on the attraction of homogenous ellipsoids in his paper from 1813?

This is a very partial answer, but i had to write down the information i collected up to now. One of the best sources on Gauss's article on ellipsoids attraction is Harald Geppert's treatise on Gauss'...
3 votes

Did Gauss know the residues theorem in complex analysis in 1811?

For the completeness of the discussion in this post i must add a link to another relevant question - Meaning of passages by Gauss on the "convergence of expansions (in infinite series) of the (...
user2554's user avatar
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