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27

According to an American Scientist article (Gauss' day of reckoning by Brian Hayes, Volume 94 p. 200) mentioned in the comments, the original source for this story, or at least a story very similar to it, was Gauss zum Gedächtnis, a memorial written very soon after Gauss' death by Wolfgang Sartorius, a colleague of his at Göttingen (however, I am not sure if ...


21

I was originally looking for the first documented reference of another contemporary mathematician calling Gauss the prince to no avail. What we do know is that he was considered, by at least many of his contemporaries (by some accounts all), to be the greatest among them. I do see in The Beginnings and Evolution of Algebra, Volume 19 I. G. Bashmakova, G. S....


14

Gauss portrait was printed on German paper money until recently (10 Mark note), before the introduction of the Euro. However my experience shows that the "general public" in many European countries does not recognize the people whose portraits are printed on their money:-) You can still buy some of these notes here http://www.kleinbottle.com/gauss....


10

Wikipedia also says:"this is not a quote by Gauss, but is (a translation of) the end of a sentence from the biography of Eisenstein by Moritz Cantor (1877), one of Gauss's last students and a historian of mathematics, who was summarizing his recollection of a remark made by Gauss about Eisenstein in a conversation many years earlier". Human memory is tricky ...


10

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 philosopher that are not mathematicians, namely [...] look around at modern philosophers [...] don't their definitions make your hair stand on end? Read in ...


7

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. I will give you a translation here, and some comments of mine. Beforehand, though, I think it is fair to say hat you seem to have been misled when you wrote ...


7

"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 resonances does not require one body to revolve around the other, and Jupiter exerts a major pull on the asteroid belt just as a planet would on its moons. ...


6

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 published (by Lobachevski), it had a poor reception in the beginning. Even among some mathematicians (for example Ostrogradskii). Later when Riemann published his ...


6

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 few correspondents in private letters, Bolyai senior, Gerling, Olbers, Taurinus and Bessel. English translations of relevant excerpts are collected by Burris in ...


5

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] E[xpectationibus] G[eneralibus]; ii) With "Vicimus GEGAN" the great Gauß was alluding to his discoveries on the connection between the arithmetic-geometric ...


5

Gauss's ratio was that of the mean motions $\mathit{[M]}$ (⚴) and $\mathit{[M']}$(♃) of Pallas and Jupiter. (Instead of these letters he used planet symbols, which are shown in their unicode version in brackets.) As can be seen in his Nachlass (Werke, vol. 7, e.g. p. 553), he was expressing the perturbations of Pallas elements as sums of dozens of ...


5

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 mathematical expression for the coefficients of the trigonometric series (Fourier series) for the difference between true anomaly $v$ and mean anomaly $M$: $$v - M = ...


5

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 specialized) method of Gauss. BACKGROUND In 1758, Johann Heinrich Lambert published Observationes Variae in Mathesin Puram (Various observation on pure mathematics) ...


4

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 because he himself worked on this and really read a lot of Gauss's writings. It seems to me from this book that Gauss did not know about the connection with non-...


4

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 title question). Notation In all of Gauss's posthomous papers on elliptic and theta function (which are notoriously difficult to read!) he employs several ...


4

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 for this book. Since the desired reference is reference 279, the relevant pages of Gauss's Nachlass are p.56-57 of volume X,1, which are entitled "Hauptmomente ...


4

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 $f,g$ are polynomials of degree 3. First such transformation was discovered by Landen in 1775, and it is called Landen's transformation. Independently it was ...


4

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 and youth of Gauss. Basically, we have to satisfy ourselves with the bare data of his biography and that kind of information which can be induced from a ...


4

It was Jean Richer who demonstrated the fact that, described in a modern conceptual framework, there were variations in the strength of the earth's apparent gravitational field (in the earth-fixed frame) from point to point. His result was published in 1679. However, the interpretation was complicated and led to a controversy between Newton and Cassini as to ...


3

Gauss derived a new condition for the angle of contact of the capillary surface with the surface of a solid, that was a consequence of his new variational approach to the theory. Before him Laplace and Poisson derived the capillarity theory from hypotheses about molecular forces, which were little known at the time, and so open to criticisms, by Young among ...


3

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's activities in fields related to classical mechanics. According to this treatise, the structure of Gauss's paper can be described in this way: Historical ...


3

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 (elliptical) equation of the center"? . The answer to this question, if interpreted appropriately, indicates that already in 1805 Gauss had deep insights on ...


3

Although it's an old question, but perhaps this insight would be beneficial to those stumbling on this question. Gauss wasn't the first to derive this formula per se. Algebraically, you'd see "how" to derive the formula by working through Gauss' derivation. Purely by observation you'd see that you can pair up the extreme values to get the same sum and just ...


3

Undoubtedly, Gauss' name is attached to the name of the Gauss-Newton method due to his pioneering role in the development and application of the least-squares method to non-linear least-squared problems. As to whether he actually conceived of and employed the Gauss-Newton method to solve such problems, the paper "A Gauss-Newton method for convex composite ...


3

"Curtius's problem" is Schumacher's personal name repeated only by Dickson. By scaling, one can reduce the problem to that about triangles with rational sides and the circumradius, which is equivalent to the more commonly considered problem about triangles whose sides and the area are rationals, since $r=abc/4A$. These, or the version where the sides and the ...


3

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 other, concerning his insights into the orientation of surfaces and non-orientable surfaces. The first question is addressed to some extent in Was Kant a factor ...


3

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. Halley (1693) is credited as the first who wrote the formula algebraically. Dijksterhuis in Lenses and Waves gives detailed description of Huygens's Dioptrica (...


3

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. Waltershausen, "Gauss zum Gedächtniss." Leipzig: Salomon Hirzel 1856 On page 79, we find: Die Mathematik hielt Gauss um seine eigenen Worte zu gebrauchen, ...


3

First of all, one would need to define the meaning of conformality of a map $f$ from a nonregular surface $S$ to the plane at points $p$ of where $S$ is non-regular. This is actually a nontrivial issue. One possibility is to use the "tangent cone" (if it exists, which is not always the case!) $C_p(S)$, and then require for the map $f$ to preserve ...


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