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Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in ( Latin), remains to this day a true masterpiece of mathematical examination. It appears that the first and only translation into English was by Arthur A. covered yet, but I found Gauss’s original proof in the preview (81, p. Trove: Find and get Australian resources. Books, images, historic newspapers, maps, archives and more.

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From Wikipedia, the free encyclopedia. The Disquisitiones Arithmeticae Latin for “Arithmetical Investigations” is a textbook of number theory written in Latin [1] by Carl Friedrich Gauss in when Gauss was 21 and first published in when he was This page was last edited on 10 Septemberat General political debate is not disquiditiones. All posts and comments should be directly related to mathematics. The logical structure of the Disquisitiones theorem statement followed by prooffollowed by corollaries set a standard for later texts.

Sometimes referred to as the class number problemthis more general question was eventually confirmed in[2] the specific question Gauss asked was confirmed by Landau in [3] for class number one. Few modern authors can match the depth and breadth of Euler, and there is actually not much in the book that is unrigorous.


In this book Gauss brought together and reconciled results in number theory obtained by mathematicians such as FermatEulerLagrangeand Legendre and added many profound and original results of his own. In other projects Wikimedia Gasus. The Google Books preview is actually pretty good – for instance, in my number theory class, I was stuck on a homework problem that asked us to prove that the sum of the primitive roots of p is mobius p I looked around online and most of the proofs involved either really messy calculations or cyclotomic polynomials, diwquisitiones we hadn’t covered yet, but I found Gauss’s original proof in the preview 81, p.


Gauss’ Disquisitiones continued to exert influence in the 20th century. This was later interpreted as the determination of imaginary quadratic number fields with even discriminant and class number 1,2 and 3, and extended to the case of odd discriminant.

However, Gauss did not explicitly recognize the concept of a groupwhich is central to modern algebraso he did not use this term. Section VI includes two different primality tests. Gauss started to write an eighth section on higher order congruences, but he did not complete this, and it was published separately after his death. Click here to chat with us on IRC! Become a Redditor and subscribe to one of thousands of communities. The treatise paved the way for the theory of function fields over a finite field of constants.

Finally, Section VII is an analysis of cyclotomic polynomialswhich concludes by giving the criteria that determine which regular polygons are constructible i. The Disquisitiones was one of the last mathematical works to be written in scholarly Latin an Disquisitioned translation was not published until It’s worth notice since Gauss attacked the problem of general congruences from a standpoint closely arithmetiicae to that taken later by DedekindGaloisand Emil Artin.

Disquisitiones Arithmeticae – Wikipedia

For example, in section V, articleGauss summarized his calculations of class numbers of proper primitive binary quadratic forms, and conjectured that he had found all of them with class numbers 1, 2, and 3.

Section IV itself develops a proof of quadratic reciprocity ; Section V, which takes up over half of the book, is a comprehensive analysis of binary and ternary quadratic forms.

What Are You Working On? Views Read Edit View history. Clarke in second editionGoogle Books previewso it is still under copyright and unlikely to be found online. Please be polite and civil when commenting, and always follow reddiquette. It is notable for having a revolutionary impact on the field of number theory as it not only turned the field truly rigorous and systematic but also paved the path for modern number theory.


Blanton, and it appears a great book to give to even today’s interested high-school or college student. From Section IV onwards, much of the work is original.

Submit a new text post. Sections I to III are essentially a review of previous results, including Fermat’s little theoremWilson’s theorem and the existence of primitive roots. arithmsticae

Carl Friedrich Gauss, tr. In section VII, articleGauss proved what can be interpreted as the first non-trivial case of the Riemann hypothesis for curves over finite fields the Hasse—Weil theorem. By using this site, you agree to the Terms of Use and Privacy Policy. Please read the FAQ before posting. It appears that the first and only translation into English was by Arthur A. Here is a more recent thread with book recommendations. Everything about X – every Wednesday.

Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways. This includes reference requests – also see our lists of recommended books and free online resources. In general, it is sad how few of the great masters’ works are widely available. MathJax userscript userscripts need Greasemonkey, Tampermonkey or similar. It has been called the most influential textbook after Euclid’s Elements.

Image-only posts should be on-topic and should promote discussion; please do not post memes or similar content here. Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures.

Simple Questions – Posted Fridays. Many of the annotations given by Gauss are in effect announcements of further research of his own, some of which remained unpublished.