Customer Reviews

Disquisitiones Arithmeticae

5 star:		(9)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

This is a great book. It's the place where modern number theory begins. It's also well enough written that it's enjoyable to read today.

There are two editions and you have to choose carefully. I don't know whether my review will appear on both editions or just one. The softcover is only $47. The hardcover is $129, but it is a REVISED translation. A single person, who does not seem to be have been a mathematician, made the first translation from Latin in 1965. That was revised by a team of 4 scholars in 1986.

That turns out to be important, because the original translator got a few things wrong, like the logic of a double negative. So there are some places where the first (cheaper, softcover, Yale) edition is either wrong or unclear. Many of these problems have been fixed in the second (more expensive, hardcover, Springer-Verlag) edition.

I bought the first edition and I have no regrets, but you will get extra value for your extra money if you buy the second edition.

What blows my mind about Gauss's Disquisitiones is that it is understandable to people like me who don't have an advanced background in mathematics. You just need to move through it slowly and carefully. There is a certain joy that comes along with making the discoveries that Gauss walks you through. A book that will change your outlook on life by enhancing what you see as the basic philosophy underlying numbers and mathematics. Mathemtical magicians like Euler and Lagrange will just confuse and dazzle you with their tricks, but Gauss will give you understanding.

One of the most important books in the history of human thought, and certainly among the top five in the history of mathematics, by the most important mathematician ever. I enjoy reading Gauss' own methods. Especially interesting if you study congruences, cyclotomy, etc.

To add to what's been said about translation errors in the softcover edition, a very large portion of the equations in section V have been carried over incorrectly. Gauss' convention of writing indices in superscript instead of subscript seems to have confused the translator to no end, and indices on variables multiplied together were combined like exponents wherever possible. For instance, what was "t_i t_i" (variable t with an index of i, multiplied by itself) in the original Latin was converted to "t_2i" (variable t with an index of 2i). In the worst example, about HALF of the equations in articles 200-201 are incorrect as given. I haven't seen the revised edition, but I would hope this was corrected.

Apart from this, there are plenty of other, scattered typos, but these are for the most part easy to catch and tolerable. The original Latin version is available for free online on the Gottingen University library website, and it may be worthwhile to keep it handy to double check the equations.

As for the book itself, I cannot possibly recommend it highly enough. It was the first serious math book I ever read, and it inspired me to take up math as a profession. While the actual material covered in D.A. may be a bit outdated, it is a great window into the mind of one of the greatest mathematicians in history. It is a masterpiece, and worth the time (and $40) of any serious math student or professional.

This is an incredible work, painstakingly and lovingly translated by someone with more patience than I might ever have. Thank God there are people out there who can do such tedious things so we can all enjoy these great works in English. This book shows how a master thinks about mathematics. It rolls out of his head like you and I might talk about the weather. If you get but one new idea from this book, it was worth the price. Gauss' contribution of "clock" or modular arithmetic will change the way you think about numbers.

Reading the works of Euler, Gauss, Galois, etc., may seem out of fashion sometimes and in this case this book could be regarded as a little out of date. Nevertheless, always keep on mind Abel's wise words: "Read the masters"! There are plenty of things Gauss may be able to tell us yet.

Gauss wrote Disquisitiones between 1795 and 1801. If I can read and understand Clarke's translation in less time than it took Gauss to write the original, I will be doing well. The mathematics has not been superseded and the historical aspect is extremely valuable.

Before reading (i.e. studying) this book, I thought Hardy's and Apostol's books on the theory of numbers were the best... Those are very good indeed but Gauss's treatment is that of a MASTER !

Once you get used to the symbols, the journey is thrilling : you're dealing with a genius, willing to guide you...

Don't throw your money away in buying the paperback edition, buy the hardcover edition where most of the errors have been corrected and which is much better structured and provides ample space for annotations... i.e. allow yourself a gift and enjoy it !

This book is very good, but not quite excellent. Gauss spent, in my opinion, too much time on the theory of binary forms and too little on the general second-degree equation in two variables that the theory is such a big part of. However, the rest of the book was first-rate, well suited to one of the greatest mathematicians of all time. I considered it money well spent.

A nice fat book filled with arcane mathematics and recondite ideas. If you even know about the existence of this book then you already know whether or not you're going to buy it.