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I'm wondering if it's advantageous to read the original works of Gauss, Jacobi, Cauchy and others (in particular, Jacobi).

Many people say that it's worth it to read original (not translated) works of literature - you have the author's own diction and get a better feel of his/her cogitation. I wonder if it's the same way for mathematics textbooks - is it worth it to study some Latin and etc., and struggle through strange notation, to read the masters?

Apologies if such a question has been asked already, I didn't find it here.

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  • $\begingroup$ Similar question on mathoverflow: mathoverflow.net/questions/28268/do-you-read-the-masters $\endgroup$
    – Anonymous
    Jun 13, 2012 at 14:33
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    $\begingroup$ I've read a little in Jacobi's Vorlesungen über Dynamik, and I found it to be quite readable. He really makes an effort to explain thing thoroughly and clearly, so I would recommend that one (provided that you can read German, of course). $\endgroup$
    – Hans Lundmark
    Jun 13, 2012 at 15:10

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If you're looking to understand the concepts well, rather than get some historical background, I would actually advise against this. More modern treatments will use up to date language, tie theories in with newer concepts that the original authors didn't know about, and have the exposition guided by understanding the ideas in a wider context.

I even find that for research topics barely a decade old, a survey article written a few years later is often better to learn from than the first paper - by knowing some of the results that follow, the survey article authors can phrase the definitions and exposition in a way that makes them seem natural, in a way that the original authors couldn't.

That's not to say there aren't good reasons to read these older works of course, but I find it's much more helpful to have a reasonable understanding of the wider theory first.

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I would agree entirely with Matt's comment about use of up-to-date concepts and notation, and add that there are also possible confusions when reading the original, as sometimes terminology has changed over the years, and can be confusing when a modern term is used by an older author with a somewhat old-fashioned meaning.

On the other hand, I must say that I found it quite a revelation reading Gauss' Disquisitiones Arithmeticae (alas, not in the original Latin, but in a modern-ish translation). BUT I was already pretty conversant with modern treatments of the subject material, and am pretty sure that reading it without knowing the material would have been much less useful.

I guess my advice then would be: yes, it is a good idea to read the original sources, but only after you have a good understanding from modern treatments.

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I will add one thing; I want to answer directly the question appearing in your second paragraph. Indeed, reading the original work of an author (i.e. in the original language) is important in order to get the original feeling and to understand the original meaning. For example, I remember reading about a confusion over Michel Foucault's work: some American philosophers disagreed with the meaning of a certain word in the author's work, but actually the misunderstanding arose from the translation (I think the word was "folie", which can be translated as both "insanity" and "folly"). This issue can sometimes be resolved by returning to the original version, where nothing can be lost in translation.

However, you ask if the same is true of mathematics. As noted above, the answer depends on your intentions. When you are learning mathematics itself, you don't need to understand the author's cogitation. First of all, the results stand by themselves, regardless of whom discovered them. Moreover, what is really needed in general is motivation, which comes from within mathematics, and not from the author's cogitation. And again, the main issue has to do with notation and concepts, which evolves constantly and at an ever more rapid pace.

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I think that studying the genesis of the ideas through history could be very useful to gain a deep comprehension. You can also study authors that explain mathematics from a "genetic" point of view, for example Otto Toeplitz. I leave you one of his quotes:$ \\$

...Mathematics and mathematical thinking are not only part of a special science, but are also closely connected with our general culture and its historic development of mathematical thinking, a bridge to the so called Arts and Sciences and the seemingly so non-historic exact sciences can be found...Our main purpose is to help build such a bridge. Not for the sake of history but for the genesis of problems, facts and proofs, for the sake of the decisive turning points of that genesis. By going back to the roots of these conceptions, back through the dust of times past, the scars of long use would disappear and they would be reborn to us as creatures full of life."

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