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I'd like to know if there is a site, or maybe a collection of books, where I can read old articles in mathematics in order to study topics directly from the source, instead reading books in the field. I always feel that my study is incomplete when I don't know the motivation, or the history backgrounds, of the definitions or theorems (even when I read good and classical books).

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20 years ago the answer to your question would have been that the library of your university/math institute is the place you have to consult. I'm quite curios how the internet may be a replacement for that nowadays. –  user20266 Dec 27 '11 at 18:11
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One thing to remember when approaching old papers, the fact that they were "the originals" does not mean they are the best source. First proofs are often cluttered and cumbersome, and it takes a while before people come up with sleek and pretty proofs. Nice examples are Goedel's completeness theorem; ramified vs. unramified forcing; morasses in set theory (I've been told that this makes an excellent example); and there are probably dozens of other great examples. Books, on the other hand, can give you a better retrospective view to understand the theorem and the proof better. –  Asaf Karagila Dec 27 '11 at 19:12
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In addition to my previous comment: the typeset; the terminology; the language; the notation... all underwent several changes - some major - which make old papers very hard to decipher sometimes. –  Asaf Karagila Dec 27 '11 at 19:13
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Something else to notice when looking at old papers: the significance of a result is often not realized at the time it is made. While working on A the author develops B. Nobody nowadays cares about A, but B is what posterity remembers. –  Robert Israel Dec 27 '11 at 20:06
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I completely agree with Asaf's comment. Another great example of this phenomenon is the original proof to the Szemeredi-Trotter inequality in incidence theory. The original proof is 100+ pages long and involves an intricate cell decomposition argument. The slick proof follows from some simple properties of multigraphs, and it takes about no more than 2-3 pages to get through. –  JavaMan Dec 28 '11 at 5:28

6 Answers 6

up vote 3 down vote accepted

Stephen Hawking's God Created the Integers: The Mathematical Breakthroughs That Changed Historycontain many old articles. (as Bruno mentioned already)

Timothy Gowers' The Princeton Companion to Mathematics contain concepts in article form by contemporary mathematicians.

Stewart Shapiro's The Oxford Handbook of Philosophy of Mathematics and Logic contains many papers on logical concepts, again, by contemporary authors.

Blackwell guides can be useful such as The Blackwell Guide to Philosophical Logic (Blackwell Philosophy Guides).

As for online versions please see the related link: List of Interesting Math Blogs

And you are perhaps already familiar with Stanford Encyclopedia of Philosophy; for mathematical biography Mactutor History of Mathematics is resourceful.

Finally, I personally visit Interactive Mathematics Miscellany and Puzzles to understand basic concepts.

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OP is asking for old articles, not encyclopediaeic sources. –  Soarer Dec 28 '11 at 3:41
    
I edited in Stephen Hawking's reference. Some of the encyclopedic sources I cited contain many articles but by contemporary authors but I added them since OP wanted the historical background. –  Sniper Clown Dec 28 '11 at 4:03

Many of the old journals are available online, though some may require subscription. For example, Crelle's Journal, going back to 1826, is freely available at http://gdz.sub.uni-goettingen.de/no_cache/dms/load/toc/?IDDOC=238618

Or you could consult the works of Gauss

http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN235957348

or Euler

http://www.eulerarchive.org/

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There's also Gallica. –  J. M. Dec 28 '11 at 2:40

I haven't browsed their collection in detail, but Numdam has a lot of good stuff.

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http://www.archive.org/ has lots of old stuff.

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Many authors have pre-publication versions of articles they wrote on their personal web page and sometimes old articles are now in the public domain. You can often locate these articles using either: http://scholar.google.com/ or http://www.scirus.com/srsapp/ by searching using some appropriate string or using the author's name.

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There's a wonderful and comprehensive site for finding old papers and book about mathematics. It's called a "library". It probably even has comfortable chairs for sitting and reading...

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I don't really care if I'm downvoted; however, I want to emphasize that this is a serious answer. If you restrict yourself to reading things that are available online, then you are being intellectually lazy. Many, many important papers/books are not available on the internet. –  Adam Smith Dec 28 '11 at 21:00
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Of course, this assumes that the libraries easily accessible to you are indeed well-stocked. For developed countries, this is not much of a problem. For developing countries, it's a bit hit-and-miss. –  J. M. Dec 28 '11 at 23:55
    
@AdamSmith I downvoted your answer and upvoted your comment. ㋡ –  I. J. Kennedy Aug 12 at 21:33

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