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Most mathematical textbooks start a subject by going backwards, historically. They will define the terms that were invented to solve a problem in their polished form and then use these definitions and structures to solve a problem towards the end of the book, if at all. This is conceptually clear but often obscures motivation.

One glaring example of this is Galois theory. The original solution of the problem progressed through steps that barely resemble the final product. While some motivation is given, I have not found any book that goes through the historical steps that led to galois theory.

I would like any articles or books that motivate subjects through their historical roots/problems. I think what I am really asking for is a book/article that focuses on problems used to generate theory rather than the construction of a general theory that is later used to solve problems. For instance, I would like a book/article that explains what Lame's approach to fermat's last theorem was and how it failed and led to ideals.

I am particularly interested in books that focus on algebraic number theory, but other fields are very welcome too.

Edit: Thanks for the comment, I forgot to mention that it is crossposted here

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closed as off-topic by Andrés E. Caicedo, Daniel Loughran, Andy Putman, Stefan Kohl, paul garrett Sep 9 '14 at 15:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Andrés E. Caicedo, Daniel Loughran, Andy Putman, Stefan Kohl, paul garrett
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Crossposted at MSE. Already has two answers there. $\endgroup$ – Andrés E. Caicedo Sep 9 '14 at 14:31
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    $\begingroup$ I found the books H.M. Edward:"Fermat's Last Theorem", Cox: "Primes of the Form x²+ny²" and Cohn: "Introduction to the construction of Class Fields" very nice and good. $\endgroup$ – Thomas Riepe Sep 9 '14 at 14:37
  • $\begingroup$ I disagree with those who closed the question. I second for the Edwards book. Books like this are rare and useful, and certainly relevant to those doing "research mathematics". $\endgroup$ – Alexandre Eremenko Sep 10 '14 at 2:57
  • $\begingroup$ I feel that a split of "Questions" into strictly mathematical, and the other more general, educational, philosophical (:-), etc., is long overdue. Perhaps we could have the less strictly mathematical q's in meta, together with entertainment like anecdotes, trivia, mathematical news, even history, etc. $\endgroup$ – Włodzimierz Holsztyński Sep 10 '14 at 6:38
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    $\begingroup$ On my point of view history of mathematics is a part of mathematics, and it does not have to be separated. Same applies to the questions about math literature (of graduate+ level). What is wrong with placing such questions here ? $\endgroup$ – Alexandre Eremenko Sep 10 '14 at 17:55