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Results tagged with big-list
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user 3777
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
6
votes
books well-motivated with explicit examples
Milne's lecture notes contain many good, standard examples discussed in depth. For example, in Algebraic Number Theory, in the section about Frobenius elements, Milne proves quadratic reciprocity (whi …
5
votes
Books you would like to see translated into English
The Collected Work of Carl Ludwig Siegel.
28
votes
Theorems with unexpected conclusions
The Taniyama-Shimura conjecture (now proved, by Wiles and others): all elliptic curves over $\mathbb Q$ are modular. It's magical that one can give a "formula" for the numbers of points on the curve m …
12
votes
Books you would like to see translated into English
Don Zagier's German book about quadratic forms.
9
votes
Ways to prove the fundamental theorem of algebra
There's a linear algebra proof by Harm Derksen: https://www.jstor.org/stable/3647746. You can also find the article posted here: https://math.berkeley.edu/~ribet/110/f03/derksen.pdf