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Results tagged with big-list
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user 461
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.
3
votes
Examples of common false beliefs in mathematics
Here are two beliefs. I think everybody will agree that one of them, at least, is false. I adhere to the second one.
Belief 1. The simplest way to compute the exponential $e^A$ of a complex square mat …
5
votes
Examples of common false beliefs in mathematics
Here are two beliefs. I think everybody will agree that one of them, at least, is false. I adhere to the second one.
Belief 1. There is no simple generalization of the Hodge Theorem to noncompact mani …
18
votes
Examples of common false beliefs in mathematics
By googling one sees that each of the following statements has a significant number of believers:
(1) the vector space {0} has no basis,
(2) the empty set is a basis of {0} by convention,
(3) the s …
56
votes
Quick proofs of hard theorems
Cantor's proof of the existence of transcendental numbers. With a (now) obvious one-line argument he showed that there are uncountably many of them --- when Liouville, Hermite and others had to take ( …
1
vote
What are examples of mathematical concepts named after the wrong people? (Stigler's law)
I think the Kazhdan-Lusztig Conjectures are due to Vogan.
EDIT.
True or false, the claim is mainly based on the very first two paragraphs of
[II] Irreducible characters of semisimple Lie groups II. T …
7
votes
Suggestions for good books on class field theory
Among the few books on class field theory I tried to read, Weil's Basic Number Theory is the one I found most accessible. By far.
3
votes
Math paper authors' order
It seems to me nobody mentioned the Zariski-Samuel and Grothendieck-Dieudonné cases.
18
votes
Errata for Atiyah–Macdonald
EDIT OF JULY 26, 2017
Proposition 2.4 page 21 reads:
Let $M$ be a finitely generated $A$-module, let $\mathfrak a$ be an ideal of $A$, and let $\phi$ be an $A$-module endomorphism of $M$ such tha …
48
votes
19
answers
16k
views
What is your favorite proof of Tychonoff's Theorem?
Here is mine. It's taken from page 11 of "An Introduction To Abstract Harmonic Analysis", 1953, by Loomis:
https://archive.org/details/introductiontoab031610mbp
https://ia800309.us.archive.org/10/item …
9
votes
Applications of the Chinese remainder theorem
The Chinese Remainder Theorem gives a way to compute matrix exponentials.
Indeed, let $A$ be a complex square matrix, put $B:=\mathbb C[A]$. This is a Banach algebra, and also a $\mathbb C[X]$-algeb …
2
votes
Shortest/Most elegant proof for $L(1,\chi)\neq 0$
I know it's not an answer to the question, but rather another (probably naive) question suggested by the original question.
It seems to me that proving the prime number theorem for arithmetic progres …
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