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Results tagged with big-list
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user 3901
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.
11
votes
Examples of math hoaxes/interesting jokes published on April Fool's day?
I saw Doug Ravenel give a talk that began with him announcing a proof of the Riemann Hypothesis. It was beautifully done, I thought. I didn't even realize what date it was.
http://www.math.wayne.edu/ …
7
votes
Examples of theorems with proofs that have dramatically improved over time
The first proof of the Hopf invariant one theorem due to Adams is very technical. It involves decomposing $sq^{2^n}$ as a composite of secondary cohomology operations when $n\geq 4$. Then Atiyah and A …
5
votes
What out-of-print books would you like to see re-printed?
I don't know much about the book, since it is out of print and i am young, but Stong's Notes on Cobordism Theory.
5
votes
Describe a topic in one sentence.
Algebraic Topology: Geometry is hard, and Algebra is easy so...
(I am sure this applies to many other fields, and certainly algebra is hard.)
3
votes
How to present mathematics to non-mathematicians?
Their are two things I say to people when I am in such a situation:
1) I think of math as being divided into 3 parts: Algebra, Analysis and Topology. Each of these comes from starting with a set and …
13
votes
'Important' applications of p-adic numbers outside of algebra (and number theory).
The $p$-adics come up in homotopy theory. The main reason is because of their usefulness in the theory of formal group laws.
They are also relevant in certain parts of algebraic geometry, they are (o …
36
votes
Colloquial catchy statements encoding serious mathematics
"If it walks like a sphere and it quacks like a sphere then it is a sphere."
A professor at my university explained the Poincaré Conjecture to his 1st semester abstract algebra students this way. I th …
3
votes
Short Course Suggestions For High School Students
I realized recently that you can do something really cool with good students after they learn the standard forms for conic sections: you can compute the compactifications of their moduli spaces. I gav …
3
votes
Why is a topology made up of 'open' sets?
I found that the comment box underneath andrews response wasnt large enough for what i had to say. I think that before i continue in my answer i should mention that i study homotopy theory, and maybe …
5
votes
Most helpful math resources on the web
The manifold atlas is pretty cool. I haven't spent enough time on it though... It seems like a different type of mathematical venture. Hopefully, it will inspire other similar projects.
http://www.map …