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Results tagged with big-list
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user 30684
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.
57
votes
Every mathematician has only a few tricks
Integration by parts has allegedly earned some people big medals.
34
votes
Publishing conjectures
Depending upon the content of the paper, you may look at the new Arnold Mathematical Journal (http://www.springer.com/mathematics/journal/40598).
From their site, "Problems, objectives, work in progr …
20
votes
Mathematical conjectures on which applications depend
Navier Stokes equations are believed to be well-posed.
16
votes
A search for theorems which appear to have very few, if any hypotheses
Any linear bounded operator on a Hilbert space can be written as linear combination of four unitary operators.
10
votes
What are some deep theorems, and why are they considered deep?
Kolmogorov-Arnold-Moser (KAM) theorem in the study of perturbed Hamiltonian systems. This landmark theorem clarified a major point in the field, and answered in positive the question of existence of s …
9
votes
Open problems in PDEs, dynamical systems, mathematical physics
Dynamical systems is a huge field, with at least 3 (or more) subdisciplines which often interact with each other, but also have self-contained advances. Ergodic theory, topological dynamical systems, …
8
votes
Proofs where higher dimension or cardinality actually enabled much simpler proof?
Not a single theorem per se, but in dynamical systems, it is often very useful to translate questions about properties of a continuous system $\dot{x}=f(x)$ or discrete-time system $x_{k+1}=f(x_k)$, w …
6
votes
Open problems in mathematical physics
The following contains several open problems (as of 2001, but most are still open I believe) in topological fluid dynamics by Moffatt :
Some Remarks on Topological Fluid Mechanics
4
votes
Practical applications of Sobolev spaces
Formulating optimization/control problems in Sobolev spaces often lead to better numerically conditioned problems, and more practically implementable solutions.
E.g: Consider the problem of devising …
- 2,281
4
votes
Most helpful math resources on the web
http://www.proofwiki.org
It is a Wikipedia, for proofs.
3
votes
Where can square roots come from when they are not distances?
Polar decomposition of square matrix $A$ involves square-root of $A^*A$
3
votes
Mathematicians with both “very abstract” and “very applied” achievements
Jerrold Marsden made major contribution to symplectic geometry but also was a key contributor to problems in celestial mechanics and numerical methods.
2
votes
Online high quality colloquium talks
If applied math is allowed, here's one about invariant manifolds and interplanetary superhighway (Restricted three body problem)
http://www.podcast.ethz.ch/episodes/?id=1269