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Results tagged with intuition
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user 3634
Questions asking for the intuition behind some definition, conjecture, proof etc. In other words, questions designed to improve or to acquire understanding on a conceptual or intuitive level, as opposed to on a technical or formal level. When asking such a question it can be helpful to include a rough description of ones understanding of the subject at hand (on a technical level).
13
votes
What is the intuition behind the Freudenthal suspension theorem?
The suspension map $\Sigma: [A, X] \to [\Sigma A, \Sigma X]$ (of which yours is a special case) is adjoint to a map $[A, X] \to [A, \Omega\Sigma X]$ which is induced by the map
$\sigma: X\to \Omega\S …
- 12.5k
7
votes
Surprising and Useful Physical Intuition for Mathematical Objects
Archimedes figured out the area of a parabolic section by slicing it into pieces and moving the pieces to the other side of an imaginary lever and observing that they balance a certain triangle.
14
votes
Proof synopsis collection
Toda's Proof of the Bott Periodicity Theorem:
The homology algebras of $\Omega SU$ and $BU$ are isomorphic: they are polynomial algebras on the image of the maps induced by certain maps $f: \mathbb{ …