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Results tagged with soft-question
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user 4991
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
15
votes
How can I visualize the nontrivial element of $\pi_4(S^3)$ and $\pi_5(S^3)$ ?
Through the Pontrjagin-Thom construction, a framed $n-k$ manifold in $S^n$ determines a map from $S^n$ to $S^{n-k}$. $\eta$ is represented by $S^1$ in $S^3$ with framing which "twists around once". …
- 4,990
35
votes
How do you approach your child's math education?
I have been trying to make sure that my daughter hears me say with some frequency "I don't know (but I'm curious)" and "I'm wrong (but I'd like to know what's right)," since that's the best way for he …
11
votes
Mathematicians with both “very abstract” and “very applied” achievements
Gunnar Carlsson
In pure math, he works in homotopy theory, having resolved the Segal Conjecture, as well as in manifold topology, with cases of Borel and Novikov conjectures, and also in algebraic K- …
22
votes
Accepted
Advantages of working with CW complexes/spaces over Kan complexes/simplicial sets?
I think there are many times that simplicial sets are preferable (e.g for classifying spaces the simplicial construction is often advantageous), but to answer the stated question:
CW complexes conne …
7
votes
Examples of advance via good definitions
The definition of a fibration by Serre is by far my favorite example. There, if I recall correctly, leaders in the field were actively looking for the right definition and knew that it would "quickly …