Reputation
12,286
Next privilege 15,000 Rep.
Protect questions
Badges
3 30 89
Newest
 Nice Answer
Impact
~484k people reached

Jun
24
comment Integral becomes improper after a substitution
@AdamHughes: I'm sorry, but I don't quite see how this answers the question. What specifically is wrong with $\int_{\pi/4}^{\pi/2}\frac{1}{\sin(x)}\,dx = \int_{1/\sqrt{2}}^1 \frac{1}{z\sqrt{1-z^2}}\,dz$? (Do you agree that these two integrals are equal?) The question is: why should the substitution $z = \sin(x)$, where $x \in (\pi/4, \pi/2)$ return an improper integral?
Jun
21
comment Is $(-\infty, \infty)$ an interval?
@BenjaminRoycraft: "If a function is continuous on a closed interval, then it's bounded." That statement assumes that your definition of "interval" is "bounded interval." Because if you consider the closed interval $[0, \infty)$, say, then that statement is false.
Jun
15
awarded  Nice Answer
Jun
3
comment How to study math to really understand it and have a healthy lifestyle with free time?
I may be misreading this post, but there seems to be a suggestion that it isn't worth pursuing an academic career in pure mathematics if one is mediocre or second-rate. I'm not sure how I feel about that suggestion. There's also no mention of that other part of being a professor, namely teaching. That omission makes me uneasy: there are reasons other than research to consider academia.
May
30
comment Non Existence of a proper holomorphic map from the punctured unit disc to an Annulus
Not every continuous map is proper.
May
26
revised gauge-theory wiki description
added 318 characters in body
May
26
revised gauge-theory wiki excerpt
added 359 characters in body
May
26
wiki created gauge-theory description
May
26
wiki created gauge-theory excerpt
May
26
suggested approved edit on gauge-theory tag wiki
May
26
suggested approved edit on gauge-theory tag wiki excerpt
May
26
awarded  Taxonomist
May
23
revised What are some simple examples illustrating the definition of “cover”
edited body
May
22
comment Good sources to learn about Geometric Analysis
@AbrahamRabinowitz: To be honest, I wish I knew. There's a pretty substantial chapter on it in Evans' book on PDE, but other than that I don't know.
May
21
answered Good sources to learn about Geometric Analysis
May
20
comment Why are diffeomorphism-invariant PDE not elliptic?
@aes: Thank you. Could you please turn your comment into an answer?
May
12
asked Why are diffeomorphism-invariant PDE not elliptic?
Apr
26
comment General setting of Varadhan's result for distance functions and heat kernels
Interesting! Looking forward to answers. If you end up not getting an answer, though, you might consider asking this question on MathOverflow.
Apr
22
answered symplectic manifolds
Apr
22
comment symplectic manifolds
Whether there exist non-degenerate $2$-forms (not necessarily closed) is a purely topological question; a complete characterization of such manifolds can be given in terms of characteristic classes. But it's not clear which of those also support a non-degenerate $2$-form which solves $d\omega = 0$. (Just as it is not clear, for example, which smooth manifolds admit integrable complex structures.)