9,300 reputation
13455
bio website research.microsoft.com/~cohn
location Cambridge, MA
age 39
visits member for 4 years, 1 month
seen 4 hours ago

1d
awarded  Enlightened
1d
revised I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
corrected reference, added link
1d
awarded  Nice Answer
2d
revised I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
made continuity hypothesis explicit
2d
answered I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
Apr
15
comment Limit of distance between two random points in a unit-radius $n$-sphere
I'm not sure there's such a contrast between cubes and spheres. In high dimensions a unit cube is vastly larger than a unit sphere, as measured by diameter or volume, so it's not as fair a comparison as the word "unit" suggests.
Apr
12
comment Geometric explanation of Hutton's formula?
Roger Nelsen gave a proof without words in Math Magazine 86 (2013), 350. See www.jstor.org/stable/10.4169/math.mag.86.5.350.
Apr
8
comment Positive Semidefinite Kernel?
No, it's not. For example, let $\alpha=1$ and take your set of points to be $\{1,2\}$ (in a one-dimensional space); then the resulting $2 \times 2$ matrix is not positive semidefinite. This is not really on topic here, since mathoverflow is aimed at research questions, but math.stackexchange.com could be a better place for it.
Mar
23
comment Bessel function integral
But I think math.stackexchange.com would be a better place for this. (Maple can evaluate the integral.)
Mar
23
comment Bessel function integral
I interpreted it as $\int_0^\pi J_1(2 x \sin(\theta/2)) \, d\theta$, which equals $(1-\cos(2x))/x$ (the Struve function can be evaluated in closed form when its index is half an odd integer).
Mar
21
answered Theta series for the Leech lattice
Mar
18
awarded  Yearling
Mar
17
answered Inequality for Laguerre polynomials
Mar
16
comment Analogues of P vs. NP in the history of mathematics
I didn't downvote it myself, but since no other explanation seems to be forthcoming: the runtime fence problem for TMs fails to satisfy Scott's second criterion ("Mathematicians conjectured that the two classes were unequal, but were unable to prove or disprove that for a long time..."), since Viola gave a proof 20 minutes after you posted the question on cstheory.stackexchange.com. I don't really understand what you mean by the runtime fence problem for languages, but it apparently doesn't satisfy the third criterion ("Eventually, the conjecture was either proved or disproved").
Feb
11
comment What does a Zonal sphere harmonic look like?
Is there an explicit formula for the $L^p$ norms of zonal spherical harmonics? The paper faculty.fiu.edu/~decarlil/Preprints/Proc4.pdf proves estimates for them, which suggests that no such formula is known.
Jan
30
awarded  Enlightened
Jan
30
awarded  Nice Answer
Jan
24
comment Is Kolmogorov complexity (KC) relevant for proof theory?
This is why people don't use Kolmogorov complexity to measure proof length: it's not very meaningful to compress a proof of the classification of finite simple groups all the way down to essentially saying "it's the shortest proof of the classification of finite simple groups". I wouldn't interpret Kolmogorov complexity as "bits of inspiration", though, since almost all these bits are just stating the theorem and describing the formal proof system. All you need is one bit of inspiration: if you know there is a proof, then you can definitely find it by brute force if you search long enough.
Jan
2
awarded  Nice Answer
Dec
23
comment Examples of major theorems with very hard proofs that have NOT dramatically improved over time
I agree that the four-color theorem's proof is "so large and complicated that it was considered impossible for a single individual to understand them completely and convincingly", but is that really the case for Feit-Thompson? My impression is that Feit-Thompson was chosen as a step towards the classification of finite simple groups (for which that statement would certainly be true).