bio  website  research.microsoft.com/~cohn 

location  Cambridge, MA  
age  40  
visits  member for  4 years, 7 months 
seen  9 hours ago  
stats  profile views  4,006 
1d

comment 
Who first defined quantum integers?
I believe Gauss introduced Gaussian binomial coefficients in 1811 in Summatio quarumdam serierum singularium. I just flipped quickly through it, and I couldn't see any explicit discussion of quantum integers per se, but Chris Godsil is certainly right that they are implicit since they are the special case $m$ choose $1$ (and in any case I might have missed some broader discussion). 
Oct 3 
comment 
Translative packing constant strictly larger than lattice packing constant
Yeah, I think it's very plausible that one could construct an example in a much lower dimension, and conceivable that one could prove it rigorously. I haven't thought much about how hard the difficulty of proving that a lattice packing is optimal varies with dimension (for convex bodies). The BetkeHenk paper deals beautifully with polyhedra in three dimensions, but I have no idea how hard four, five, or six dimensions would be. 
Oct 3 
comment 
Translative packing constant strictly larger than lattice packing constant
I don't know of an example, and I wouldn't be surprised if nobody knows one (but I'll be very pleased if I'm wrong about this). 
Sep 30 
awarded  Explainer 
Aug 24 
comment 
Time in Girard's Geometry of Interaction
My first thought upon seeing the question title was that it was going to be about mustard watches. 
Jun 22 
comment 
polynomial with rational coefficients
@ToddTrimble: I see how to do this if $f(n)$ is an integer for all $n$, but how do you handle the case where this is true for some arbitrary infinite set? (I may be missing something obvious.) 
Jun 22 
comment 
polynomial with rational coefficients
Maybe I'm missing a nice way to do it via calculus of finite differences, but that feels like overkill to me. If $f$ has degree $d$, then it's determined by its values at $d+1$ points, and polynomial interpolation preserves rationality. 
May 25 
awarded  Enlightened 
May 24 
awarded  Nice Answer 
May 24 
answered  Can the Legendre symbol be calculated in polynomial time? 
May 17 
comment 
What is known about $\displaystyle \sum_k{a^{b^k}}$?
If $b$ is an integer and $a$ is the reciprocal of an integer, then you get a beautiful continued fraction expansion (see the articles dx.doi.org/10.1016/0022314X(79)900404 and dx.doi.org/10.1016/0022314X(82)900476 by Jeffrey Shallit). 
Apr 23 
comment 
Is anything known about which numbers appear in the continued fraction expansion of $\pi$?
Hopefully someone can expand on this (to make it more suitable as a formal answer), but the quick version is yes: (a) and (b) were true in 1978 and remain true today. 
Apr 21 
comment 
Why can't there be a problem both in P and NPC
You're right that the illustration you link to assumes that P ≠ NP. Note that on the P versus NP Wikipedia page, it has the caption "Diagram of complexity classes provided that P ≠ NP." 
Apr 19 
awarded  Enlightened 
Apr 18 
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 
Apr 18 
awarded  Nice Answer 
Apr 18 
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 
Apr 18 
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 unitradius $n$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. 