bio | website | research.microsoft.com/~cohn |
---|---|---|
location | Cambridge, MA | |
age | 40 | |
visits | member for | 5 years, 2 months |
seen | 11 hours ago | |
stats | profile views | 4,297 |
May 15 |
awarded | Enlightened |
May 15 |
awarded | Nice Answer |
Apr 15 |
awarded | Nice Answer |
Apr 14 |
comment |
Question on the irrationality of $e$
Incidentally, $\int_0^1 (1-x)^k e^x dx = k!(e - \sum_{0 \le i \le k} 1/i!)$, so if you use $(1-x)^k$ instead of $x^k$ you get the usual approximation to $e$ through Taylor series. |
Apr 4 |
comment |
Open problems in continued fractions theory
What's the question here? The title and answers look like you are after a list of open problems or conjectures on continued fractions, but the body of the question focuses 100% on one conjecture. If you want a list, it would be clearer to ask for that in the body of the question and move the current content to an answer. |
Apr 1 |
comment |
Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$
Oops, I was being silly (and had somehow convinced myself this wasn't enough to get full independence for more than two). |
Apr 1 |
comment |
Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$
How do you get independence for different primes? They are certainly pairwise independent, but I don't see how to deduce mutual independence for more than two primes. |
Mar 18 |
awarded | Yearling |
Mar 9 |
comment |
Factorization when a factor is partially known
(I edited the answer to try to clarify this, since the original version did make it sound like the assumption of equal-sized factors might be essential.) |
Mar 9 |
revised |
Factorization when a factor is partially known
added 148 characters in body |
Mar 9 |
comment |
Factorization when a factor is partially known
Knowing the first 75 digits of $a$ is essentially the same as knowing them for $b$ (since you know all the digits of the product $ab$ and can do approximate division), so you can still apply Coppersmith's algorithm to $b$. It's a little less efficient if you don't know how big the numbers are: the setup I have in mind requires knowing the number of digits, but you can brute force this since there are only 125 possibilities. |
Mar 9 |
answered | Factorization when a factor is partially known |
Jan 21 |
comment |
algebraic topology and 3d/4d printing
Thanks for the link! My first thought was that it was the analogue of 3d printing for people who live in $\mathbb{R}^4$. |
Jan 21 |
comment |
algebraic topology and 3d/4d printing
The title refers to "printing" (what's 4d printing?), but the body of the question does not. What are you looking for? I don't think the question can be given a useful answer without more details. |
Nov 30 |
comment |
The resolution of which conjecture/problem would advance Mathematics the most?
One somewhat objective way to answer this question is by asking about the known consequences. In that case it's probably hard to beat the Riemann hypothesis and P vs. NP, but deducing consequences directly from a single statement is a pretty limited notion of advancing mathematics. The deeper question is what the proof techniques could tell us if we had them, but that's really not easy to predict. (For example, before the elementary proof of the prime number theory, people imagined it would lead to a revolution in number theory, but that turned out not to happen.) |
Oct 27 |
comment |
Proving the Irrationality of this Number
Incidentally, Schanuel's conjecture would imply that this number is transcendental. |
Oct 24 |
comment |
How to visualise Bollobas' 1965 theorem?
Proof 2 in the question seems about as good an explanation as you're likely to find, and one could draw a picture to explain why the events are mutually exclusive (so it's at least kind of visual, in the same way the proof of the LYM inequality is). What more are you hoping for? If you had mentioned only Proof 1 and someone had responded with Proof 2, it would seem like a great answer to me, so I'm not sure what you're looking for. Is there some other sort of visualization you would prefer? |
Oct 20 |
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 Betke-Henk 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). |