Peter Shor
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 Feb 17 awarded Good Answer Dec 3 awarded Yearling Nov 15 awarded Nice Answer Aug 1 comment Lower bounding the probability that $\gcd(t,N)≤B$, for a random $t$ and fixed (large) $N$ After seeing the proofs here, I'm not at all embarrassed that I didn't remember Odlyzko's proof (if the proof had been easy, I probably still wouldn't remember it, but I'd be embarrassed about it). Jul 17 awarded Good Answer May 10 comment A claim from “Graph minors - a survey” by Robertson and Seymour Isn't this straightforward induction? Jan 4 comment Transforming a binary matrix into triangular form using permutation matrices This just had an answer which got deleted. Here's a simplification of it (definitely based on it). (a) prove that any row with a single 1 can serve as the first row. (b) use the following algorithm: choose a row with a single 1 for the first row. Delete the column that 1 is in. Then recurse. How do you prove any row with a single 1 can serve as the first row? Consider an $n \times n$ matrix $M$ with $M(i,j) = 1$ if $j \leq i$ except for row $i'$, which has exactly one $1$ in position $(i',j')$ with $j' \leq i'$. Cyclically permute the rows from $1$ to $i'$, and the columns from $1$ to $j'$. Dec 10 comment Can we cover the unit square by these rectangles? @L Spice: It's rigorous. You find a subsequence in which the packing of the first $k$ rectangles converges to a fixed configuration. This fixed configuration (the one to which the first $k$ rectangles converges) is the one that doesn't change position when you take a subsubsequence of this subsequence. Dec 3 awarded Yearling Jun 1 awarded Nice Answer May 8 awarded Notable Question May 8 revised Defining a canonical ordering of matrix rows/columns added 178 characters in body Apr 6 comment What areas of pure mathematics research are best for a post-PhD transition to industry? What do you mean coding theory is not pure math? Coding theory spans a spectrum from extremely pure math to extremely applied. Of course, you do run into the problem that pure coding theory is somewhat different from applied, but if you can find an advisor in the math department who does coding theory, I think this would be an excellent area. Jan 6 awarded Enlightened Jan 6 awarded Nice Answer Dec 3 awarded Yearling Sep 30 awarded Caucus Sep 18 comment point in polytope It needn't actually double the number of constraints; you can replace the inequality $\lambda_i \geq 0$ by $\lambda_i - x \geq 0$, to get the same number of constraints and one more variable. I expect you'll still take a performance hit, but less of one. Sep 17 awarded Enlightened Sep 17 awarded Nice Answer