http://gowers.wordpress.com/2009/11/17/problems-related-to-littlewoods-conjecture-2/#comment-4377

]]>Also, I find the problem (2) interesting in itself, so am not put off by the possibility that there might exist such a set of points even if the Littlewood conjecture is true. It would even, in a modest way, shed some light on the Littlewood conjecture, since it would demonstrate that the problem was “genuinely number-theoretic”. I say “in a modest way” because I get the impression that the experts more or less take for granted that it is a problem in number theory, so a conclusion of that kind would not change the way people think. But it would also provide some kind of explanation for why the problem is hard.

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