If it helps … I know at least one paper by him, where I can tell you explicitly, where it does not work. Unfortunately, it is none with the smoothing technique. These I just do not understand. I really tried this for the paper that you linked.

Calling him a crackpot is not correct, because he has several correct and interesting publications (e.g. the wrong two pages paper mentioned above refers to a correct paper by the mathematician in question).

Also relevant is this question from a few days ago …

]]>I wanted to participate in the relaunch (EDP 24 or so), but September is a busy month for academics. Late December/January is ideal for my schedule for getting completely absorbed into something.

]]>And recently solved Erdos discrepancy problem https://gowers.wordpress.com/2015/09/20/edp28-problem-solved-by-terence-tao/

]]>Indeed “imbalance” is better. We can also say “complete fairness is impossible,” (or even “complete justice is impossible,” 🙂 ) or “The principle of unavoidable bias”

As far as the proof goes it seems that we have here a principle of bias coming from balance (or imbalance coming from balance), as the bias in EDP is coming from the balance of pairwise sign patterns.

]]>I think “imbalance” is better than “disorder” there, since a constant sequence would count as complete order in a Ramsey context, so it seems a little strange to consider it as disorder in a discrepancy context. Also, random sequences tend to be quite well (though not perfectly) balanced. So I’d go for “complete balance is impossible”.

]]>I suggested (from my non-expert perspective) that it betrays the multiplicative structure of the integers: we have maps dZ –> Z that jointly cover Z, but which aren’t disjoint enough for bonded-discrepancy sequences to be glued. The trouble is that sequences in dZ and d’Z eventually run into each other at lcm(d,d’). The analogy is with bounded functions on a countable family of intervals covering R: they may not glue to a bounded function.

]]>If a slogan for the Ramsey phenomenon could be “complete disorder is impossible” maybe for the discrepancy phenomenon it is “some disorder cannot be avoided”.

]]>Maybe one could say something along the lines of its being impossible to find a red-blue colouring of the integers that is “perfectly balanced” in every times table. That’s not quite a slogan, but perhaps it could be worked into one.

]]>I haven’t met anyone who has taken the time to read this paper to a point where they can conclusively say “this proof can/cannot work because…”.

Blinovsky has three other papers using the same proof technique each of them claiming to solve reasonably well known combinatorics problems (one of which is published http://link.springer.com/article/10.1134%2FS0032946014040048).

Whether or not his papers are correct, their existence seems to have discouraged people from working on the relevant conjectures, which is a shame.

I guess that one positive outcome of a polymath project about Frankl’s conjecture is that it would help the combinatorics community decide on the correctness of these papers.

]]>I can’t quite tell — is this in jest? Or do you really think someone lurking is on the verge of proving something about Frankl’s conjecture?

]]>@Maxi Anand: Without actually trying to read this thing, I have a hunch [1] that the “approach” you’re referring to will not work.

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