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The conjecture states that if $A$ is a set of natural numbers and $$\sum_{n\in A}\frac1n=\infty,$$ then $A$ contains arbitratily long arithmetic progressions.

I wonder has it been proved?

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    I edited it so curious people don't need to visit wikipedia if they don't know the conjecture. Anyhow, it is a safe bet that if it had been proved, or even if a credible proof claim had been announced, the wikipedia article would have said so.2012-11-07
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    @HaraldHanche-Olsen, ok. thank you.2012-11-07
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    I've deleted my answer to this post (that the resolution of this conjecture is likely years away), as it is unhelpful.2012-11-09

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