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# Truth of the sunflower conjecture

### Question

One of Paul Erdős' favorite problems was the sunflower conjecture, due to him and Rado. Erdős offered \$1000 for its proof or disproof.

The sunflower problem asks how many sets of some size $n$ are necessary before there are some $3$ whose pairwise intersections are all the same. The best known bound was improved in 2019 to something the form $\log(n)^{n(1+o(1))}$; see here for the original paper and here for a slightly better bound. The sunflower conjecture asks whether there is a bound $c^n$ for some constant $c$.

Is the sunflower conjecture true?

This question will resolve positively in the event of a publication in a major mathematics journal proving the sunflower conjecture. It will resolve negatively in the event of a publication in a major mathematics journal disproving the sunflower conjecture.

If there is no such proof by 2300-01-01, the question will resolve ambiguous. If a proof is published, but not confirmed by peer review by 2300-01-01, the question may wait to resolve until peer review has reached a consensus.

[EDIT] Sylvain 2021-09-08 : changed the resolution date from 2121 to 2300.

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