Balogh and Solymosi's new paper
constructs \(n\) points in the plane, no four in line, with max general-position subset size \(O(n^{5/6+\epsilon})\), much better than the previous \(o(n)\). I recently rescued a Wikipedia article on Solymosi,, adding book references for his results, but omitted my favorite (this one) because it wasn't published. Now it is, but the book reference would be too self-serving to add...

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