Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
7 problems
Lassak conjectured that a reduced planar convex body of thickness Δ has area at most (π/4)Δ^2, the value for the disc. False: an explicit reduced body of thickness 1 has area 0.786215… > π/4 = 0.785398…, given by a closed-form support…
Conjectured upper bound on how many pairs among n points in the plane can be exactly one unit apart.
For an arrangement of n hyperplanes in P^3_C with ℓ intersection lines and p intersection points where at least three hyperplanes meet, the refined form of Purdy's inequality expects p - ℓ + n + 2 ≥ 0. An explicit arrangement built from…
Wegner conjectured in 1965 that every finite family R of axis-parallel rectangles satisfies τ(R) ≤ 2ν(R) - 1, where τ is the minimum number of piercing points and ν the largest pairwise-disjoint subfamily. False, by an explicit…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For a family F of an odd number n of unit disks in the plane, let OA(F) be the area covered by an odd number of disks. It was conjectured that OA(F) ≥ π, the area of a single disk. False: configurations exist with smaller odd area.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.