Will it be proven that there are finitely many different 3x3 magic squares of distinct perfect squares by end of 2025?

Question

i.e. what the famed "Parker Square" was hoping to be: a 3x3 square of distinct perfect square integers such that each row, column, and diagonal sums to the same number. Two such squares are considered "different" for this market if one cannot be obtained from the other by rotating, reflecting, and/or scaling all numbers by a constant.

On Numberphile (https://www.youtube.com/watch?v=U9dtpycbFSY), it is conjectured that such a square is impossible. However, a potential step in the proof is proving that there's only a finite number, which is a weaker result. Will this weaker result be proven?

See also

[markets]General policy for my markets: In the rare event of a conflict between my resolution criteria and the agreed-upon common-sense spirit of the market, I may resolve it according to the market's spirit or N/A, probably after discussion.

Manifold Markets · Accepted Answer

No — resolved on Jan 1, 2026 by Manifold Markets prediction market.