Another "Moderately interesting" question from the FrontierMath: Open Problems list has been solved (originally announced here in the form of a puzzle lol). This comes from Levent Alpöge, Saul Reynolds-Haertle, Philippe Voinov, and of course Claude. Their solution includes Hadamard matrices of all admissible orders up to 2000. Despite that it seems as though the Hadamard conjecture still remains open.