The following feels like a community wiki question, so I do it here:
Recently we have heard of a new proof of the Circulant Hadamard conjecture of Ryser (a long standing difficult conjecture):
There is no Circulant Hadamard matrix with more than $4$ columns
Barry Hurley, Paul Hurley, Ted Hurley, The Hadamard circulant conjecture, Bulletin of the London Mathematical Society, Volume 44, Issue 1, February 2012, Page 206, https://doi.org/10.1112/blms/bdq112
More recently a gap was found in the proof:
Question: What is the real status of this Conjecture ?