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`

see

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:

see

https://www.sfu.ca/~jed/Papers/Craigen%20Jedwab.%20Circulant%20Hadamard.%20Preprint.pdf

Question: What is the real status of this Conjecture ?

3more comments