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

http://blms.oxfordjournals.org/content/early/2011/01/24/blms.bdq112.abstract

More recently a gap was found in the proof:

see

http://people.math.sfu.ca/~jed/Papers/Craigen%20Jedwab.%20Circulant%20Hadamard.%20Preprint.pdf

Question: What is the real status of this Conjecture ?