Quoting Jake Boggan
I was a graph theory junkie long ago and even moved to Budapest for awhile to study among the greats. While I was there I started working on Barnette's Conjecture which came to occupy my thoughts over the next 24 years of my life, on and off as I worked in many different fields. Last summer I even thought for a few days that I had actually solved it. But it's supposedly proven here - problem 180…
We haven't written up this one. Simon Willison has the full story — the link below goes straight to it.