A new mathematical proof was in the news this week, which partially solves the Erdos Discrepancy Problem. The proof was described as “bigger than Wikipedia”. I attempt to explain the problem using a puzzle which you can try at home.
The puzzle was my idea to explain it to you – that’s not really how the problem is stated.
New Scientist: http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html#.UwdX6_l_uSp
The Independent: http://www.independent.co.uk/life-style/gadgets-and-tech/news/computer-cracks-erds-puzzle–but-no-human-brain-can-check-the-answer-9137097.html
Tim Gowers Blog: http://gowers.wordpress.com/2014/02/11/recent-news-concerning-the-erdos-discrepancy-problem/
PolyMath Project: http://michaelnielsen.org/polymath1/index.php?title=The_Erd%C5%91s_discrepancy_problem
The paper: http://cgi.csc.liv.ac.uk/~konev/SAT14/sat14.pdf
Boris Konev’s webpage: http://cgi.csc.liv.ac.uk/~konev/SAT14/
One page proof that a sequence of twelve has discrepency of 2 http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf