Has Terence Tao solved Erdos Discrepancy Problem?
While a part of the solution was probably solved (?) last year, Terence Tao suggest he might have come to a full solution. He has posted an article on Arxiv and the whole first piece to Discrete Analysis.
The Erdos Discrepancy Problem (EDP) was posed by Hungarian mathematician Paul Erdos (here with Tao) during the 1930s. At its simplest, when you toss a coin a sequence of heads and tails is created, for example, when a tail is assigned the value -1 and a head is assigned the value 1. As the coin is tossed repeatedly, it has the potential to create infinite sequences.
Erdos was interested in to the extent at which these sequences contained patterns of numbers, or values. If an infinite sequence is cut at a random place, finite sub-sequences are created. If a mathematician was to add up the values in one of these subsequences, the figure he arrives at is called a discrepancy. According to Erdos, if you place 12 values of 1 and -1 in a row, the total of the numbers in the subsequence can equate to 1.
However, Erdos wanted to know if it was possible to prove, mathematically, if the sum of subsequence could ever equal more than two.