Maths problem solved but it’s impossible to check
Dr Boris Konev and Dr Alexei Lisitsa are now running software in an attempt to find a result for discrepancy 3 University of Liverpool academics made significant progress towards solving an 80 year old maths puzzle using a computer programme, but the resulting proof is so massive it's impossible for any human to check. Computer scientists, Dr Boris Konev and Dr Alexei Lisitsa successfully cracked Erdos discrepancy problem (for a particular discrepancy bound C=2) and in the process produced more data than the entire written contents of Wikipedia. Infinite sequence The riddle was proposed in the 1930s by the Hungarian mathematician Paul Erdos, who offered $500 for its solution. Erdos was fascinated by the extent to which an infinite sequence of numbers containing nothing but +1s and -1s contains internal patterns. One way to measure that is to cut the infinite sequence off at a certain point, and then create finite sub-sequences within that part of the sequence, such as considering only every third number or every fourth. "It is true that our computer-generated solution is beyond the reach of humans to fully understand, but it does not mean that a human-comprehensible solution could not (or will not) be found in the future” - Adding up the numbers in a sub-sequence gives a figure called the discrepancy, which acts as a measure of the structure of the sub-sequence and in turn the infinite sequence, as compared with a uniform ideal. Dr Konev and Dr Lisitsa took a sequence 1,161 numbers long and managed to demonstrate that an infinite sequence will always have a discrepancy larger than two.
