An important step towards evidence of a mathematical puzzle was carried out by two mathematicians with the help of electronic computer. Μοναδικό πρόβλημα στην αξιολόγηση της εργασίας τους, είναι πως το αρχείο που περιέχει τις πράξεις τους έχει μέγεθος 13 Gigabyte, when for example the entire electronic encyclopedia Wikipedia is less than 10 Gigabytes in size.
In the 1930 decade, Hungarian mathematician Paul Erdős dealt with the behavior of infinite sequences of 1 and -1 numbers that are repeated in random order, looking for patterns appearing in the individual sections. One of the ways that she thought to study such an infinite sequence was to focus on one part of it and create smaller subsections, taking into account every ninth digit, such as, for example, every second, third, or sixth digit. Then she set her size disagreement, as the sum of the digits of each sequence.
Erdős's suspicion was that for every infinite sequence there is a finite subsequence whose discrepancy is greater than any number one can choose. Not even succeeding in demonstrating his claim, he also announced the 500 $ prize to anyone else who did it, but this did not happen for the next 80 years.
The problem for short sequences is relatively simple: for example in 12-digit sequences, it is possible to prove even by hand that there is always a subset whose discrepancy is greater than 1. But as the number of digits increases the problem becomes more and more complicated.
Alexei Lisitsa and Boris Konev, researchers at the University of Liverpool, with the help of a computer program, extended the solution for 1161 digits, demonstrating that there is always a subsequence with a discrepancy greater than 12, and in infinite sequences showed that there is always a subsequence with a mismatch greater than 2.
Although the work/labour them an important step in the investigation of Erdős's claim, its assessment is practically impossible, due to the volume of acts contained which correspond to millions pages. As the scientists explain, the investigation of the behavior of infinity sometimes leads to "non-human" mathematics.
However, scientists believe that if other programs reproduce the same results, then there will be an indirect confirmation of their results, which they are trying to do in the meantime for mathematicians at the University of Jerusalem.
