Erdös Discrepancy and a Wikipedia-size proofLisitsa
, of the University of Liverpool, UK, have just come up with the longest proof of the History of #mathematics
. This #proof
was generated by a computer, and is contained in a 13 giga-byte file
. This is more than the size of Wikipedia, and thus more than what any human being can ever read (or will ever be willing to read)! And yet, their monumental effort is still worlds away from solving the Erdös discrepancy problem
is one of the most influential mathematicians of the 20th century, notoriously homeless and jobless by choice. Back then, whenever and wherever a mathematician would come up with great ideas, he'd invite Erdös, who'd immediately abandon everything to work with that mathematician. This led Erdös to publish more joint works than any other mathematician!
Erdös is also known for his eccentricity. He'd often mention some Supreme Fascist
who supposedly knows all the most beautiful proofs of mathematics, which he elegantly wrote in The Book
. Erdös once said: "You don't have to believe in God, but you should believe in The Book". Erdös loved telling math problems as stories which opposed mathematicians to the all-knowing Supreme Fascist.
The Erdös discrepancy problem
is one of these. Assume you lived on a line of length n
. The Supreme Fascist
asks you to write down an infinite series of Left
moves, but he can choose to have you following every 1 move or every 2 moves, or every k
moves. Is there a length n
large enough and an infinite series of moves, so that no matter which k
the Supreme Fascist chooses, you'll always stay on the line?
proved is that, if n=6
, no such infinite series of moves exists. In fact, the Supreme Fascist
wins for series of moves of length at least 1161. They're now tackling the case n=8
. Even then though, we'd still be far away from the solution to the Erdös discrepancy problem. But, hopefully, these are the first (very long) steps towards a solution!DOCUMENTAL - PAUL ERDOS - N IS A NUMBER - THE MAN MADE OF MATHS (DOCUMENTARY BBC)http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html#.UwzB-PR5NRYNew Wikipedia sized proof explained with a puzzle