From what he says, he foresaw the same doom that the Atlasia had calculated and became insane, so he attempted to reach a miracle known as The Sixth in order to create an impossible future. Either The Sixth would be a means to stop this or the actual method by which the destruction would be brought over.
Since The Sixth is described as an impossible miracle, it makes one think of True Magic (Sorcery in the Mirror Moon/Revolve translations), except there we only five of those left. Might be the reason for why Arcueid says it was pointless even to try. What exactly The Sixth would mean is unknown, but given scattered comments, it doesn't seem like something that would fit with the current world order/laws very well, probably a miracle that would mess up a lot of stuff.
There?s also the sixth imaginary element, which are the demons born from human belief. Might not hold a relation, but it does seem quite similar to how the Tatari are formed.