One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gรถdels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!
John D. BarrowAll our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
John D. Barrow