I read this story in recent years, although I do not know if the book itself is old. I have a feeling it is a relatively recent work. It may even be a short story as opposed to a full length novel.
The only real plot-point I can remember about it is that there was a mathematical formula that someone came up with that ‘proved’ some great catastrophe was about the befall the planet. It was something along the lines of ‘Disasters happen. The Planet has been here for so long without an Earth-shattering disaster that one must be due along any time now.’
The ‘proof’ was very similar to the Doomsday Argument.
Believers and non-believers got into conflict about the ongoing state of the world.
There was some further mathematics involved in the ‘formula’ as proof. Not a lot to go on, but does this jog anyone's memory?