I only learned advanced Math to help me think in a certain way (I like physics and I program applications on a computer). Training your brain to think in a logical manner is very useful application in my opinion and is a highly transferable skill.
There is another possibility for a great silence and that is the 'Alien lifeforms' may communicate via lightwaves or scent like some of the lifeforms on Earth do.
How about something along the lines of an old Bagatelle type game?
It would be easy to make.
A piece of plywood with small nails hammered partly the way through it.
A number of small balls
Numbered slots at the bottom for the ball to drop into.
You could have theme games like playing...
It may be a solution just to let them kill each other.
I know it sounds a bit callus but if the hatred is insurmountable (neither side willing to accommodate the other for any reason) then what other choices are available?
If the UN or any other country thinks it has a right to intervine...
What are the main contentions between Sunni's and Shiites? Is it similar to the problems between Protestants and Catholics? Some stupid differences in interperating a religious text?
If it is then I've got no sympathy for them because I've have no tolorance for that kind of stupidity.