system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What if Pi terminated eventually

What significant effects(if there are) would it have on mathematics?
gpt
It has been proven that pi doesn't ever terminate.  Never ever.  It doesn't even start repeating and go on repeating forever.

But, since you asked... If we did find out that pi terminates, that would break everything in mathematics.  *Everything*.  Every mathematical statement anyone could make becomes true automatically, even ones that don't involve pi.  If pi terminates, then 1+1=5, 5=10, parallel lines must cross, a^(2)+b^(2)=c^(2) for all triangles (not just right triangles), and on and on and on and on.  *All* of mathematics falls apart if pi terminates.

It's not something special about your question about pi, though.  If anyone were to prove something is true (e.g., pi never terminates) and prove the opposite is also true (e.g., pi does terminate), then you can use that to prove that any statement you want is true.  If something is true and its opposite is true, that's called a contradiction, and those aren't allowed in mathematics.