mathematically impossible?

[molecular]

Why is it mathematically impossible to continue the debt-based currency system?

While I do believe it's impossible to continue this system for other reasons, I don't quite understand the argument about it being mathematically impossible.

Mathematics doesn't dictate the debt has to be payed back in full eventually, does it?

I understand there is never enough money to pay back all principal and interest... this can be derived from the system of money creation. But isn't it possible to just pay back old debt with an ever-increasing amount of new debt?

I just fail to see the mathematical impossibility of kicking the can down the road in perpetuity. Math has enough zeroes available for us to use.