re: When does it make sense, mathematically, to accelerate mortgage payments?

I'll give a different set of advice. There's 0 reason to pay the bank more than your payment until you can pay the entire thing. The bank having more of your money doesn't change your future payments. Better advice would be to put away money into an interest accruing account like a money market or investment account and save up until you can pay your mortgage off.

If you ever need the money for an emergency, its a hell of a lot easier to use your own money then get a bank loan.

Paying extra on your mortgage really doesn't get you any perks from a banker. It just pays your loan down. Yes more will go to your principle, but I'm not convinced that's better than saving it in a 3rd account. If you are responsible enough to pay extra then you are likely responsible enough to do this.