Basically same situation as iowajes.
I'm personally paying off our mortgage before investing beyond our tax-advantaged accounts, but the math is clearly on the side of investing. If we were being totally rational, we'd have taken out a 30 year, and paid it off as slowly as possible. Put another way, 2.875% is super cheap money - pretty likely you'll make more on investments than the mortgage is costing you.
Also, in our case, the mortgage and the house itself are a pretty small part of our overall financial picture (house price was like 70% of annual income), so it is not like we'll be paying extra on it for 10 years or something, where this choice might have larger effects.
Ultimately, pay it off, don't pay it off - if you didn't buy too much house in the first place, you'll be OK.