They weren't great phones, and the iPhone definitely did a lot to push UI/UX forward, but the iPhone was most definitely not the first smart phone.
I'd argue that the Blackberry was the first practical smartphone, released in: 2003. I remember being blown away by the Wizard before the iPhone was a rumor.
Edit: Changed year from 1999 to 2003, 1999 was the 2-way pager, 2003 was the first device that resembled a smartphone.