Donald A. Norman in The Design of Everyday Things, 1988:

Would you like a pocket-size device that reminded you of each appointment and daily event? I would. I am waiting for the day when portable computers become small enough that I can keep one with me at all times. I will definitely put all my reminding burdens upon it. It has to be small. It has to be convenient to use. And it has to be relatively powerful, at least at today’s standards. It has to have a full, standard typewriter keyboard and a reasonably large display. It needs good graphics, because that makes a tremendous difference in usability, and a lot of memory - a huge amount actually. And it should be easy to hook up to the telephone; I need to connect it to my home and laboratory computers. Of course, it should be relatively inexpensive.

What I ask for is not unreasonable. The technology I need is available today. It’s just that the full package has never been put together, partly because the cost in today’s world would be prohibitive. But it will exist in imperfect form in five years, possibly in perfect form in ten.

In my opinion, even if PDAs have existed for quite a long time, almost 30 years later, the first device that actually meets every criteria mentioned by Norman (apart from the cost maybe) is the iPhone.