Were people a 1000 years ago as smart as us today?

I don't think so. Ever heard of the Flynn Effect, it is the rise in average IQ scores over time. Even though IQ is by no means a perfect test of intelligence, I think it represents an overall pattern. Reasons why people are smarter today: nutrition, less susceptible to diseases, better schooling, and more intellectual environment.

My personal theory is yes, they would be just as smart. However, I think that intelligence is in part based on how our environment challenges us. Look at say, technology today, vs 1000 years ago. The more challenged you are mentally, the further you go intellectually. If 1000 years ago, all you had to do to survive was kill game for food, make simple tools, don't eat the yellow snow...and you did do those things, then you were a genius.

Well people around that time, no they weren't because firstly, they didn't know as much as we do now about everything i.e the universe. Also, education was not as high standard as it is these days, and they didn't get taught enough. I suppose if you were too steal a baby then yes, because its not about the brain its about what gets taught. If we taught it everything we know then send it back, people would be much cleverer. If that's a word :')

Yes assuming the baby was healthy and well nourished. A thousand years isn't long enough for people to evolve greater intelligence.