Medieval man definitely had the same genome, but not the same body. Factors such as availability of good food influence your growth. Medieval people were, compared to us, rather small, which can be seen from both their skeletons and various objects of daily use (height of doors, armors).

This indicates insufficient nutrition for most of the population. Famines were common approx. 5-7 years, so if you were one of the small folk, you experienced two to three of them as a juvenile.

And bad nutrition has some effect on brain, too, after all it is part of the body. I do not want to claim that medieval people would be unable to learn calculus, but those with worst food security might struggle.