They had to know their stuff, because it was before electronic calculators and computers. They made many of their calculations with slide rules, a huge blackboard (or whiteboard) and a ladder.
Pictures and descriptions of the main characters are at the link -- scroll down.
I saw the movie and have no doubt the characters were smart and able to do math. That was real physics. They were also a part of a huge team that made the space program possible.
Thats not the same as a high schooler claiming she can prove something with circular logic that the greatest minds in history have failed to prove over centuries.
Computers existed!
https://astronomy.com/news/2019/05/apollo-computers-when-ibm-engineers-gave-rockets-a-brain