Robert Langdon has to decide whether or not he will solve the masonic pyramid to save his friend. If he doesn't then his friend will most likely die a horrible and painful death. Robert would clearly have saved his friend if he didn't have specific directions from the same man that he was never to solve this puzzle under any circumstances. That is the internal conflict. The external is whether or not Robert Langdon is capable of solving the masonic pyramid. It is an extremely complex puzzle which has remained unsolved for centuries. If anyone is able to solve this then it will be Langdon. He has extensive knowledge in stuff like this since he is a symbology teacher at Harvard university.