As a science teacher, Ian Chesterton believes only when he can see proof. This makes him initially sceptic when he finds himself in the TARDIS, asked to believe that it can travel in time and space. As he tells The Doctor, it is a scientific dream he does not expect to find in a junkyard. The Doctor's response is typically unforgiving : 'Your arrogance is nearly as great as your ignorance.'
In fact, Ian is neither arrogant nor ignorant. 'But I want to understand,' he tells the Doctor, and once he has proof, once he has seen and convinced himself, he turns out to be the most practicle of the travellers. It is Ian who struggles to free them from the ropes that bind them in The Cave of Skulls, and it is Ian who eventually manages to make fire. In The Daleks he loses no opportunity to quiz the Doctor about the TARDIS systems and how they work.
Ian is not short of common sense. he can see the strength of Barbara's desire to return to the TARDIS rather than to explore the Dalek City on Skaro (The Daleks) and stands up to the Doctor to make sure they leave safely. He is also headstrong and stubborn. When one of the travellers must go back for drugs, Ian is insistant that it must be him-despite the fact that his leg has been paralysed by the Daleks, and that only the Doctor and Susan can open the TARDIS doors. This same headstrong stubborness is what drives him to risk his life and warn the Thals that the Daleks are about to ambush them, and later to persuade the pacifist Thals they must fight to survive.
Never short on bravery and courage, Ian wins the Doctor's respect to the point where the old man treats him almost as an equal almost as a friend. Before long he is revelling his new life and is even knighted by King Richard the Lionheart (The Crusade). Eventually he and Barbara make it back to Earth in The Chase. Ian travelled with the Doctor from An Unearthly Child to The Chase.