obdurate
Very stubborn and refusing to change your mind.
Obdurate means stubbornly refusing to change your mind or soften your position, even when you have good reasons to do so. An obdurate person digs in their heels and won't budge, no matter what evidence or arguments others present.
Imagine a student who insists they're right about a math problem even after the teacher carefully explains the error, or a friend who refuses to apologize after clearly hurting someone's feelings. That rigid, unmovable attitude captures what obdurate means.
The word carries a negative tone. Being firm in your beliefs can be admirable, but being obdurate suggests you've crossed into unreasonable territory. You're closed off to new information and unwilling to reconsider, even when reconsidering makes sense, showing a rigidity that goes beyond confidence or principle.
You might encounter this word in historical writing: “Despite the evidence of his innocence, the judge remained obdurate and refused to reopen the case.” Or in describing conflicts: “The two sides held obdurate positions, making compromise impossible.”
An obdurate person has hardened their heart and mind like concrete, making it difficult for reason or compassion to get through.