Haddest nose grindstone is an archaic way of describing someone who is stubborn or inflexible in their thinking. There are several modern-day synonyms for this phrase that can be used to convey the same idea. For instance, you could call someone closed-minded, obstinate, or pig-headed. Each of these terms connotes a lack of willingness to listen to other viewpoints or adjust one's perspective. Other possible synonyms include rigid, unbending, and unyielding. No matter which term you choose, the underlying message is clear: the person in question is not open to negotiation or compromise.