The movie never showed the doctor succeeding at anything.
He succeeded with Louisa's face graph/transplant.
Keep silent unless what you are going to say is more important than silence.

The movie never showed the doctor succeeding at anything. I took this as another way to show that the doctor acts more like a kid burning an ant with a magnifying glass, as if he's always eager to prod around in the troubles people have, but we never see him actually fix someone. That kid may have been a new patient, but I took it that he was someone who had already been worked on by the doctor, and like everything else, was a failure. I thought that scene added to his character, more than anything else we'd seen in the movie, by further enforcing him as an emotionally detached guy who is in the field for glory, without having anything to truly care about in his life. The daughter said it best, when she referred to herself as his lab experiment.
I know what gold does to men's souls.

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Yes, good answer. Makes perfect sense now - not a scene in the movie was wasted.

Sure, there's the element of contrast, as he's the face without eyes, but it's also an opportunity to show two aspects of the doctor's character in a context where he has nothing personal at stake. His compassion and his overconfidence. He seems to care about the boy's condition, and he assures the mother that he will correct the problem (although it seems to be suggested that this is impossible). He feels for the mother with her son (who are reflections of himself and his daughter) and believes that his genius is sufficient to overcome any obstacle.
"In Texas, only Texans can rob banks!"

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Thank you.

Great observation! Wow, I never thought of it that way

Perhaps as contrast with the daughter who was "eyes without a face", this boy was "a face without eyes".

The doctor also switches his glasses during the scene. Another reference to a possible eye replacement operation.
:wq

I just watched the movie myself and I was wondering the same thing. I think ultimately what it meant was either to show that the doctor had a simpathetic side or, he was planning and trying to replace his eyes. Remember the boy had trouble seeing the doctor's fingers? Well when they left the room, both doctors looked at each other and they nodded saying that they were thinking the same thing. I don't know. I just think that maybe he wanted to try and do the old switcheroo that he was doing with all the women.