The article you linked (thanks for the unpaywalled link, by the way) describes him only as an amateur mathematician, but describes Barreto as a math student. If they were both math students, I feel it would say so?
Or perhaps you're arguing it's implicit in him having solved the problem? If so, you're just assuming your conclusion. "AI didn't prove it by itself; Price was a mathematician. Well, he must have been a mathematician to be able to prove it!"