I maintain that the pressure at the center of the earth is zero. Matter there is subject to a uniform force field generated by the uniform distribution of matter around it. When I've discussed this with geology professors on my occasional college visits, they have either been speechless or asked if I would be interested in writing a paper. (I'm not, and my credentials are minimal. I am a non-academic with math degrees.) When the geology professor asked if you would be interested in writing a paper on the subject, that was the equivalent of a nice southern grandma saying “Why, bless your heart” : ),