Continuing my line of thought from here: Could you cool the earth's mantle and then bore into it? You cannot bore into the mantle by cooling it as you go because the pressure would crush your little shell of cooled rock. (As explained by the accepted answer)
Could you mine down to the maximum depth possible using the original method, and then start pushing through a pipe into the core. (like a straw that sucks from the bottom of the glass) The pressure would be equal inside and out and would push the magma up the pipe to the surface like a volcano of valuable minerals.
- How hot is the earth's core?
- Are there any heat resistant materials up to the task?
- How can you prevent magma from shooting up the outside of your pipe?
- Or is there some other plausible way to access the core?