A Bitcoin does not have any pre-defined value. The value of Bitcoin keeps fluctuating, and historically has risen dramatically from its initial value of 0. If this weren't the case, there would be no investment/speculation in Bitcoin because there would be no potential for any ROI.

In reality, the value of Bitcoin is determined by humans (even if indirectly, not by planning), and I think the OP’s point may have been that maths proofs can be regarded similarly. No intrinsic value, just what humans find in it.

If there's a machine that automatically turns electricity into proofs then mathematics becomes a different thing altogether.