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Eugine_Nier comments on Stuff That Makes Stuff Happen - Less Wrong
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Your prediction is a prediction of what someone else will conclude, given a set of initial conditions (the mathematical problem) and a set of rules to apply to these conditions. The conclusion that you arrive at is a causal descendant of the problem and the rules of mathematics; the conclusion that the other person arrives at is a causal descendant of the same initial problem and the same rules.
That's the causal link.
That's my point. Specifically, that one should have nodes in one's causal diagram for mathematical truths, what you called "rules of mathematics".
Surely the node should be "person X was taught basic mathematics", and not mathematics itself?
The point of having the node is to have a common cause of person X's beliefs about mathematics and person Y's beliefs about mathematics that explains why these two beliefs are correlated even if both discovered said mathematics interdependently.