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Are We Pruning Paths or Drowning in Complexity in Wolfram’s Entailment Graph?
- The idea of applying these entailment graphs to automated theorem proving (ATP) left me similarly skeptical.
- Wolfram’s vision was ambitious: not just an ATP that cranks out symbolic proofs but one that functions as an exploration of a multiway system, a concept I found abstract, and frankly, difficult to ground in practical terms.
- The proof might be there, but what of the understanding? I could not help but wonder whether the allure of discovering new lemmas came at the expense of genuine insight, creating proofs that felt hollow because their true meaning was lost in the machinery that produced them.
- Beyond curiosity, I found myself questioning the real utility of this exercise. Can we genuinely gain a new perspective on mathematics by rejecting the very axioms that link it to our experience of the physical world?
- The idea of a vast landscape, an infinite graph where nodes are statements and edges represent proofs, is evocative. But does such a broad view help us solve the problems that matter, or does it overwhelm us with possibilities that lead nowhere?
- We prune as we go, searching for meaningful paths, but what if the paths we choose to prune are simply those that seem easier to manage, rather than those that reveal the most profound truths?
- The value of mathematics might lie in the journey, but I questioned whether we were genuinely capable of appreciating the true breadth of that journey.
- How much of what we believe to be mathematical truth is just the outcome of convenient pruning, of avoiding paths that seem too difficult or too abstract?
- Understanding how our mathematical truths are tied to computational limits may reveal more about both the potential and boundaries of our exploration.
- Wolfram’s work in computational irreducibility intersects here. He suggests that, in many cases, the entailment cone is not only vast but irreducibly so.
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