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We prove there is no sentence in the monadic second-order language MS0 thatcharacterises when a matroid is representable over at least one field, and nosentence that characterises when a matroid is K-representable, for any infinitefield K. By way of contrast, because Rota's Conjecture is true, there is asentence that characterises F-representable matroids, for any finite field F.

Yes, the "missing axiom" of matroid theory is lost forever