We prove that the computational successes of string theory are consequences of two mathematical structures: the four normed division algebras and the axioms of two-dimensional conformal field theory. Eight results are established. (1) The Green-Schwarz critical dimensions D in 3, 4, 6, 10 are classified by normed division algebras via the Hurwitz theorem. (2) The Veneziano amplitude and the celestial MHV coefficient are both uniquely fixed by Haar measure on (R+, x). (3) Shadow symmetry Delta2-Delta and T-duality Ralpha'/R are both induced by the unique involutive automorphism t->1/t of (R+, x). (4) The KLT double-copy relation is the amplitude-level consequence of the Sugawara construction. (5) Anomaly cancellation on Gr (2, 4) forces exactly three fermion generations. (6) All four-dimensional black hole entropies are reproduced by the Cardy formula applied to the near-horizon 2d CFT, without strings. (7) The Veneziano Regge tower is the off-principal-series (complementary series) component of the Mellin spectral decomposition. (8) The celestial CFT is the unique infrared fixed point of any consistent 4D quantum gravity with the Standard Model.
Daniel Toupin (2026) studied this question.