Quantum gravity was born as that branch of modern theoretical physics thattries to unify its guiding principles, i.e., quantum mechanics and generalrelativity. Nowadays it is providing new insight into the unification of allfundamental interactions, while giving rise to new developments in modernmathematics. It is however unclear whether it will ever become a falsifiablephysical theory, since it deals with Planck-scale physics. Reviewing a widerange of spectral geometry from index theory to spectral triples, we hope todismiss the general opinion that the mere mathematical complexity of theunification programme will obstruct that programme.
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