= Michael Atiyah
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<Michael Atiyah> connected <topology>, <geometry> and <analysis>. With <Isadore Singer>, he proved the <Atiyah-Singer index theorem>, relating an analytic index of an elliptic operator to topological data. Oxford's mathematical memorial explains its connection with <Riemann-Roch theorem> and <Gauss-Bonnet theorem> formulas.https://www.maths.ox.ac.uk/node/31190[Institutional mathematical account of the index theorem]{ref}
His work with <Raoul Bott> provides another local-to-global bridge: a <holomorphic Lefschetz fixed-point formula> expresses a global alternating trace in terms of contributions at fixed points. Such results make local geometric calculations determine invariants of global spaces of solutions.<A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications by M. F. Atiyah and R. Bott>[Theorem 4.12]{ref}
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