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.[ref]
https://www.maths.ox.ac.uk/node/31190. Institutional mathematical account of the index theorem
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.[ref]
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Sir Michael Atiyah (1929–2019) was a prominent British mathematician known for his contributions to various fields, particularly in geometry and topology. He is best recognized for his work in the development of the Atiyah-Singer Index Theorem, a fundamental result in differential geometry and analysis, which connects geometric and topological properties of manifolds with analytic properties of differential operators.