Reid was awarded the Senior Berwick Prize in 2006 for his paper with Alessio Corti and Alexander Puklihkov, “Fano 3-fold hypersurfaces”, which made a big advance in the study of 3-dimensional algebraic varieties.
Examples of topologies include the Zariski topology in algebraic geometry that reflects the algebraic nature of varieties, and the topology on a differential manifold in differential topology where each point within the space is contained in an open set that is homeomorphic to an open ball in a finite-dimensional Euclidean space.
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André Weil's famous Weil conjectures proposed that certain properties of equations with integral coefficients should be understood as geometric properties of the algebraic variety that they define.