He worked entirely in his head, barely writing anything down, let alone using a computer. It establishes that an area of math called real functional analysis still works if you replace topological spaces with condensed sets. That project includes a particularly important, difficult proof that Scholze worked out himself during a consuming week in July 2019.
In this new perspective, topological spaces are thought of as being assembled from infinite points of dust glued together.
Their goal is to create new foundations for topology, replacing the traditional notion of a topological space - whose examples include the sphere and the doughnut - with more versatile objects that the authors call condensed sets.
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