But over the past decade, Peter Scholze(opens a new tab) of the Max Planck Institute for Mathematics in Bonn and Dustin Clausen(opens a new tab) of the Institute of Advanced Scientific Studies in France have sought to replace topological spaces. They have defined a new category of mathematical objects called condensed sets, which resemble a sort of infinitely fine dust and retain all the nicest properties of topological spaces without the drawbacks. Dust, it turns out, is a better foundational material than the pebbly, well-understood soil of topological spaces.

“They are solving a problem we didn’t know we had,” said Ravi Vakil(opens a new tab), a mathematician at Stanford University and president of the American Mathematical Society, “because we already had what we thought were reasonable solutions.” As a result, “a whole slate of mathematics has become much simpler.”