The physics Nobel laureates were able to use ideas from geometry to understand some exotic forms of matter made possible by the effects of quantum mechanics

Vasudevan Mukunth in The Wire:

The 2016 Nobel Prize for physics recognises a set of breakthroughs starting in the 1970s that breached parts of the complexity barrier using techniques borrowed from mathematics. Specifically, the new laureates – Duncan Haldane, John Michael Kosterlitz and David Thouless – were able to use ideas from geometry to understand some exotic forms of matter made possible by the effects of quantum mechanics. They were able to provide their peers with a set of techniques that could be used to explain why the forms behaved the way they behaved, and build upon their results to think about applications.

The efforts of the trio is exemplified by a famous experiment that two of them, Kosterlitz and Thouless, performed in the 1970s. Their goal was demonstrate that the theories of their time that were used to explain the properties of superfluids were incomplete. Superfluids are fluids that flow with zero viscosity; liquid helium is a notable example: it can even flowup walls. This is explained by the fact that helium atoms start behaving like the fundamental particles called bosons at very low temperatures, forming a so-called Bose-Einstein condensate. The theoretical foundation for this was developed by Satyendra Nath Bose and Einstein in 1924.

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