“Hou, later joined by Chen, took advantage of the fact that, upon closer analysis, the approximate solution from 2013 seemed to have a special structure. As the equations evolved through time, the solution displayed what’s called a self-similar pattern: Its shape later on looked a lot like its earlier shape, only re-scaled in a specific way.

As a result, the mathematicians didn’t need to try to look at the singularity itself. Instead, they could study it indirectly by focusing on an earlier point in time. By zooming in on that part of the solution at the right rate — determined based on the solution’s self-similar structure — they could model what would happen later on, including at the singularity itself.”

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