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I don’t particularly like the title. The mathematicians showed some intuitive properties of equations that are used to model ice melting are correct. They did not prove anything about the actual physical process of ice melting, which would be something done in a physics or chemistry lab. This reminds me of when pop-sci articles discuss new developments in string theory as fact, when there has been no experimental evidence for the existence of strings.

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This criticism seems really unwarranted

The full title and subtitle is

“ Mathematicians Prove Melting Ice Stays Smooth:

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.”

Hard to think of a more concise and accurate way to describe the problem. The article does a nice job describing the problem, and like all quanta articles links the arxiv paper in the first few paragraphs

https://arxiv.org/abs/2103.13379

The title is to catch your interest, the subtitle provides an accurate summary, if you have a more advanced understanding of math the arxiv link is included at the beginning, otherwise the article is a nice summary…

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