Ukrainian mathematician Maryna Viazovska solves task many scientists failed to tackle for centuries

Mathematician Maryna Viazovska made a scientific breakthrough, having solved the problem of cramming balls in Euclidean space. Scientists have grappled with this problem for many centuries.

Censor.NET informs referring to a New Scientist article.

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As reported, mathematicians have proved that they know the best way to pack spheres in 8 and 24 dimensions - the first time this problem has been solved in a new dimension in almost 20 years.

The sphere-packing problem asks a deceptively simple question: What arrangement allows you to cram the most spheres into a limited volume?

In 1611, Johannes Kepler suggested that the best arrangement for stacking 3-dimensional spheres like cannonballs or oranges is a pyramid. But it took until 1998 for Hales to publish his proof - and it took another 16 years and computer assistance to formally verify it.

Now, Ukrainian-born Maryna Viazovska of Humboldt University of Berlin has proved that a uniquely useful grid called the E8 lattice is the best packing in 8 dimensions, and almost immediately teamed up with Henry Cohn at Microsoft Research New England in Cambridge, Massachusetts and other researchers to prove that a related arrangement called the Leech lattice is best in 24 dimensions.

As noted, for reasons mathematicians do not quite understand, such lattices do not show up in other dimensions. But they're widely regarded as being the most efficient arrangements in the dimensions they apply to. "These are unbelievably good packings," Cohn says. "The spheres in these dimensions fit perfectly, it works in ways that do not happen in other dimensions."

"Unfortunately, it's not obvious how to extend this proof to even more dimensions. But this is not just a mathematical game. The sphere-packing problem in 24 dimensions has applications in wireless communication, and has been used to communicate with spacecraft in the distant solar system," the article reads.Источник: https://en.censor.net.ua/n383011