Mathematicians Solve Decades-Old Classification Problem

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If you’re conducting a census of all the plants growing in a specific region, rather than tally every single plant, you might decide to organize them by species. Doing this along certain stretches of the Tuscany coast would not be too difficult, said the University of Turin mathematician Gianluca Paolini, because you’ll mainly find a single plant — maritime pine (pinus pinaster). If you were in the Amazon rainforest, by contrast, you’d face a much bigger challenge trying to work out the names and numbers of all the species that have taken root there. Doing so fully would, in all likelihood, be impossible.

Mathematicians Solve Decades-Old Classification Problem | Quanta Magazine

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

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