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acid andy [soylentnews.org] writes:

https://www.popularmechanics.com/science/math/a45533729/periodic-table-of-shapes/ [popularmechanics.com]

Just as molecules can be broken down into atoms [popularmechanics.com], so too can mathematical shapes be broken down into more basic components. These components are known as Fano varieties—named after Italian mathematician Gino Fano—and understanding them can help mathematicians make major discoveries.

There’s just one problem. Fano varieties are notoriously difficult to categorize.

That’s what scientists at the Imperial College of London discovered when they set out to create a “periodic table of shapes” more than a decade ago [eurekalert.org]. Similar to how elements are grouped together with like elements on the periodic table, this geometric table aims to group related Fano varieties together. Easier said than done.

So, the Imperial team—which also includes scientists from the University of Nottingham—turned to AI and machine learning [popularmechanics.com] to help speed up the process. The results of this novel method were published in the journal Nature Communications [nature.com] in early September.

“Fano varieties are basic building blocks in geometry—they are ‘atomic pieces’ of mathematical shapes,” the study reads.

[...] Fano discovered the first of these “atomic” shapes back in the 1930s. More have been discovered since, but so far, they lack any organizing principle. Once categorized in a periodic table defined by a shape’s unique quantum [popularmechanics.com] period, gaps could help tell mathematicians where new shapes could be discovered (much like what the periodic table does for chemists and physicists).

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