Mathematicians Are Close to Building the Perfect Periodic Table of Shapes

mathematicsalgebraic-geometrymachine-learningfano-varietiesai-in-science

Abstraction: ML used to classify Fano varieties toward a geometric periodic table

Key points:

Fano varieties — named after Italian mathematician Gino Fano (first "atomic" shapes discovered in the 1930s) — are the irreducible building blocks of mathematical geometry, analogous to atoms in chemistry
Imperial College London and University of Nottingham teams have worked for over a decade to build a "periodic table of shapes" grouping Fano varieties, with results published in Nature Communications (September 2023)
The ML model assigns a "barcode" (numerical encoding of shape features) to each Fano variety and predicted shape properties from barcodes with 99% accuracy
Key conjecture supported: the quantum period of a Fano variety uniquely determines that variety, providing the organizing principle needed for the periodic table
Machine learning excels at identifying structure in complex mathematical data where theoretical understanding is lacking — analogous to calculators or computers as step-changes in mathematical practice
Gaps in the completed periodic table could point toward undiscovered Fano varieties, mirroring how Mendeleev's table predicted missing elements

Connections: Imperial College London · Machine Learning · AI In Science · Algebraic Geometry