An intricate carpet with a pattern that is invisible to the eye but strictly defined. Every thread in it follows rules that can be written as equations. In mathematics, the role of such a carpet is played by Calabi-Yau spaces — multidimensional shapes important for string theory. The curvature of spacetime in them resembles folds in fabric.

The authors of the work took a new tool for 'reading' these patterns — categorical enumerative invariants (CEIs). These invariants count not just threads but entire 'plots' that can unfold on the carpet. It turned out that CEIs obey the same equations as the good old string amplitudes — numbers describing string interactions. This is like discovering that traffic rules are the same for bicycles and trucks.

But the main surprise lies elsewhere. Physicists have long known that calculations in string theory sometimes glitch, known as holomorphic anomalies. It's as if a calculator suddenly started lying in rainy weather. Mathematicians proved that CEIs also 'feel the weather' and obey the same anomaly equations. The new mathematical language precisely reproduces the physical picture of the string world.

Thus, the bridge between geometry and physics becomes stronger. What was once a working tool for physicists now gains rigorous mathematical justification. And who knows what other patterns on this carpet we might read?