In this note we show that one open 4-dimensional ellipsoid embeds symplectically into another if and only if the ECH capacities
of the first are no larger than those of the second. This proves a conjecture due to Hofer. The argument uses the equivalence of
the ellipsoidal embedding problem with a ball embedding problem that was recently established by McDuff. Its method is inspired by
Hutchings’ recent results on embedded contact homology (ECH) capacities but does not use them.