He studied botany at the University of Copenhagen from 1911 under the professors Eugenius Warming, Christen C. Raunkiær, L. Kolderup Rosenvinge og W. Johannsen.
Hagerup’s scientific works concern evolution, polyploidy and pollination, among other things.
He put forward the hypothesis that the ploidy level is an important factor in the distribution and ecology of plant species.
In contrast, another of his scientific ideas has been disproven by later modern research – the idea of a direct ancestry of the centrosperms (approximately equal to Caryophyllales) from the gymnospermous Gnetophyta and, hence, two separate evolutionary lineages within the flowering plants.
Many of Hagerup’s studies were concerned with plant species of the Ericaceae, Empetraceae and related families, or ’’Bicornes’’ as they were known in the Wettstein system.