  Given $mp$ different $p$-planes in general position in $(m+p)$-dimensional
space, a classical problem is to ask how many $p$-planes intersect all of them.
For example when $m = p = 2$, this is precisely the question of "lines meeting
four lines in 3-space" after projectivizing. The Brouwer degree of the Wronski
map provides an answer to this general question, first computed by Schubert
over the complex numbers and Eremenko and Gabrielov over the reals. We provide
an enriched degree of the Wronski for all $m$ and $p$ even, valued in the
Grothendieck-Witt ring of a field, using machinery from $\mathbf{A}^1$-homotopy
theory. We further demonstrate in all parities that the local contribution of
an $m$-plane is a determinantal relationship between certain Pl\"ucker
coordinates of the $p$-planes it intersects.
