  We construct irrational irreducible components of the Hilbert scheme of
points of affine n-dimensional space, for n at least 12. We start with
irrational components of the Hilbert scheme of curves in P^3 and use methods
developed by Jelisiejew to relate these to irreducible components of the
Hilbert schemes of points of A^n. The result solves Problem XX of [J.
Jelisiejew, Open problems in deformations of Artinian algebras, Hilbert schemes
and around, arXiv:2307.08777, 2023].
