TITLE: Explicit Hamel basis of real numbers
QUESTION [20 upvotes]: Is there an explicit construction of a Hamel basis of the  vector space of real numbers $\mathbb R $ over the field of rational numbers $\mathbb Q $?

REPLY [3 votes]: Re Andreas' comment, I have a writeup of a generalization of Miller's result:  https://ivv5hpp.uni-muenster.de/u/rds/talks_kiel.pdf