A pilgrimage through the lands of structure, in seven waystones — being the field-theoretic arc of Pinter's A Book of Abstract Algebra, chapters XXVII–XXXIII, and the end of three roads.
The second road ended at a cold forge, and the smith keeping it said this: "Beyond here the fields stack into towers, a straightedge and compass fail at three ancient problems, and a boy of twenty explains why the quintic keeps its secret. The third road runs from this pass."
This is that road, and it is the last one. Fields stack on fields and the stack has a height that multiplies as you climb — and that one fact kills two problems the Greeks left open for two thousand years. Then the ladder of fields is set against a ladder of groups, upside down, and every question about equations becomes a question about symmetry. Seven waystones. At the seventh, a young man is sitting on the step writing by lamplight, and he has until dawn.
Sworn testimony of chapters already mastered. Waystones up to and including this one stand unlocked.
Beyond the seventh waystone stands the Gate of Galois — the end of three roads. It does not open for the unproven.