Item from The Library at Mount Char by Scott Hawkins
Peter's domain — the mathematical substrate of reality itself, not human math but the actual equations that hold the universe together.
The catalog of mathematics contains the actual code that reality runs on. Not mathematics as humans understand it — not calculus or algebra, though those are crude approximations of what's here — but the fundamental equations, proofs, and structures that determine how the universe behaves at every scale. Peter's mastery of this catalog gives him the ability to manipulate physical reality by editing its mathematical underpinnings. This looks like magic to anyone who doesn't understand what he's doing, which is everyone except Father.
The math catalog is the most abstract section of the Library. Some of it looks like a normal academic space — blackboards, papers, chalk. But the deeper you go, the more the space itself starts expressing mathematical concepts. Walls curve according to equations. Light behaves in patterns that encode information. The floor isn't always there in a physical sense — sometimes it's a mathematical proof that you're standing on, and it holds your weight because the proof is sound. Peter finds this comforting. Everyone else finds it deeply unsettling.
Also known as: the math catalog, Peter's catalog, the mathematics stacks