Follow the story. Try a proof. Let curiosity choose how deep you go.
Walk in through the manga: seventeen chapters, sixty-four pocket pebbles, zero required formulas. The Lean source stays behind glass until you ask for it.
Straight to the mathematicsBegin at the proof map — thousands of named theorems — then climb the full ladder from clock inverses to R = T. The story keeps telling itself beside you; it will keep you honest.
Made for company: one reader who loves math and one who does not — one sofa. Whatever each of you finds carries over to the tea salon.
Seventeen chapters, one extraordinary argument. One small discovery is enough for today.
Pip’s rule: mistakes are clues. Every chapter is open, and every question allows another try.
Modularity, the 3–5 trick, and compatible pieces.
Search the local catalogue in English or Japanese. Major landmarks have Japanese titles. Open the full original proof on GitHub for the complete context.
A deformation ring R represents a constrained deformation problem. A Hecke algebra T carries modular Galois data. The universal property supplies an algebra map R→T compatible with representations, and the cited theorem proves it surjective. The broader Taylor–Wiles strategy uses additional patching and algebraic control; do not replace this theorem’s existential-surjection conclusion with an unproved R≅T.
Annotated original · not a live Lean statePoint to a story clue or a highlighted term to connect the two.
Try this logical move →Source: anthropics/fermats-last-theorem @ aa2d8b3. Upstream reports verification; this reader has not independently rebuilt the project. Manga explanations are not formal proofs.
Source license & attributionOne workshop builds possible lifts. The other builds modular ones.
The earlier chapters used lifting as a tool. We now look inside its algebraic machinery: deformation data and Hecke data are connected by a map. The distribution story practiced reading algebraic structure, but does not prove the ring comparison here.
These links explain the reading route. A story analogy is not a proof of this theorem.
Already familiar? Keep reading. Otherwise, open a word or follow the prerequisites from the beginning.
Story → proofThe two workshops represent deformation data and Hecke data. The stated comparison map must reach every target element.
Every target order is reachedFunction.Surjective φStory → proofThe order form is universality: an allowed lift determines the comparison map, rather than an arbitrary factory connection.
The universal order formD.universalStory → proofEvery filled tray slot illustrates surjectivity. The invoked theorem supplies the reason every target order is reached.
Why every order is reachedH.surjective_of_isEquiv_baseChangeAlongStory → proofThe bridge and guarantee card are the map and its compatibility evidence. Surjectivity alone does not guarantee an isomorphism.
Compatibility comes with the maphφ, heA deformation ring R represents a constrained deformation problem. A Hecke algebra T carries modular Galois data. The universal property supplies an algebra map R→T compatible with representations, and the cited theorem proves it surjective. The broader Taylor–Wiles strategy uses additional patching and algebraic control; do not replace this theorem’s existential-surjection conclusion with an unproved R≅T.
The story and source are readable here. Enable JavaScript to edit proofs, try quizzes, and explore the interactive map.
Short scenes. Real logical goals. A pigeon who is very invested in your success.
Opening the casebook…
The workshops agree
Start with the cake-scale story. You only need to read one small piece at a time. If you are in the Fermat story, start with Story depth, then the words listed before the chapter.
You do not need to know Lean, symbols or university mathematics to begin. Definitions come first in the small stories.
Look at the small example before the general formula. Ask what changed and what stayed the same.
Close this panel to return to the exact place you were reading. These are prepared hints for this page.
Start with the first small story →