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.
The auxiliary W′ is nonsingular and semistable, with W′[3] irreducible and its 5-torsion suitably matching W[5]. The displayed theorem exports congruences of aℓ at common good primes ℓ≠5. Modularity of W′ and those congruences subsequently give residual modularity of W at five. This theorem alone does not assert modularity of W.
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 & attributionA second curve joins the cast. Pip requests a stunt double too.
The direct modulo-3 route has conditions and may not apply. The 3–5 strategy introduces an auxiliary curve with matching residual information, so the argument can return through another entrance.
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 yellow helper is useful because its mod-three representation is irreducible. A lookalike alone cannot do the job.
A helper suitable for threeW'.ModRepIsIrreducible 3Story → proofThe helper’s certificate is supplied by an existence theorem with conditions. Mika does not simply assume the helper is available.
A theorem supplies the helperthreeFiveAuxiliaryCurveExistsStory → proofMatching cards, rather than matching hats, stand for arithmetic compatibility. The transfer also requires conditions at each relevant prime.
Keep each prime conditionfun ℓ hℓ hℓW hℓW' hℓ5Story → proofReturning the card transfers congruence of coefficients back to the original model at common good primes.
Transfer the congruenceapOfModel_congr_of_torsionGaloisCongruentThe auxiliary W′ is nonsingular and semistable, with W′[3] irreducible and its 5-torsion suitably matching W[5]. The displayed theorem exports congruences of aℓ at common good primes ℓ≠5. Modularity of W′ and those congruences subsequently give residual modularity of W at five. This theorem alone does not assert modularity of W.
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Short scenes. Real logical goals. A pigeon who is very invested in your success.
Opening the casebook…
Borrow a better passport
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 →