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A MATHEMATICAL ADVENTURE FOR CURIOUS MINDS

A small why. A big adventure.

Follow the story. Try a proof. Let curiosity choose how deep you go.

No account. No API key. Just curiosity.

Two ways in. One table between them.

I'd rather not fight math today

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 mathematics

Begin 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.

Start with “I don’t know yet.”

Seventeen chapters, one extraordinary argument. One small discovery is enough for today.

17 chapters · LeanOriginal source ↗

Pip’s rule: mistakes are clues. Every chapter is open, and every question allows another try.

Lower the level. Empty the room. Close the case.

Choose your depthProof terms and exact dependencies.
Explore the whole proof29,511 theorems · original statements · dependencies

Search the local catalogue in English or Japanese. Major landmarks have Japanese titles. Open the full original proof on GitHub for the complete context.

Your discovery in this chapter

Follow the exact collision: f ≠ 0 meets f = 0.

hf : f ≠ 0
A proof of f=0 → False; feed it an equality proof to derive False.
Unused hypothesis
A theorem can accept a parameter that its proof does not actually depend on. Read the implementation to detect this.
Where the metaphor ends

The room represents one specific vector space of cusp forms. It does not say all modular forms vanish. Level lowering is a deep arithmetic result, not simply shrinking an object.

</>S_FreyPackage_no_frey_package.lean
Original source ↗ · L139–147Pinned revision aa2d8b3
theorem Wiles_Frey (P : FreyPackage) :
¬ GaloisRepIsIrreducible (K := AlgebraicClosure ℚ) ℚ P.freyCurve P.p := fun hirr =>
let ⟨f, hf⟩ := level_lowering_to_two P (frey_isModular P) hirr
end FreyPackage
theorem solution (P : FreyPackage) : False :=
FreyPackage.Wiles_Frey P (FreyPackage.Mazur_Frey P)

👩🏻‍🎨 Mika · Source reading guide

Wiles_Frey returns a negation, implemented as fun hirr => … . The let-pattern unpacks ∃ f, f ≠ 0. Since hf : f = 0 → False, applying it to S2_Gamma0_2_eq_zero f produces False. solution supplies Mazur_Frey P to this negation. In the linked lowering implementation, hmod is formally unused: modularRepOfConductorLevel rederives the needed modular information.

Annotated original · not a live Lean state

Point to a story clue or a highlighted term to connect the two.

Try this logical move →
Source and verification details

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 & attribution
Chapter 16/17 · Lean

The room with no room

A nonzero guest. A room where every guest must be zero.

How we got here

One branch produced f ≠ 0; the other gives f = 0 in the same space. These cannot both hold. We return to the hypothetical solution in chapter 1 and reject the assumption that it exists.

These links explain the reading route. A story analogy is not a proof of this theorem.

Take it to the tea salon
ARCHIVIST
“The box beside it is a certified void: every form of that same space equals zero. Other rooms, no comment.”
A strict occupancy policy

Story → proofThe empty display box is the theorem that every form in that same space equals zero. Other spaces are not claimed to be empty.

The same form must be zeroModularForm.S2_Gamma0_2_eq_zero
MIKA
“The stone and the box share one address. Applying the nonzero evidence inside the zero theorem is the fastest end on record.”
The impossible guest

Story → proofThe stone beside the empty box is one and the same f with evidence for f ≠ 0 and f = 0. Applying hf gives the contradiction.

Nonzero meets zerohf

The idea behind the story

Wiles_Frey returns a negation, implemented as fun hirr => … . The let-pattern unpacks ∃ f, f ≠ 0. Since hf : f = 0 → False, applying it to S2_Gamma0_2_eq_zero f produces False. solution supplies Mazur_Frey P to this negation. In the linked lowering implementation, hmod is formally unused: modularRepOfConductorLevel rederives the needed modular information.

What is hf (ModularForm.S2_Gamma0_2_eq_zero f)?

  • A numerical test that evaluates f.
  • A proof of False obtained by applying a negation to an equality proof.

The story and source are readable here. Enable JavaScript to edit proofs, try quizzes, and explore the interactive map.

The case is closed. But who checks the detective’s paperwork?

Read. Try. Make it click.

  1. Read the manga and choose Story, Math, or Lean depth.
  2. Open the proof playground. Edit the tactics and watch the goals change.
  3. Select a state, term, or hint. Wrong turns are part of the story.

The playground checks a small propositional language. FLT excerpts are editable reading material, not live-checked Lean proofs. The complete FLT build remains an upstream verification report.

I’m lost · Help

Mika’s help desk

The room with no room

One thing at a time

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.

In simpler words

You do not need to know Lean, symbols or university mathematics to begin. Definitions come first in the small stories.

A small clue

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 →