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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 · StoryOriginal 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 depthStart with the intuition.
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

Learn that the empty room is a proved mathematical fact, not an unlucky search for a form.

Arbitrary
No special example was chosen; the argument applies to every allowed input.
Vanishing
Being identically zero.
Where the metaphor ends

An empty concert is a picture of a zero vector space. Checking a few candidate forms would not prove this universal vanishing statement.

</>S_ModularForm_S2_Gamma0_2_eq_zero.lean
Original source ↗ · L195–206Pinned revision aa2d8b3
theorem S2_Gamma0_2_eq_zero' (f : CuspForm (CongruenceSubgroup.Gamma0 2) 2) : f = 0 := by
have hweight : (2 : ℤ) * Nat.card ((↑(CongruenceSubgroup.Gamma 1) : Subgroup (GL (Fin 2) ℝ)) ⧸
(↑(CongruenceSubgroup.Gamma0 2) : Subgroup (GL (Fin 2) ℝ)).subgroupOf
(↑(CongruenceSubgroup.Gamma 1))) = 6 := by
rw [card_quotient_eq_three]; norm_num
have hf0 : (f : ℍ → ℂ) = 0 :=
(CuspForm.norm_eq_zero_iff (↑(CongruenceSubgroup.Gamma 1) : Subgroup (GL (Fin 2) ℝ)) f).1
(S6_levelOne_eq_zero' hweight
(CuspForm.norm (↑(CongruenceSubgroup.Gamma 1) : Subgroup (GL (Fin 2) ℝ)) f))
exact DFunLike.coe_injective (hf0.trans CuspForm.coe_zero.symm)

👩🏻‍🎨 Mika · Source reading guide

This room plays the vanishing theorem: inside one exact weight-and-level space, every cusp form is zero — the stage stays silent, no guest exists. Counting the three archways (the subgroup index) converts the setting into a weight-six, level-one space, where another silence is already on record, and equality of the underlying functions pulls the empty verdict back home.

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 15/17 · Story

The concert of absolute silence

Pip sold tickets before checking whether any music could exist.

How we got here

Level lowering led to a form that should be nonzero. Now a different result says all forms in the specified space are zero. Keep the space and its conditions fixed; the contradiction requires the same object and conditions.

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

Take it to the tea salon
PIP
“My stage is silent tonight. Not one performer: the theorem says every form in this exact space is zero.”
Ready for applause

Story → proofThe silent stage means every form in this exact space is zero. It is stronger than failing to find a performer.

Every such form vanishesf = 0
MIKA
“Three archways, counted once each: the subgroup index supplies the factor that turns weight two into weight six upstairs.”
Count the structure

Story → proofThree archways stand for the subgroup index. Counting them supplies the factor that changes weight two to weight six.

Count the quotientcard_quotient_eq_three

The idea behind the story

This room plays the vanishing theorem: inside one exact weight-and-level space, every cusp form is zero — the stage stays silent, no guest exists. Counting the three archways (the subgroup index) converts the setting into a weight-six, level-one space, where another silence is already on record, and equality of the underlying functions pulls the empty verdict back home.

What establishes that the room is empty?

  • Trying ten thousand forms.
  • Proving that an arbitrary allowed form equals zero.

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

Now bring the two conclusions together: a nonzero form must exist, and every such form is zero.

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 concert of absolute silence

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 →