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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.

Powers, smaller problems, and a suspicious parcel.

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

Understand how assumed numbers become a mathematical object carrying evidence.

Dependent field
A field whose type mentions values in earlier fields.
Projection
P.hFLT extracts the equality proof stored in a package P.
Where the metaphor ends

The parcel is hypothetical. Defining its type does not construct a counterexample. The curve picture is an artistic metaphor, not a plot of an actual solution.

</>Def_FLTPrelim_FreyPackage.lean
Original source ↗ · L17–38Pinned revision aa2d8b3
structure FreyPackage where
a : ℤ
b : ℤ
c : ℤ
ha0 : a ≠ 0
hb0 : b ≠ 0
hc0 : c ≠ 0
p : ℕ
pp : Nat.Prime p
hp5 : 5 ≤ p
hFLT : a ^ p + b ^ p = c ^ p
hgcdab : gcd a b = 1
ha4 : (a : ZMod 4) = 3
hb2 : (b : ZMod 2) = 0

👩🏻‍🎨 Mika · Source reading guide

FreyPackage is a structure with data fields and dependent proof fields. hFLT’s type refers to a, b, c and p defined earlier. pp : Nat.Prime p and hp5 : 5 ≤ p are stored witnesses. The terms ha4 and hb2 are equalities in finite quotient rings, not equalities of integers.

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 5/17 · Lean

The suspicious parcel

One hypothetical counterexample. An unreasonable amount of baggage.

How we got here

The previous chapter prepared the hypothetical numbers and their conditions. Now we build a curve from that package. The right-triangle story connected numbers to a shape; this is a new, more advanced construction, not the same theorem.

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

Take it to the tea salon
PIP
“Three stones in the parcel: a, b and c, straight from the forbidden equation. The sandwich is a one-time type joke.”
An evidence-only suitcase

Story → proofThe three stones are placeholders for integers a, b and c. The sandwich joke marks the required type, not an extra input.

Integers in the parcela : ℤ
MIKA
“Before sealing: the exponent must be a real prime, and at least five. The smaller exponents have folders of their own.”
The customs inspection

Story → proofInspecting the seal stands for checking the package’s conditions, including a prime exponent at least five.

The prime needs a lower boundhp5 : 5 ≤ p
PIP
“Packed tight — the gcd-one field certifies that no shared factor rides along. A normalized parcel ships better.”
Standardize the suspect

Story → proofThe carefully packed device represents normalized data. The gcd-one field rules out a shared factor.

A normalized parcelhgcdab : gcd a b = 1

The idea behind the story

FreyPackage is a structure with data fields and dependent proof fields. hFLT’s type refers to a, b, c and p defined earlier. pp : Nat.Prime p and hp5 : 5 ≤ p are stored witnesses. The terms ha4 and hb2 are equalities in finite quotient rings, not equalities of integers.

What does ha4 : (a : ZMod 4) = 3 mean?

  • a is exactly 3 as an integer.
  • a is congruent to 3 modulo 4.

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

This strange curve has an arithmetic fingerprint. Someone else is playing the same tune.

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 suspicious parcel

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 →