Jacobian Conjecture for Baby

Summary

Jacobian Conjecture for Baby A step-by-step guide, starting from zero, to a famous math problem that stayed open for 87 years and then fell in July 2026. Every idea is shown as an animation, and you can check the final discovery yourself. This bending can be perfectly undone. Look at this animation. A flat grid gets bent into a strange curved shape. It looks like the grid is ruined. It is not. This bending can be perfectly undone. There is a second simple rule that moves every point back to exactly where it started. Nothing is lost. In 1939, a mathematician named Ott-Heinrich Keller asked a simple question about maps like this one. His question became one of the most famous unsolved problems in mathematics. Many mathematicians published proofs. Every proof turned out to be wrong. The problem stayed open for 87 years. Then, in July 2026, it fell. Only partly, and in a way nobody expected. (The original two-dimensional case is still open.) This article explains the whole story from zero. You do not need any math background. Each chapter is one small idea, explained with a picture first. At the end, you can check the 2026 discovery with your own hands, using simple arithmetic. (Everything here is backed by an open repository: github.com/muchmirul/conjectures. It contains the code for every animation and a test suite that re-checks every mathematical claim.) Here is the plan. Chapters 1 to 8 build the ideas one by one. Chapter 9 states the famous question. Chapters 10 to 12 tell what happened to it. 1 · Functions are machines 2 · The undo machine 3 · Polynomials 4 · Maps of the plane 5 · Straight maps and the area factor 6 · Bending the grid 7 · The microscope 8 · Local vs global 9 · The conjecture 10 · Test it yourself 11 · Why it was so hard 12 · The fall Where to go next 1 · Functions are machines We start with the smallest idea: what a “function” is. A function is a machine. You feed it a number. It gives you back a number. That is all. One number at a time: 3 to 7,...