How an 87-Year-Old Math Problem Finally Fell in July 2026
Jacobian Conjecture for Baby
I built a step-by-step guide to the Jacobian Conjecture, a famous math problem that remained unsolved for 87 years before a surprising partial solution emerged in July 2026. Using simple animations and zero prior math knowledge, I explain how polynomial maps bend grids and why reversing them is so difficult. You can verify the final discovery yourself with basic arithmetic, exploring a story where every previous proof failed until now.
Undoing fails the moment information is destroyed.
- johnfn
This is really good - miles ahead of almost all other math writing I have read. One particular thing I really liked was the explanation of the determinant. When I was in college I spent a very long time trying to get some intuitive explanation for a determinant of a matrix and the best I could get is that you just multiplied and subtracted some numbers and poof there you go. I KNEW there had to be some more comprehensible explanation and it drove me crazy that people just parroted textbooks without any real understanding.
This reminds me of that silly video everyone was shown in middle school about inverting a sphere :-)
I am very curious how it was written (will there be a write up to the write up?!). It feels likely AI assisted, but this seems to me to be the best possible use of AI -- crunching out a bunch of visualizations of complex ideas so that they are easy to understand just by looking. The writing also feels a little AI written but definitely feels very human-assisted.
- neuralkoi
This was an excellent write-up and taught me more in 20 minutes than my linear algebra teacher did in 6 months.
The material however, got fairly dense. After chapter 10, it is no longer "baby" material in my opinion.
- y-curious
I followed very loosely and still got it. Very cool, the kind of math that gets close to feeling like "real life". I was really hoping that your mentions of "solving it by hand" and "you can prove it to yourself by hand" at the end were going to come to some clever maneuver I could do with my own hand (like the physics magnetism hand rule). Still, awesome.