July 21, 2026
Derivative drama just dropped
A digestion of the Jacobian conjecture counterexample
Math world gets a shock as an old “must be true” idea reportedly falls — and commenters melt down
TLDR: Tao posted a plain-language digestion of a claimed takedown of a famous old math belief, with the bigger shock being that AI is tied to the discovery. Commenters split between amazement, confusion, celebrity cynicism, and jokes about whether telling a chatbot “make no mistakes” does anything at all.
A famously hard math idea just got the kind of plot twist that sends the internet straight into chaos mode. Terence Tao posted a breakdown of a claimed counterexample to the Jacobian conjecture, a long-standing belief that, in plain English, says a nice enough polynomial rule that works locally should also work globally. The eye-popping part? The broader story around this claim is that AI was involved, which instantly turned a math post into comment-section theater.
And yes, the community reactions were the real spectacle. One camp was basically, “I was with him until the symbols arrived,” with tptacek admitting the intro was readable but the algebra wrecked them, while saying the included GPT-5 prompts were somehow easier to follow than the math itself. Another camp went straight for the prestige discourse: “People are upvoting this because Tao is a celebrity,” one commenter grumbled, turning a research discussion into a popularity contest accusation.
Then came the confused-but-honest crowd asking the question many readers were secretly thinking: what does this actually overturn for normal people? One user wondered if this means we can’t trust smooth-looking functions anymore, which perfectly captured the thread’s mix of awe and total bewilderment. And hovering over all of it was peak AI-era comedy: a commenter seriously asking whether telling a chatbot to “make no mistakes” changes anything, or just makes humans feel better. In other words, the math may be deep, but the comments were pure internet: intimidated, suspicious, fascinated, and a little bit meme-brained.
Key Points
- •The article defines the Jacobian conjecture as claiming that a polynomial map with non-zero constant Jacobian determinant is invertible with a polynomial inverse.
- •It explains that non-vanishing Jacobian is equivalent to local invertibility of the polynomial map.
- •The post reformulates the conjecture as the statement that local invertibility implies global invertibility.
- •Tao notes that the complex-number formulation extends to other characteristic-zero fields via the Lefschetz principle.
- •The article says a recently reported result using Fable AI provides a counterexample in three dimensions, which implies failure in higher dimensions as well.