The Jacobian conjecture problem and solution, presented visually. For people like me who don't read math jargon.

This doesn’t explain anything.

Much like this comment 🤷‍♂️

"But no blob is ever crushed: every speck keeps its full volume, everywhere" - while showing connected points moving around (no blobs... no specks...). 'Everything should be made as simple as possible, but not simpler.'

I tried many different versions. the "speck" visualization was more confusing. You should play with it and improve it:

Your visualization explains nothing and only harms the discourse, plotting a complicated polynomial isn't a visualization >_<

Same as your comment! 😀 Please do explain though!

@eigenstate Smooth transformations over the reals on compact domains are very substantially different than algebraic/polynomial transformations over fields like C to the point that they are different fields of mathematics. Hope this helps!

@eigenstate Here is a version fable thinks you'll be somewhat happier with.

maybe this will help, jacobian conjecture for baby

@afterthesoul This is nice!

hope it help many math noob lads!

Does it not get tiring reading this AI slop? How about prompting it to avoid random dramatic sentences and "it's X, not Y" language?

Ha yeah and this was after I iterated on the language a bit. Still, I correctly thought the visualization of the solution would be interesting to people. Besides, fable solved the problem, so it’s fitting fable would get to speak however it wants describing it.

Here is the Claude artifact version of the video where you can interact with the plots.

God i hate seeing this garbage in my feed

You clearly don't understand any of the math behind this. This "explanation" is not even wrong

No explanation claimed. but please do enlighten us

this is a real stupid attempt at explaining it! do you actually understand the conjecture itself? if not, why do you think you're capable of explaining it to others

The comments are brutal. I liked the explanation. Thanks

what is this music?

"Recursive Bloom" Suno AI Prompt: Ambient electronica with IDM micro-detail at 80 BPM in 4/4, built from Euclidean polyrhythms, interlocking prime-cycle pulses, and generative arpeggios that permute across a 24-bar arc. Verse-like openings breathe with granular textures; midsection thickens via spectral blooms and cellular glitches; final bars narrow to a hard stop. Pristine, warm, geometric mix with luminous precision., electronica, edm, soft, warm, ambient

This sounds similar but not the same? A different run, or did you edit it?

hmm yeah it cut off the beginning. I was trying to be fancy with the visualization. will just post a boring version now

alright, alright

Sublime music here

@grok how they go from, theorem is 2 points on a map wont occupy same space, and present a grid map to show, then proceed to disprove it with some wiredly shaped set or arcs

the cusp in the map is making me so angry rn also why doesn't the map x + iy --> (x + iy)^2 nvm i did some research and whar the determinant can be nonconstat and it represents the amount of "scaling (chiral)" at a point; the conjecture concerns itself with maps of CONSTANT det

@grok I’m one of the people who would rather see the math jargon then watch a video. Can you break down what he’s talking about mathematically thank you.

I don't think that summary is really accurate - the conjecture is a statement about polynomials specifically, not arbitrary maps with constant Jacobian.

I agree its a very lossy simplification. The design constraint I gave myself for the video was: it must be understandable by a non-math person. I think the video is "accurate" in what it talks about about but "inaccurate" in the sense that it leaves out details and constraints. Based on feedback from others I tried for an improved version but its still a simplification and it breaks the no-math constraint. If you have ideas on how to do a better visualization that makes it more intuitive I'd love to hear it.

"The one you use to center divs" - somehow I feel attacked. Best insults are difficult to defend against.

The so called jargon IS the math. If you don't understand the statement then you don't understand anything.

Very well explained!

So is Claude Fable something other than an LLM? Because my understanding is that LLMs are simply token prediction tools, trained on input data. It can't think. It can only string tokens together. To me that would mean that somewhere in the training data, a human solved it, and here Fable just pulled that solution. I don't know.

Here's what I got. It said it's the cusp catastrophe.

You are the noise in the conversation

Is it still valid for 2 dimensions as shown in the explanation of the conjecture in the first part of the video?

now do my one

Front end devs are silently vindicated to find out that their work is only slightly easier than finding counter examples to mathematics conjectures that have stood the test of time.

I highly doubt claude found a solution in its own. Likely it was used to help the mathematician.

This is truly an amazing talent, capable of turning what I imagine into something visible to everyone.

Wow you make more videos like this?

Who solved the problem?

👀 wow 🤩

Love this 👏