Common AI Myths Debunked by Mathematics
How Geometry, Symmetry, Topology, and Curved Space Challenge What We Assume About AI
We are surrounded by myths all the time. Yes, even in science and technology.
By the time scientific results reach the public, they have often passed through expectations, money, marketing, and a lot of storytelling. The mathematical details that spoil a good headline rarely survive the trip intact.
AI is the extreme case
We have built an astonishingly powerful machine, but also an increasingly complicated one. When something breaks, the instinct is often to scale the machinery instead of questioning the mathematics underneath it.
But what if scale is not the problem at all? What if better mathematics can eliminate the problem before brute force even begins?
A small group of researchers is already exploring exactly that through geometry and symmetry, equivariance, topology, curved and hyperbolic representations, and related mathematics.
Most of this work still barely reaches the mainstream AI conversation.
That is where this story begins.
We are going to take some of the most familiar beliefs about AI and expose their weaknesses, and in some cases their outright falsehoods, using the mathematics that a more structurally sound AI could be built on.
You will see it for yourself through original animations that make these geometric and topological ideas almost impossible to miss: the real problem with AI may not be that our models are too small, but that we built them in the wrong mathematical space.
Don’t believe me?
Keep reading. By the end, your view of AI will be completely turned upside down.
Most of the AI World Still Isn’t Having This Conversation in Public
This is not another debate about consciousness, AGI, or whether AI will take your job.
I am talking about the mathematics underneath the models. As mentioned before, a small group of researchers is already working on geometry, equivariance, hyperbolic representations, symmetry, topology, and related ideas. But most of that work is still scattered across papers and small technical communities.
Meanwhile, if you are working on AI models or simply using them, you are probably getting tired of the same recipes for the shortcomings of current AI:
Bad representation? Add dimensions.
Weak understanding? Add examples.
Poor memory? Add context.
Weak performance? Train more.
Not enough capability? Give the model more freedom.
Sometimes that works, though with sloppy mathematics.
Often, it just gives you a bigger version of the same problem.
Which leaves a much more interesting question:
How much of what we force AI to learn by brute force is really a consequence of choosing the wrong mathematics in the first place?
That is the question behind everything that follows.