A Technical Blog Series

The Broken
Math of
Modern AI

Everyone obsesses over parameters and benchmarks. Nobody reads the equation. This series is about the equation, and why it is structurally, mathematically broken.

7
Chapters
2
Published
∞
Wrong assumptions
Read the series
The Series

Seven Chapters.
One Uncomfortable Argument.

We take every major LLM architecture decision and run it through rigorous mathematics. The results are not flattering.

01
Dynamical Systems · Numerical Methods
The Curse of Euler Integration
Why the world's most advanced AI runs on the crudest numerical integrator known to man, and why that explains every drift, hallucination, and overcommitment you've ever seen.
Live
02
Contraction · Lyapunov · Spectral Stability
The Unconstrained Machine
Even with a perfect integrator, the Transformer violates every mathematical condition required for stable memory: no contraction, no Lyapunov function, no spectral constraint. Five conditions. Zero satisfied.
Live
03
Attention Mechanism · Reasoning
Attention Is Not Reasoning
Softmax attention is a weighted average over value vectors. We prove why this operation is structurally incapable of logical inference, and what that means for every "reasoning" benchmark.
Coming Soon
04
Energy · Thermodynamics · Depth
The Energy Explosion
A Transformer of depth L has energy that grows linearly with L, with no structural ceiling. We derive the exact bound and show why very deep networks are thermodynamically incoherent.
Coming Soon
05
Autoregression · Error Propagation
Autoregressive Instability
When a model generates its own input, every structural flaw compounds. We analyze the error propagation dynamics of autoregressive decoding and show why long outputs degrade mathematically, not just empirically.
Coming Soon
06
Scaling Laws · Parameter Efficiency
Why Scaling Fails
More parameters do not fix a broken integrator. More data do not add a missing Lyapunov function. We show why the structural flaws in this series are scale-invariant, and what scaling actually does and doesn't fix.
Coming Soon
07
Synthesis · The Path Forward
The Uncomfortable Conclusion
Everything we've shown points to one thing: the Transformer architecture is not a foundation we should keep building on. We look at what a mathematically honest alternative looks like, and why it matters now.
Coming Soon
About This Series

Why This Needs to Be Said

The AI industry is moving at extraordinary speed, mostly in one direction: scale. More parameters. More data. More compute. Almost no one is asking whether the mathematical foundation is sound. This series is that question, asked rigorously, with equations, with proofs, and without apology.