# Why a high-school dropout is currently outperforming PhDs in AI > Source: > Published: 2026-08-15 22:13:06+00:00 # Why a high-school dropout is currently outperforming PhDs in AI The core of the problem is that natural language is too ambiguous for complex math. When an AI tries to solve a hard geometry problem in English, it often makes a "leap of faith" that looks correct but is logically bankrupt. The breakthrough comes when we force the AI to work within a formal language—like Lean or Isabelle—where every single step must be mathematically verified by a kernel. If the kernel says the step is wrong, the AI can't just "convince" the user it's right; it has to backtrack and try a different logical path. For those trying to build a similar AI workflow for technical tasks, here is a practical tutorial on how to implement a basic verification loop: 1. **Define the Formal Target**: Instead of asking for a solution in text, require the output in a formal language. For example, use a Lean 4 snippet to define the theorem you are trying to prove. 2. **Implement the Generator**: Use a high-reasoning model (like [Claude](/en/tags/claude/) 3.5 Sonnet or GPT-4o) to generate a candidate proof. 3. **The Verification Gate**: Pass that output through a compiler or formal verifier. ``` # Example of running a Lean file to check for errors lean .my_proof.lean ``` 4.**Error Feedback Loop**: If the compiler returns an error, feed the exact error message back into the LLM. This creates a self-correcting loop where the AI learns from the formal constraints of the math, not just the patterns in its training data. **Standard LLM approach:** Probability-based guessing, high hallucination rate in multi-step logic, looks plausible but often fails.**Formal Verification approach:** Deterministic correctness, zero tolerance for logical gaps, slower generation but 100% reliability once verified. This shift proves that the next era of LLM agents isn't about bigger datasets, but about better "guardrails" for reasoning. By combining the creative intuition of a model with the rigid laws of formal mathematics, we are seeing AI solve problems that were previously thought to require human-level insight. It's a reminder that the most effective prompt engineering often comes from people who aren't afraid to break the "standard" way of doing things. [LLMs are just massive pattern libraries for math proofs 3h ago](/en/news/6491/) [Claude Code actually solved a math problem I'd been stuck on for 4d ago](/en/news/5956/) [Next Two American Airlines 737s nearly collided because they were →](/en/news/6512/) [these AI tool field notes](https://tanyan888.com/), with plenty of directly applicable cases.