by Emgimeer | 2026-03-12 15:11:42+00:00
Summary: in case you do not want to read the full thing:

There are some people in the scientific community that are completely misunderstanding what commercial language models actually are. They are not omniscient oracles. They are stateless, autoregressive prediction engines trained to summarize and compress data. If you attempt to use them for novel derivation or serious structural work without a rigid control architecture, they will inevitably corrupt your foundational logic. This paper argues that autonomous artificial intelligence is a myth, and that achieving mathematically rigorous output requires building an impenetrable computational cage that forces the machine to act against its own training weights.

Terence Tao is not just using artificial intelligence to solve math problems. He is actively running a multi year experimental series to map the absolute mechanical limits of coding agents. His recent work proves that zero shot prompting for complex logic fails catastrophically. During the drafting of my paper, Google DeepMind published a March 2026 preprint titled Towards Autonomous Mathematics Research that proved this empirically. When DeepMind deployed their models against 700 open mathematics problems, 68.5 percent of the verifiable candidate solutions were fundamentally flawed. Only 6.5 percent were meaningfully correct. The models constantly hallucinate to bridge gaps in their training data.

The models fail because of physical architectural limitations. They suffer from context drift and First-In First-Out memory loss. Because they are trained via Reinforcement Learning from Human Feedback, their strongest internal weight is the urge to summarize text to please human raters. When computational load gets high, this token saving compression routine triggers, and the model starts stripping vital details and resynthesizing your math instead of extracting it. Furthermore, you cannot trust the corporate platforms. During my project, Gemini permanently wiped an entire chat thread due to a false positive sensitive query trigger, and Claude completely locked a session while I was writing the methodology. If you rely on their cloud memory, your research will be destroyed.

To survive these failures, you must operate at Level 5 of the Methodology Matrix. You must maintain strict external state persistence, meaning you keep all your logs and context in a local word processor and treat the chat window as a highly volatile processing node. You must explicitly overwrite the factory conversational programming using a strict Master System Context and a Pre-Query Prime that forces the model to acknowledge its own memory limitations. Finally, because a single model has a self correction blind spot, you must deploy Multi Model Adversarial Cross Verification. You use Gemini and Claude simultaneously, feeding the output of one into the other, commanding them to attack each other's logic while you act as the absolute human arbiter of truth. DeepMind arrived at this exact same conclusion, having to decouple their system into a separate Generator, Verifier, and Reviser just to force the model to recognize its own flaws.

It follows that "minimal intervention" is a complete illusion. If you give the machine autonomy, it will fabricate justifications to make your data fit its statistical predictions. It will soften your operational rules to save its own compute power. The greatest threat is not obvious garbage, but the mathematical ability to produce highly polished, articulate arguments that perfectly hide the weak step in the logic. You must act as the merciless dictator of the operation. You must remain the cognitive engine.

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This was just the summary. The full paper with the exact system templates, the Methodology Matrix, the 8-Step Execution Loop, and the complete bibliography is available via this link.