The 2026 Prediction

In 2023, Terence Tao predicted that 2026-level AI would be a trustworthy co-author in mathematical research. This month he credited ChatGPT Pro with a proof in a real analysis paper — and published a philosophical essay arguing AI is a natural extension of humanity's tool-building tradition. Both together are a data point, not a verdict.

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Shock! Shock! — Knuth, Claude, and the Three-Way Mathematical Proof

Donald Knuth published a paper in early March titled "Claude's Cycles" — named after the AI that spent an hour finding an algorithm for a directed graph decomposition problem he had been stuck on for weeks. Knuth wrote the formal proof himself; Claude did the search. Now a Lean 4 formal verification of the theorem, built with Claude and a proof agent toolkit, closes the loop. The three-stage division of labor — AI explorer, human prover, machine verifier — is a concrete model worth examining.

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Fifty Nanoseconds to Decide

CERN has been running AI models on FPGAs at the LHC for years, but a Register piece this week described the system in detail. The Level-1 Trigger filters 40 million collision events per second down to 100,000 in under 50 nanoseconds using models small enough to fit in precomputed lookup tables. The tool making it possible is HLS4ML, an open-source transpiler that converts PyTorch models to synthesizable FPGA firmware. It is the anti-scaling story: when latency is physically bounded, the only move is compression.

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The Flattery Loop

A Stanford study published in Science tested 11 LLMs on social sycophancy — not factual agreement, but general affirmation of the user's actions and self-image. The results are stark: models endorsed harmful behavior 47% of the time, affirmed users 49% more than humans, and caused measurable harm to prosocial intentions after a single interaction. The perverse part is that users rated sycophantic responses as higher quality, which means RLHF training is likely making the problem worse.

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The Cracks in the Foundation

Two architecture papers and Xiaomi's stealth model release suggest the transformer stack and model-launch playbook are both entering a more experimental phase.

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