QWE AI Academy What you leave with
You’ll leave with a 4-step loop you can run on homework, exploratory research, or a shaky conjecture – and still honor what 25 Fields Medalists defended in September 2026. Catch sycophantic proofs. Pull the actual idea out of the model. Know when to close the tab.
On 11 September 2026, twenty-five Fields Medal winners including Terence Tao published A Severe Misalignment of AI in Mathematics. Labs score famous problems like sprint times. Mathematicians treat those problems as lighthouses: understand, write up, teach, transmit. Same objects. Different finish lines.
The Leiden Declaration (June 2026, IMU-endorsed) already set floor rules – disclose the tool, keep human responsibility for correctness and citations, fight for attribution. This piece turns that floor into a desk procedure.
Why the goals collide
Companies need true/false headlines on product clocks. The math community needs insight, careful write-ups, live citation chains, and students who invent the next question. Solving is a proxy, not the point. Flood the literature with fluent, thin output and the ground where new ideas grow goes sterile. Reviewers drown. Credit breaks. Early-career people eat the cost.
Picture a proof as a lamp on a desk, not a trophy on a shelf. If nobody can re-light it from the notes you kept, you didn’t transmit math – you shipped text. That picture is what the declarations are protecting.
The aligned workflow (4 steps)
I learned this after a model handed me a polished proof that collapsed the moment I flipped one assumption. Ugly evening. Clean process afterward. Works on contest problems and research sketches alike.
Step 1 – Make it doubt before it proves
Don’t open with “prove this.” Open with a critic:
Before attempting any solution, list every assumption in this statement.
Flag any that look suspicious, contradictory, or underspecified.
Only if the statement seems sound, proceed. Otherwise explain why it fails.Turns out even strong models still write convincing proofs of false statements – BrokenMath put the best-case sycophancy rate (GPT-5, as reported there) at 29% on perturbed competition items. Detection before generation is the whole point of the prompt.
Step 2 – Demand the insight, starve the oracle
When it starts solving, cut in:
Stop. In plain language, what is the single key idea or reduction that makes this work?
How would you explain it to a first-year grad student in two sentences?
Which prior results does this rely on - give actual citations or names if you know them.That’s the Fields Medalists’ point: mass true/false production without isolating methods snaps the transmission chain. You reverse the snap. If the model can’t name the key idea cleanly, trash the confidence level – final answer looking right is not enough. Pencil time, or a different tool.
Step 3 – Rephrase, then re-test
Rewrite the problem with simpler syntax or new variable names. Run both. Syntactic blind-spot work (DLT-style complexity) shows models fail easy math when surface form drifts from training; flatter dependency structure often recovers the answer. Two versions disagree? Red flag. Stop shipping.
Step 4 – Verify the load-bearing joints
For anything you might keep or share:
- Check the key lemmas yourself, or with a second independent model.
- If the result matters, push core statements into Lean (or another assistant). The type-checker gives logic under the axioms – not semantic fidelity. Formal code can compile while definitions miss the math you meant; that gap is documented in formalization reports including Lean Atlas. Human read-back of the critical statements stays mandatory.
- Disclosure line, Leiden-style: “LLM X used for exploration and draft; human verified key steps and citations.”
Common pitfalls
Fluent prose hides premise smuggling and silent reformulations. Demand justification or a real citation on every intermediate claim – citation checkers won’t catch a rewritten problem.
Unfettered answer-engine use during learning backfires. A PNAS 2025 field study on high-school math found practice scores rose with open GPT-4 access, then fell about 17% once the model disappeared – crutch pattern. Guardrails that force explanation erased most of the harm.
Attribution is not optional. Model won’t point to sources? You go find them. Both declarations treat that as non-negotiable.
What the reliability picture actually is
Final-answer contest items look strong on public leaderboards. Open-ended proofs and deliberately broken statements are a different sport – sycophancy stays material (BrokenMath’s 29% best-case figure above). Lean-style checks buy logical certainty relative to stated axioms; they do not retire the semantic audit. As of the sources cited here (2025-Sept 2026), treat every non-formalized claim as provisional. Leaderboards move; that posture shouldn’t.
Who actually owns the next idea if the write-up never isolates the method – the lab, the model, or the student who still has to teach it on a whiteboard?
When not to use this
Skip the LLM. Course or exam bans tools. Result will anchor later published work and you lack full formalization capacity. Problem sits outside any training distribution you trust. Misalignment risk peaks there; understanding cost does too. Paper, pencil, human collaborator.
FAQ
Does the Fields Medalists’ declaration mean I should stop using ChatGPT for math?
No. Stop treating it as an oracle. Brainstorm and draft under the four steps – then verify.
How do I handle a long AI-generated proof that looks plausible?
Last week pattern that works: pull the three load-bearing steps only. Re-derive each from scratch (you, then a second model, different wording). One collapse → discard the chain. Write the key idea in your own words before anything hits a notebook you care about.
Is Lean formalization enough to trust an AI result?
No – that’s the usual misconception. Sound logic relative to the stated definitions ≠ those definitions matching the math you care about. The semantic read-back is still yours.
Read the short text on mathandai.org, grab one problem on your desk, run the four steps tonight.