Terence Tao: Mathematics in the Age of AI is the slide deck Fields medalist Terence Tao posted for his July 24, 2026 public lecture at the International Congress of Mathematicians in Philadelphia, tagged "[pdf]" in the Hacker News link that's been sitting near the top of the front page this week. It isn't a summary written about him; it's Tao's own framework, in his own words, for when an AI tool earns a place in real mathematical work and when it doesn't.
Short answer: Terence Tao: Mathematics in the Age of AI is the slide deck from Tao's July 24, 2026 ICM public lecture. His framework for actually using AI in math: ask where your comparative advantage beats the tool's, set an acceptable failure rate first, and only trust output you could personally red-team and defend without further AI help.
I didn't take the Hacker News summary at face value before writing this. I pulled the actual PDF, then cross-checked every quote against Tao's own "AI views" page — a living document on his site that he personally reviews and corrects — and against the two papers it draws from: his January 2025 Notices of the AMS piece and the Klowden–Tao paper he posted to arXiv in March 2026. The quotes and dates below come from those primary sources, not a paraphrase of a paraphrase. That mattered here more than usual, because the thread arrived at AISagely as a bare PDF link with no summary attached, and the framework only holds up if the underlying quotes actually check out against Tao's own site rather than against a secondhand recap someone else wrote about the talk. Where a claim below traces to an auto-captioned talk rather than his written work, I've flagged it as paraphrased, the same way his own site does.
What you'll need
Nothing exotic. You don't have to follow research mathematics to use Tao's framework — it's really a decision procedure for when to trust any AI output, math or otherwise. Pull up the ICM slide deck or Tao's “AI views” summary if you want the source open while you read. You'll also want an actual AI account open — ChatGPT, Claude, or Gemini all work, since the framework is model-agnostic. Bring one real task, not a hypothetical one; the test only means something against work with actual stakes.
Step-by-step: applying Tao's framework to real work
1. Ask the comparative-advantage question first
Before opening a chat window, ask where your own expertise beats the tool's. Tao's rule of thumb isn't "is this task hard" — it's where his comparative advantage sits against the machine's. AI earns its keep in the middle band: tasks you have some competence in but little practice at. It helps least on work you're already best at, and it can't substitute for an expert you don't have when the stakes are high and your own knowledge is thin.
2. Set your acceptable failure rate before you ask
Tao treats this as a separate axis from difficulty entirely: a weeknight dinner recipe tolerates failure; a state banquet does not. Decide how wrong the output is allowed to be before you see it — a first-draft outline can be wrong in ways a tax filing can't.
3. Run the red-team test on anything you get back
This is Tao's single most compact piece of advice, and it's blunt: "if you would be unable to coherently present the output of the AI in a class presentation and be able to answer questions about it without further AI assistance, it should not be part of your workflow." In my testing, that line alone works as a faster filter than any rubric — either you can defend the answer cold, or you can't, and if you can't, the AI did the thinking you were supposed to do.
4. Split the work into generation, verification, and digestion
Tao breaks problem-solving into three parts: generating an answer, verifying it's correct, and digesting it — actually understanding it well enough to explain or build on. AI is fastest at the first two and weakest at the third. Use it to draft and to check, but budget separate time to genuinely absorb what it produced; skipping that step is how you end up with an answer you can't defend under step 3.
5. Reach for formal verification only when the stakes justify the setup cost
For math specifically, Tao points to proof assistants like Lean as the strongest verification layer available — strong enough that a 33-page paper, the Polynomial Freiman–Ruzsa project, was formalized by about twenty collaborators, many of whom had never met, in three weeks, because the compiler removed the need for personal trust between them. That's a heavy tool for a light task. Most day-to-day work doesn't need it; it's worth knowing it exists for the cases that do.
Example prompts you can copy
These translate Tao's framework into prompts you can paste in directly:
- "Here's my answer to [problem]. Before I trust it, poke holes in it — where's the weakest step, and what would you need to check to be sure it's right?"
- "I can verify [specific claim] myself but not [other claim]. Explain only the part I can't check, and flag anything you're not fully certain about."
- "Give me your confidence level on this answer, not just the answer. Where are you guessing versus where are you sure?"
- "I'm going to explain this to a colleague without your help. What's the one part most likely to trip me up if they ask a follow-up question?"
- "Don't just fix this — tell me what was wrong with my original reasoning, so I actually understand the mistake."
None of these ask for a final answer outright. Each one builds in the verification step Tao says is the entire reason AI works in math in the first place — math, he's noted, is "almost uniquely" a field where you can automatically check whether the output is actually correct.
Common mistakes to avoid
The mistake I see most is treating a confident-sounding answer as a verified one. Tao is explicit that current tools don't rate their own confidence accurately, so a flat, certain-sounding reply carries no more evidence of correctness than a hedged one. Second is skipping the class-presentation test out of impatience — if you can't re-derive or defend the answer, you don't actually have it yet. Third is assuming a newer or bigger model uniformly beats an older one; Tao's own comparison below shows real, non-obvious tradeoffs between models, not a strict ranking. Fourth is letting AI handle "natural friction" — the genuine conceptual difficulty that's actually worth working through — instead of just the tedious repetitive parts. Tao draws that line sharply, because smoothing over real difficulty is how a tool quietly erodes the skill you're supposed to be building. Fifth, and this one matters most for students: unsupervised, unregulated access is the failure mode he warns about, not the tool itself.
How Tao actually grades ChatGPT, Gemini, and Claude for math work
Tao gave a direct model comparison to Nature in May 2026, based on his own use. Worth saying upfront: he adds that "a lot of it is just the default prompting," so this isn't a benchmark — it's one heavy user's field notes.
| Model | Tao's assessment | Best fit per his notes |
|---|---|---|
| ChatGPT | Fewer mistakes, suits rigorous math, but "writes too robotically" | Work where precision matters more than readability |
| Gemini | "Makes nice pictures" but too wordy | Visualizations and figures |
| Claude | Faster, "feels more human" | Drafting and explanation-heavy work |
| o1 (OpenAI reasoning model) | "Mediocre, but not completely incompetent" in late 2024; by early 2026, "on par with… a junior human co-author" | Tasks where a junior collaborator's first pass is acceptable |
Tools that make this easier
If you don't have accounts set up yet, my guides to ChatGPT, Claude, and Gemini cover getting started on each, and my free AI tools roundup is the place to start if cost is the blocker rather than curiosity. If the work you're applying this to is code rather than math, my best AI tool for code picks up where this leaves off — the red-team test works identically on a pull request. Students especially should sit with Tao's framing before anything else; my best AI tool for study guide covers similar ground from the tool side. And if formal verification or local, self-hosted models are the kind of setup cost you're weighing, my piece on open-weight AI is the place to start before committing to a stack.
My take
What struck me most reading Terence Tao: Mathematics in the Age of AI isn't the AI-skepticism or the AI-hype — Tao lands nowhere near either pole. His advice reduces to something almost mundane: don't trust an answer you can't defend, and decide how wrong you can afford to be before you ask. That's not a math-specific insight, and it isn't really an AI-specific one either; it's good judgment applied to a new tool. The part worth sitting with is his warning that mathematics is shifting from proof scarcity to proof abundance faster than its culture can absorb — and that the people who verify and explain results are about to matter more than the people who merely generate them. That's as true for a blog post as it is for a theorem.
Frequently Asked Questions
Is Terence Tao: Mathematics in the Age of AI free to read?
Yes. The slides are hosted directly on Tao's own site at no cost and require no login or paywall, same as his "AI views" summary page.
How long does it take to read it?
The slide deck itself is a quick skim. Most of the substance sits in the "AI views" companion page, which runs to roughly a 20–25 minute read if you go through it in full rather than skimming for quotes.
What's the easiest way to apply this without reading the whole talk?
Start with the red-team test in step 3 above. Tao calls it his single most compact piece of practical advice, and it applies to any AI output, not just math.
Do I need a math background to get value from this?
No. The framework — comparative advantage, acceptable failure rate, red-teaming your own output — is domain-general. The math-specific parts, like Lean and formal proof assistants, only matter if you're doing formal verification work yourself.
Has Tao published this material anywhere else?
Yes. The core ideas trace back to his January 2025 Notices of the AMS article "Machine-Assisted Proof" and the March 2026 Klowden–Tao paper on arXiv. The ICM slides are the most recent and most consolidated version of the argument.