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AI Is Beating Law Professors at Their Own Job — and Mathematicians Are Sounding the Alarm About What Comes Next

AI Is Beating Law Professors at Their Own Job — and Mathematicians Are Sounding the Alarm About What Comes Next
Two separate studies published this week deliver an uncomfortable message for academia: AI is outperforming human experts in legal tutoring, and mathematicians are now formally warning that the technology threatens to corrupt the foundations of their entire discipline. This isn't a culture war debate — it's a structural crisis unfolding in real time across two of the most rigorous intellectual fields humans have built.

Since the AI capability debate shifted from chatbots to professional-grade performance, the evidence has been piling up fast. Two significant developments in the past week crystallize where this is heading.

Law Professors Rate AI Higher Than Each Other. By a Lot.

A draft study by Stanford law professor Julian Nyarko and colleagues ran a controlled experiment with 16 contracts law professors from 14 U.S. law schools. The setup was rigorous: professors wrote 40 representative exam and office-hours questions, wrote their own answers, then blind-judged 2,918 head-to-head comparisons between human responses and AI-generated ones.

The result: AI won 75.33% of the time.

The AI models used were Google's Gemini 2.5 Pro and a retrieval-augmented version of NotebookLM trained on the actual casebook the professors use. These weren't generic chatbots hallucinating case citations. They were purpose-built tools operating in the exact domain being tested.

Professors flagged AI answers as potentially harmful only 3.53% of the time. They flagged their own colleagues' answers as harmful 12.06% of the time. When blind to authorship, professors found other professors' answers more dangerous than the machine's.

According to the Volokh Conspiracy at Reason, which highlighted the study, the AI performance held up even when researchers specifically tested whether the preference was driven by polished writing style rather than substance. The content was genuinely stronger.

Law school tuition at top schools runs $70,000 or more per year. A meaningful chunk of that pays for access to faculty expertise in exactly the kind of instructional context this study evaluated.

Mathematicians Just Issued a Formal Warning

On June 2, 2026, the Leiden Declaration on Artificial Intelligence and Mathematics was published, developed over eight months by a 16-researcher working group following a September 2025 conference at Leiden University in the Netherlands. It has been endorsed by the International Mathematical Union — the body that oversees the Fields Medal, the most prestigious prize in mathematics.

According to Ars Technica, the declaration's publication came roughly two weeks after OpenAI publicly claimed one of its models had disproved an 80-year-old mathematical conjecture in geometry. The math community did not simply applaud.

The declaration outlines three specific threats:

First, AI models produce "plausible but unreliable" mathematical arguments that are difficult to distinguish from correct proofs. Leslie Ann Goldberg, head of computer science at Oxford, put it bluntly: "Inaccurate AI-generated drafts are cheap to produce, and there is a risk of cluttering the literature with claimed results that are simply wrong. Once that happens, the errors are likely to propagate as new results are built on faulty foundations."

Mathematical proofs build on each other. A buried error in a widely-cited result doesn't stay buried — it metastasizes through the literature for decades.

Second, the declaration flags that AI models trained on published mathematical works frequently fail to properly cite the human researchers whose work they absorbed — and many of those training datasets were assembled by exploiting licensing loopholes or outright violating copyright. Researchers who spent careers producing the underlying work are getting neither credit nor compensation.

Third, the declaration warns that AI use "may become incentivized for its own sake," distorting how mathematicians are hired, funded, and recognized. Kevin Buzzard of Imperial College London said: "Mathematicians should find it quite striking that tech companies are suddenly interested in their work."

The industry isn't showing up as a partner. It's showing up as a strip-miner.

The Structural Question

Most AI coverage right now falls into two camps: breathless enthusiasm or performative doom. Both miss what's actually happening.

The law professor study isn't an argument that AI should replace faculty. It signals that specific, high-cost functions — like answering student questions about contracts doctrine — are already being commoditized. Law schools that ignore this will be disrupted. Law schools that restructure around it intelligently will survive.

The mathematics declaration isn't technophobia from people who fear calculators. These are the people who build the formal verification systems that would theoretically make AI math trustworthy. When they say the current crop of AI tools is producing unreliable proofs at scale, that's the most credible warning available. The International Mathematical Union doesn't issue declarations lightly.

Institutions built around human credentialing and peer validation are being disrupted faster than they can adapt, and the people inside those institutions are only now beginning to formally organize a response.

What This Means

If you have a kid in law school right now paying $200,000 over three years, you should be asking hard questions about what exactly they're paying for. If AI already outperforms professors in the instructional context, the value proposition of that credential is changing — and tuition prices haven't reflected that yet.

If you depend on peer-reviewed mathematical research — which underpins cryptography, finance, engineering, and medicine — the Leiden Declaration signals that the quality controls on that research are under genuine stress.

Neither of these is a reason to panic. Both warrant attention.

The steam drill always wins eventually. The question is what we build after it does.

Sources

center-left Ars Technica Mathematicians warn of AI threats to profession as industry encroaches
center-right Reason Where Have All the Good Lawyers Gone?
center-right Reason Eventually, the Steam Drill Always Wins: "Law Professors Prefer AI Over Peer Answers"