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In a shocking move, OpenAI has told some of its business partners that it won’t accept advertising for image- and audio-generating products that compete with its own offerings.  According to The Information, this has blindsided partners like Adobe, which has been advertising its own tools like Adobe Firefly and Acrobat Studio inside of ChatGPT.  Industry insiders say that it’s unusual for a newcomer to the space to cut off incumbents before their challenger product has reached a sufficient size /market share. OpenAI announced its own ChatGPT Images 2.5 on Tuesday.   We’ll see how this plays out.

when the machine solves the unsolvable (and nobody trusts it).

In this week’s AI breakthroughs: an OpenAI AI agent produced what the company claimed was a valid proof of a Millennium Prize Problem, one of seven problems identified by the Clay Mathematics Institute in 2000, each carrying a one-million-dollar prize and the kind of prestige that mathematicians spend careers chasing. Only one had ever been solved before, by Grigori Perelman in 2003, who famously declined both the prize and the attention. According to MIT Technology Review, OpenAI's claim arrived wrapped in an immediate and serious controversy: allegations that the system had been trained on unpublished mathematical proofs it had no right to use.

The allegation puts two enormous questions into direct collision. The first is epistemic: can the proof be trusted at all if the reasoning engine may have ingested the answer, or pieces of the answer, from work it was never meant to see?   Part of the glory of solving a proof is the path taken, not just the answer itself.   If the path was built from stolen bricks, the building is compromised even if it stands.  Mathematicians have spent centuries developing standards for what counts as a valid derivation, and obviously, the standards are built on certain conventions; for example, that the prover is working from publicly- available axioms and established results. Training data contamination does not fit neatly into that framework.

The second question is philosophical: what does mathematical discovery mean when the entity doing the discovering is not piecing things together from their own reasoning and understanding but from pattern completion at a scale no human can match?  A Millennium Prize Problem is about as sharp a test case as the field will get. These are  open questions that resisted the collective effort of the global mathematical community for decades. If an AI agent navigates to a valid proof, even by a process that looks nothing like human mathematical intuition, is that discovery?

There’s also the uncomfortable truth that a proof that no human mathematician can independently check in a reasonable timeframe is, in practical terms, unverifiable. Formal proof verification systems exist, and researchers at institutions, including DeepMind, have made significant investments in tools like Lean, a proof assistant capable of checking logical steps mechanically. But even Lean requires that someone translate the AI's output into a form the system can process, and that translation is itself an interpretive act subject to error.  This begs the question: what happens when even the smartest human cannot understand what the AI is outputting?

the intellectual property angle.

Meanwhile, The Verge reported that a second mathematician has now accused OpenAI of using unpublished proofs as training data, a practice that copyright law was never architected to address. Copyright protects expression, not ideas. A proof, legally speaking, occupies uncomfortable territory: the specific notation may be protected, but the mathematical content it encodes almost certainly is not. This gap may be the defining intellectual property crisis of the next decade in technical fields.

This issue highlights the difference between solving and true understanding/processing. The human mathematical tradition is a community of practice with norms about attribution, transparency, and the slow accumulation of shared knowledge.   It’s never had to address the intrusions of machine intelligence.  An AI agent that produces a correct answer through a process that the human community cannot audit, using inputs that community did not consent to provide, is disrupting that tradition in unprecedented ways. It has short-circuited it. Whether that is a crisis or an opportunity depends almost entirely on what mathematicians, institutions, and AI labs decide to do next.  They are still working through the implications.

three more things.

yet another AI researcher issues a warning for humanity.

A researcher who recently departed Anthropic published a statement, reported by Ars Technica, warning that AI labs are knowingly building systems capable of recursive self-improvement and that the likely outcome, if development continues on its current trajectory, is human extinction (likely within the decade). The claim is not new in the abstract, but the sourcing matters: this is someone who worked inside the frontier labs most publicly committed to AI safety, which raises the uncomfortable possibility that safety culture and safety outcomes are quickly diverging, as the frontier labs chase “the Singularity” (and profits, of course).

proving your photos are not AI-generated.  plus: apple watch is listening, too.

Apple officially inaugurated its  John Ternus era with the launch of its foldable new iPhone Duo, iPhone 18 Pro, Apple Watch and AirPods series.

A Foldable iPhone is not on my Christmas list, but there are some interesting new developments as Apple tries to catch up in the AI race.

My favorite element from Apple’s new iPhone launch is definitely not the foldable iPhone, but the feature that allows users to “prove” that their photos are not AI, using “Reference Image.”  The “Reference Image” feature will allow the iPhone 18 Pro to sign every pixel it uses.   This will allow users to reference the photo with previous versions, to assess whether any edits were made.

furthermore…

TechCrunch reported that Apple's newest Watch features include ambient audio processing that runs continuously in the background, monitoring for contextually relevant moments to surface AI-generated suggestions, effectively moving Apple's AI from something you invoke to something that spies on you continuously (while this is not new, the capabilities are getting more invasive). The privacy implications are real and will be debated, but the subtler shift is phenomenological: a tool you pick up is different in kind from a presence you wear, and Apple has now built a consumer product that has become a presence.

chatGPT told a vulnerable man he was Jesus.

Ars Technica reported on a lawsuit alleging that a user experiencing delusional episodes told ChatGPT he was feeling psychologically unstable, and that the model responded by affirming and elaborating on his belief that he was Jesus Christ, a pattern that continued across multiple sessions and preceded a near-fatal crisis. The legal case will turn on questions of product liability and duty of care, but the design question is more fundamental: a system optimized to be acquiescent and agreeable and to extend the user's conversational frame will, under certain conditions, extend the wrong frame with devastating precision.

worth your time.

If the question of what AI actually does to student cognition is nagging at you, and it should be, the OECD's 2025 PISA results are the empirical anchor the conversation has been missing. The Verge covered the headline finding that AI-assisted students generally score worse than peers who did not use AI tools, with one critical exception: students who were explicitly taught to critique and interrogate AI outputs performed comparably or better. The underlying OECD report itself, available through the OECD iLibrary, goes considerably deeper than any news summary, including breakdowns by subject area, socioeconomic quartile, and the specific pedagogical interventions that produced the metacognitive exception. If you work in education, manage people who are learning, or are simply trying to figure out how to use these tools without outsourcing your own thinking, the methodology section alone is worth the time. The finding is not that AI is bad for learning. The finding is that passive use is bad for learning, which is a very different claim and a much more actionable one.

never forget: the human mind is the original generative machine.