NEW SAVANNA

Tuesday, June 2, 2026

Mathematicians are concerned that exploitation by the AI industry threatens the long-term intellectual interests of the field

Siobhan Roberts, As A.I. Makes Strides in Mathematics, Mathematicians Urge Caution, NYTimes, June 2, 2026.

Mathematicians issue a declaration:

On Tuesday, a group of 16 mathematicians, in consultation with colleagues and math organizations worldwide, published the Leiden Declaration on Artificial Intelligence and Mathematics. It aims to “frame the conversation about future directions,” said Dame Ursula Martin, one of the authors, and a mathematician and computer scientist at Oxford.

This effort comes as A.I. models have been making headlines with successful results in research-level mathematics. In late May, OpenAI, the maker of ChatGPT, announced that one of its models had disproved a notable 80-year-old mathematics conjecture in the field of combinatorial geometry.

The conjecture is one of some 1,200 problems posed by the Hungarian mathematician Paul Erdos. While some of these “Erdos problems” are considered throwaway questions of narrow interest, others have proved influential and field shaping. Along with a research paper describing the proof, OpenAI released a companion paper by several independent mathematicians. Jacob Tsimerman of the University of Toronto, an expert in the adjacent subfield of number theory, commented: “This is a really impressive piece of work, and I would accept it for any journal without hesitation.”

Potential problems:

Among the potential threats that the Leiden Declaration authors articulate are accuracy and reliability: Journal editors are already complaining about a flood of plausible seeming A.I.- generated papers and proofs that have turned out to be incorrect, and in ways that are difficult for mathematicians to discern.

Perhaps most pointedly, the authors raise the question of whether the many A.I. companies tackling mathematics — major players such as OpenAI, Google DeepMind and Anthropic, or start-ups such as Harmonic, Math, Inc. and Axiom Math — are keeping the field’s best interests in mind. “Technology companies’ involvement in research,” they write, “raises the risk that research questions are prioritized and incentivized because of their amenability to A.I. methods and models, rather than their deeper significance to understanding.” In turn, they point out, this disadvantages researchers who choose not to use the technology, and those who do not have access to it.

For Rodrigo Ochigame, a historian and anthropologist of computing and artificial intelligence at Leiden University in the Netherlands, and one of the statement’s authors, the latest OpenAI proof illustrates why this sort of collective reckoning in the discipline is necessary. “The story follows the same pattern as many other announcements by commercial A.I. developers,” Dr. Ochigame said. “The A.I. model is proprietary and unavailable to anyone outside the company. We get a flashy promotional video, while basic information needed to assess the scientific meaning of the result is kept secret. The company disclosed nothing about the methods, human-written prompts, training data, or computational resources consumed.”

Much of the article consists of a videoconference and email dialog with Dr. Ochigame, Dr. Martin and mathematician Michael Harris of Columbia University:

MARTIN: What OpenAI has done is throw a great deal of resources at Erdos problems, and got lucky with this one. That’s remarkable, and impressed the experts. We are not told about the model’s failures. [...]

To think of mathematics in terms of precise and neatly stated problems, like high school exams or the list of Erdos problems, is to misunderstand and diminish what makes mathematics so powerful and significant. Mathematics is not just about solving problems — it is also the cultivation of ideas, understanding, judgment, and human insight.

HARRIS The purpose, from my perspective, is to recover control of the narrative about the values and the goals of mathematics from the A.I. industry. Mathematicians are concerned that the values of the profession are being misrepresented, not intentionally but due to the media campaign on the part of the industry, which seems to want to promote the belief that they are in a position to transform mathematics — “the A.I. revolution in math,” as one headline put it not long ago. [...]

We want to affirm certain values that have characterized the profession: openness, honesty, giving credit where credit is due, sharing, transparency about methodologies, and access for independent verification of results.

An aspect of mathematics that is cherished by mathematicians is that it is one of few successful examples of a gift economy — that is to say, its economy is somehow an island of idealism in our society.

OCHIGAME Several A.I. companies are investing in dedicated teams focusing on mathematics, using problems as benchmarks and publications as training data. They are training their models to prove theorems not because they want to advance mathematical knowledge, but because they hope that such training will improve the models’ reasoning abilities more generally. [...]

MARTIN It’s important not to lose sight of the fact that what the A.I. companies are doing, what you can achieve with this technology, is absolutely extraordinary. I don’t think we’re challenging that. We’re challenging the framing, we’re challenging the behaviors around it.

I share the concern that these mathematicians express, that the commercial exploitation of mathematics is inimical to long-term research interests.

There's more at the link.

Splash! [Media Notes 183]

I’m pretty sure that I saw Splash when it appeared in theaters in 1984 but I certainly didn’t imagine that it would popularize “Madison” as a name for girls. The Wikipedia entry notes:

According to the Social Security Administration, the name Madison was the 216th most popular name in the United States for girls in 1990, the 29th most popular name for girls in 1995, and the third most popular name for girls in 2000. In 2005, the name cracked the top 50 most popular girls' names in the United Kingdom, and articles in British newspapers credit the film for the popularization.

In the movie “Madison” is the name taken by a mermaid, played by Daryh Hannah, when she emerges on land to attach herself to a forlorn Allen Bauer, played by Tom Hanks.

The first 10, 15, 20 minutes or so of the movie are about how this situation comes about, but let’s just take that as a given. This is a story about how a human male and a female mermaid meet, fall in love, and, why not? I’ll give the ending away. They swim away to, presumably, live happily ever after, under the sea.

I’m interested in the elaborate contraption that’s constructed around them. As far as I can tell that contraption exists to conceal an interpersonal problem that’s been kicking around for a long time, one identified by Sigmund Freud (e.g. ”A Special Type of Choice of Object made by Men,” 1910), played out on stage by William Shakespeare [1], and that’s been kicking around in stories and poems since forever: Men have trouble dealing with the fact that women can be both sexual and loving, passionate and beloved. Splash deals with this by presenting us with a creature that’s both human and not human (i.e. a mermaid).

Young Allen Bauer is despondent because his girlfriend’s just moved out without giving any him any inkling that she was going to do that. He just wants a woman he can love and marry and be happy with. That’s all he wants. True Romance.

And then this woman shows up. We know she’s really mermaid, but he doesn’t. He picks her up at the police station – I know, you want to know how that came about, but it doesn’t really matter, it’s just staging – takes her home and she goes to bed with him. Simple as that. No teasing or pleading, nothing resembling courtship, but there may have been a kiss (I don’t really remember). We see them walk calmly into the bedroom and that’s that. Just what happened in there, we get to imagine whatever we wish. They might have made hot passionate love, who knows, but there’s no hint of such things anywhere. I mean, she’s really a mermaid! And she’s only got six more days, until the full moon, and then she’s got to return home. But she doesn’t tell Allen where home is or what she is. But she does take the name “Madison.”

Then things get complicated, and painful (in several senses, I was all but squirming as I watched). Allen isn’t the only man involved. There’s a bizarre scientist, Walter Kornbluth, who gets wind of all this and realizes, “Ah hah! I’ll bet she’s really a mermaid.” He’s seen her before. Don’t ask. He manages to douse her with water, at a dinner for the President of the USA (don’t ask), and she’s taken by Kornbluth’s rival scientist, locked up in a lab, and subjected to tests. When Kornbluth learns that she’s going to be dissected the next day, he decides to spring her and return her to Allen.

By this time Allen knows that he’s slept with and is in love with a mermaid. Now what? Well, she’s got to return to the sea or she’ll die. If he’s willing to leave with her and never return to dry land, that can happen. He decides, no. She dives into the water and starts swimming away. He changes his mind, jumps in after her, and they swim away as the credits role.

And this point you may be thinking: “That’s crazy.” I know, and it’s even crazier. Read the Wikipedia plot summary (linked above), you’ll see. My point is that this elaborate contraption is a way of dealing with that problem that Freud named and analyzed, that men have this split image of women as both mothers and whores (if you will). Splash transforms that duality into humans and mermaids and erects an elaborate fantastical contraption to deal with it.

Given that you accept all that, I’ve got one problem with the movie. Allen should have stayed on the pier and let the mermaid go. That wouldn’t have given the audience the feel-good ending for which a movie like this is concocted, but it would have been a minimal way of acknowledging the preposterous nature of it all.

* * * * *

[1] I analyze this dynamic in some detail in my essay, At the Edge of the Modern, or Why is Prospero Shakespeare's Greatest Creation? Journal of Social and Evolutionary Systems 21(3): 259-279, 1998, https://www.academia.edu/235334/At_the_Edge_of_the_Modern_or_Why_is_Prospero_Shakespeares_Greatest_Creation

Elysian Park, Hoboken [Peekaboo Manhattan]

Monday, June 1, 2026

Hollis Robbins in AI and Education

Episode page:

This week on The Hope Axis, Hollis Robbins joins me to talk about her dense career and what it actually means to build a life dedicated to the humanities today.

Hollis, a dear friend of Interintellect and one of the first hosts, is stepping back from her role as Dean of Humanities at the University of Utah to focus on writing three upcoming books, including one with the incredible title, “Do Not Go to College Unless.”

We get into her journey, and finding room for hope and leisure in the middle of it all. Hope you enjoy!

00:00 Intro
00:38 Introduction
02:50 College, dropping out, intellectual ideals and AI
08:00 The state of universities and colleges in the time of information abundance
15:39 Intellect and technology
29:38 Anti-AI and pro-intellectual discourse is missing the point
34:17 America's higher (mid) education doesn't compete with AI
43:23 Reinventing tutoring
48:42 How is Hollis Robbins surviving in the humanities?
54:37 The process of ""dumbing down"" of the American University
01:04:41 If a specialist won't be teaching you at the university - don't go there.
01:08:02 Intellectual labour in scale economy.
01:10:40 Final thoughts

Surprise! Why it was so easy for executives and VCs to hijack the AI revolution

This is a fragment from a longer post in my ongoing commentary on Tyler Cowen's recent monograph on the Marginal Revolution.

* * * * *

OpenAI released GPT-3 in 2020 to a limited audience of insiders, who recognized that it represented a breakthrough. This level of performance came as a surprise. No one predicted it. GPT-3 was scaled up from GPT-2, which was in turn scaled up from GPT-1, but no one was making explicit predictions about the level of performance to be achieved at each step. These were experiments: “Let’s try it and see what happens.”That’s fine. That’s a good way to make progress, to try things out and see what happens. But don’t mistake a lucky trial for genuine knowledge.

Cowen mentioned GPT-3 on Marginal Revolution on July 19, and then published a Bloomberg column on it on July 21, which he excerpted in Marginal Revolution the next day: “...think of GPT-3 as giving computers a facility with words that they have had with numbers for a long time, and with images since about 2012.” I published a working paper in August, GPT-3: Waterloo or Rubicon? Here be Dragons, which I’ll discuss a bit later.

Two and a half years later, in November of 2022, OpenAI released ChatGPT to the general public. It spread like wildfire. Now the proverbial everyone witnessed what only a small group had witnessed in the summer of 2020. The machine speaks. Sorta’. But more convincingly than any machine had spoken before and in a way that had unimaginable implications for the future.

A threshold HAS been crossed, but it is not, so far as I can see, a threshold in understanding. It is a threshold in performance along a continuous line of scientific understanding and engineering design and construction, something I have documented in some detail in a recent working paper, The Origins of LLMs. As far as I can tell, there has been no paradigm shift, in Thomas Kuhn’s sense, no rank shift, in terms of cognitive rank theory. There were no fundamentally new ideas in the world by, say, late July of 2020 as a consequence consolidating GPT-3 and making it available in limited release.

“What about the scaling hypothesis,” you might ask. “Isn’t that new?” Perhaps the phrase is new, but the idea was there in Rich Sutton’s famous 2019 essay, The Bitter Lesson. Given the nature of computing, scaling up is not trivial. Hundreds if not thousands of technical details need to worked out as the size of the training corpus increases by factors of 10 or more, time after time, and as more and more GPUs are ganged together to assemble the computing power needed. But there has been no gain in fundamental understanding, not of machine learning, artificial neural nets, and certainly not about language and cognition.

Consequently our sense of possibility has expanded enormously, while our knowledge and deep understanding has remained the same. And that is what has allowed the field to be captured by businessmen, executives and venture capitalists, who have little understanding of or interest in the underlying conceptual issues. Scaling is something they understand.

Hype the dramatically increased performance and collect the cash. Purchase and deploy more resources now, reap far greater profits in a decade. Everything else is noise and friction.

But what if [the Dread] Gary Marcus and other critics are right. What if scaling LLMs is not adequate. What happens to all those investments then?

An ordinary corner on Washington St. in Hoboken, NJ

Dædalus has a special issue dedicated to AI – AI & Science: What Is the Future of Discovery?

Here's the blurb:

Continued progress in artificial intelligence, its expanding usefulness in science, and its contributions to landmark advances suggest that we may have entered a new era of AI for science.

The breakthroughs so far—such as predicting the structure of practically every known protein, with profound implications for our understanding of biology, health, and the treatment of disease—are notable not only for what was achieved but also how it was achieved and what that suggests for scientific progress.

This special double issue of Dædalus poses the question: What is the future of scientific discovery in this new age of AI?

Thirty-three scientists responded. Bringing perspectives from life sciences and medicine, cognitive science and neuroscience, the physical and earth sciences, chemistry and materials science, computer science, mathematics and the social sciences—they draw on their work at the frontier of AI and science.

The authors write with an eye to the future, not just the present. They explore what is being achieved and what possibilities lie ahead; examine AI’s limitations and efforts to move forward; and investigate the larger implications of AI-assisted science—on how science is done, the role of the scientist, and the scientific method, as well as the challenges and complexities involved.

The authors together exemplify a long-standing bidirectional relationship: AI advancing science, while science advances AI. Where that relationship will take us—a golden age of discovery? New scientist-machine collaborations? Autonomous labs? Discoveries without human understanding?—is a future we are only beginning to imagine, and one we must also shape if the beneficial possibilities are to be realized.

The full issue is available online.

Learn from your own latents and not from tokens

Daniel J. Korchinski, Alessandro Favero, Matthieu Wyart, Learn from your own latents and not from tokens: A sample-complexity theory, arXiv:2605.27734v1 [cs.LG] 26 May 2026

Abstract: Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their own latent representations of related views or masked regions, as in data2vec and JEPA – an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. Such a grammar generates strings of visible tokens by recursively applying production rules along a tree of hidden symbols of depth L. For such data, supervised or token-level SSL require a number of samples exponential in L to recover the latent tree; we prove that latent prediction achieves this with a number of samples constant in L, up to logarithmic factors. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity anal- ysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

Lest we forget...French toast! – coffee too

Anthropic is a mystery. They think they're building God.

Bill Gurley: Anthropic Thinks It’s Building God@Jason: It is the ultimate level of narcissism and delusion of grandeur to think you can create God.@bgurley:

“Anthropic is a mystery to me. I've never, ever seen a company that is both leading their field and the most… pic.twitter.com/QUefFJOrsI
— The All-In Podcast (@theallinpod) May 30, 2026

From the tweet:

“These are delusions of grandeur. Let's call it what it is.

They believe that they're so powerful, these individuals, that they can create God, and that by creating God, they are like this Prometheus kind of species.

It literally is the ultimate level of narcissism and delusion of grandeur to think you can create God.”

Sunday, May 31, 2026

A Public Agenda for AI [Ezra Klein]

Ezra Klein, We Have to Take the Future of A.I. Into Our Own Hands, NYTimes, May 31. 2026. Here's Claude's summary of the article:

Ezra Klein's piece argues that the public conversation about AI has been almost entirely focused on preventing harms, while largely ignoring a different question: how can AI actively benefit the public?

He acknowledges the skeptical climate — polling is poor, data centers are controversial, and Pope Leo XIV's first encyclical addressed AI's dangers — but insists that since AI is here regardless, the meaningful question is how it gets directed and for whom.

His core argument is that AI's public benefits won't happen automatically. They require deliberate investment in data, financing, and compute. He points to impressive examples of AI solving hard scientific problems (protein folding, pancreatic cancer detection, a new pulmonary fibrosis drug, weather prediction) to show what's possible when it's properly deployed — but notes these successes depended on pre-existing public infrastructure like the Protein Data Bank, itself publicly funded since the 1970s.

His proposed agenda includes: a publicly controlled frontier-level AI model; subsidized compute access for universities and public agencies (to close the widening gap between institutions like Goldman Sachs and public institutions); government-guaranteed markets for AI-driven solutions to public problems (analogous to Operation Warp Speed); using AI to help citizens navigate government services; and funding the creation of clean, novel public datasets.

He closes by noting that we've been consumed by what we fear AI will do to us, at the expense of asking what we hope it will do for us.