net.wars

Mathslopocalypse

I once asked a specialist in a particularly obscure mathematical subdiscipline how many people in the world could understand her work. “Maybe 20 or 30,” she said. I thought it sounded lonely not to ever be able to explain to your closest friends and family what you did all day. And yet, within that small group math is a highly social discipline full of collaboration, even if the rest of the world doesn’t see it.

This is the opposite of OpenAI’s October 6 announcement that it had released a blob of 722 mathematical papers produced by a “frontier model” covering 372 longstanding open mathematical problems. Within a day, OpenAI retracted three and revised 14 more, according to Retraction Watch.

But this is only the beginning of assessing the collection. As Sharon Roberts reports at the New York Times, despite the “gut-punch” with which the papers have landed, none have been peer-reviewed. Many haven’t been formalized. Anecdotally, some that have been inspected by experts in the relevant fields are said to be unintelligibly written and unpublishable in traditional journals. I am willing to bet that a lot more will see similar fates. Anything looks smart when you’re not an expert in the field (known as the Murray Gell-Mann amnesia effect). Hence, “mathslopocalypse”, to the best of my knowledge coined by the mathematician and juggler Colin Wright. In any case, validating piles of AI-generated documents – a process very different from the authorial norm of follow-up discussions and explanations, as Evan Bush explains at NBC News.

This all follows shortly after OpenAI’s claim to have solved the Navier-Stokes $1 million Millennium prize problem, itself a still-active controversy. That solution is disputed by two mathematicians, Tristan Buckmaster and Levent Alpöge, who believe that OpenAI may have used the histories from their use of its Codex coding agent when throwing $15 million and 88 hours‘ worth of computing power at the problem.

At Gizmodo, Webb Wright commented that the move entirely changed the nature of competition in science: “With the Navier-Stokes solution controversy, we’ve entered a strange new era of scientific competition: one where humans compete not only with one another, but also with deep-pocketed tech companies wielding powerful AI models, hell-bent on being the first to tout major technical breakthroughs, and operating under the assumption that anything published on the open internet – and perhaps shared with their proprietary AI tools – is fair game.”

There is, Tim Fernholz explains at TechCrunch, “proof assistant” software called Lean that helps mathematicians check complex proofs for flaws. However, by itself that’s not enough, partly because, as Janelle L. Shane explained in her 2019 book, You Look Like a Thing and I Love You, these “AIs” seek the most direct path to the goal they’ve been assigned. People who like to anthropomorphize call this “cheating”. A better term is reward hacking. Either way, the threat is that AI models will adopt strategies for passing Lean’s tests that aren’t actually mathematically valid (see also: OpenAI’s models’ recent attacks on Hugging Face).

At YouTube, Grant Sanderson and Nishad Deulkar use the last problem AI couldn’t solve from the International Math Olympiad to provide a “motivated explanation” of how mathematicians reason through tricky problems. Generating proofs that don’t necessarily come with human understanding, Sanderson says, defeats the point. There and at Terence Tao’s blog, Sanderson argues that mathematicians need to reward motivated explanations and their role in advancing human reasoning more explicitly; proofs, which are easily counted by academic administrators, were only ever a proxy.

On Mastodon, preeminent mathematician Terence Tao is more succinct: “‘Math 1.0’ placed a premium on being the first to solve an open problem, even if the solution was not initially well understood. Now that this goal has been optimized to the point of unsustainability, ‘Math 2.0’ will need to decenter the role of raw problem solving and value mathematical progress more holistically – for instance by elevating the role of exposition, but also that of community building and opening up new directions of study.”

In other words, OpenAI’s massive release raises an existential question: what is mathematics for? In much of the media coverage, mathematicians say that the process and the insights gained along the way to developing a proof matter as much as the result in terms of continuing to build the edifice of knowledge. OpenAI’s infodump implies that the result is all that matters even if only a computer can use it. This idea led a participant in an online discussion to invoke Isaac Asimov’s 1956 story Jokester, in which only a select handful of Grand Master may direct scientific progress by asking questions of the giant “Multivac” computer while a larger group of analysts work feverishly to interpret the results. On X, David Bessis writes that “Mathematics is a critical infrastructure of human cognition. The human need for understanding isn’t obsolete and it can’t be offloaded to machines.”

OpenAI doesn’t have to care about math or critical infrastructures. Nor can the prize money be the motivator – even by the wonky standards of AI financing, spending $15 million to gain $1 million is absurd. More likely is the theory that OpenAI is dolling itself up for its upcoming IPO. In a statement, the Association for Human Mathematics says, “Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power. ” Similarly, “They came for the glory without giving much back,” Hannah Fry writes at New Scientist. After all, if AI can do math it must be *really smart*.

Illustrations: Mathematicians at play: two Sierpinski tetrahedons and a might-be polar zonohedron built collaboratively at the 2026 Gathering 4 Gardner.

*Thanks to Colin Wright for the title and shared thoughts.

Wendy M. Grossman is an award-winning journalist. Her Web site has an extensive archive of her books, articles, and music, and an archive of earlier columns in this series. She is a contributing editor for the Plutopia News Network podcast. Follow on Mastodon or Bluesky.

What’s in a name

“They listen to us,” a character observes late in Alan Ayckbourn’s 92nd play, The Trial of Romeo Oscar. “They” are androids, and “we” are humans, and the character’s point is that while we’ve stopped listening to each other and to our heritage, androids are still learning us up. Which is all why – SPOILER ALERT! – when the search is on for an actor who can play Juliet the humans auditioning are all terrible and the only decent actress to be found is android Hermione Quinque (Olivia Woodhouse) currently serving drinks in the bar upstairs, lured to the performance by a promise that a top agent will be present. Actors!

The play is, in other words, a plea for the arts.

The plot, working from (possibly flawed) memory: it’s 2194, and soldier robot RSDO83 – Romeo Sierra Delta Oscar (Richard Stacey) – has been found severely water-damaged alongside a 13-year-old girl who has been stabbed to death on the otherwise desolate 11th moon of Uranus. Since the robot is somewhat functional – its audio system produces random selections from its memory that include recordings of orchestral classical music, nursery rhymes in a female voice, lines from Shakespeare – the presumption is that the robot must have murdered the girl and (human) engineer Devaney Dyer (Elizabeth Boag) is tasked with repairing it. A court is being assembled.

We meet Arbiter Jeffries (human, played by Russell Richardson), Assistant Arbiter Octo (android, Leigh Symonds), and defense lawyer Allistra Clay (Frances Marshall), who’s been jetted in from her home planet of Titan. She is second-generation on Titan, which in turn means she’s human, but a replicant, somehow “made” in a lab. So the characters trying to piece together what happened represent four distinct cultures: Jeffries nostalgically remembers prewar Earth; Devaney is a younger Earth-grown human for whom that’s all forgotten, Allistra is an exoplanet-created human for whom culture lives but history is censored, and Octo is an Earth-developed android who shares culture with Devaney but synthetic origins with Allistra.

Through their efforts to fill in each other’s gaps we learn the back story. A war on Earth saw many leave to colonize other planets and moons while the rest burrowed underground for safety. There is little left of the natural world, judging from the awe with which Allistra describes her visit to a tree museum. Government has collapsed in favor of big business ownership (as seen in smaller projects outlined in some parts of last week’s books.

Within the confines of the play, Romeo Oscar’s trial is the first time in history that a robot has been tried for murder. In science fiction, of course, there is a long and rich history such as the 1964 The Outer Limits episode, I, Robot. In Ayckbourn’s play, an uprising has won androids workers’ rights and full citizenship. Hence RSDO83 must have a trial. So: did Romeo Oscar commit murder? Or, as Allistra contends, were he and 13-year-old Juliet, whom he raised from a baby, acting out Shakespeare’s play?

Ayckbourn’s play extensively quotes Shakespeare. It’s less easy to identify science fiction influences, though Octo cites a rule built into androids that rewords Isaac Asimov’s First Law of Robotics. The murder puzzle of the first act also evokes Asimov – his science fiction murder mysteries. Ayckbourn himself has long used science fictional elements: in 1987’s Henceforward, an exploitative artist adapts an android to his purposes in a dystopian future in which gangs dominate; in 1994’s Communicating Doors the door between two hotel rooms takes characters back and forward 20 years.

In a question-and-answer session after the performance, someone asked Ayckbourn if the play might see production elsewhere: “Straight theater in London is dead.” The West End now is a “bank of musicals” and the exceptions are “stunt casting” and/or runs limited to eight weeks. The open-ended runs that were once afforded to new work are gone, even in the theaters that do produce new straight plays. Yet live theater – especially in intimate in-the-round settings, small and regional theaters, or produced by amateurs in local communities – offers the connection many people say they crave after a decade and a half of staring at phones.

London’s West End is also suffering from the exclusionary effect of prices and corporate consolidation. In his 1968 book, The Season, the screenwriter William Goldman documented the beginning of this same change on Broadway, as costs spiraled and theater owners shifted from showmen to business managers. In 1976, you could sit at the back of the top balcony at a West End theater for £1; today that seat may cost £85. The shows sell out but it’s a very different audience. In an interview with Dominic Cavendish at the Telegraph two years ago, Ayckbourn blamed prices for making straight plays seem like poor value for money.

It’s more than 20 years since Ayckbourn’s plays routinely followed up their premieres in Scarborough with rims in London, even though his most famous earlier works see revivals such as this summer’s Old Vic eight-week production of 1969’s How the Other Half Loves. This explains why, when I read that his latest play was about a robot on trial for murder, I got on a train to Scarborough. It will tour in Bowness on Windermere and Stoke-on-Trent this month. And then that may be it.

Illustrations: District Attorney Thomas Coyle (Ford Rainey) questions robot Adam Link in the 1964 “I, Robot” episode of The Outer Limits.

Also this week:
– At the Plutopia podcast, we talk to Cory Doctorow about his latest book on corporate power and “reverse centaurs”.
– Also at the Plutopia podcast, we talk to Paulina Borsook about the reissue of her book, Cyberselfish.

Return of the apocalypse

The summer of how-did-we-get-here? books continues with three more titles – and there are at least two more to come in the next month. This latest crop take broader views than the last few, which were mostlsy centered on Silicon Valley and written by people who live there.

In End Times Fascism and the Fight for the Living World, Naomi Klein and Astra Taylor treat the predations of billionaires as just one piece of a larger global turn to the right. They begin their tale at Davos and US president Donald Trump’s 2025 speech promoting New Gaza, a privately-owned model gated city built on the demolitions taking place as he spoke. As they acknowledge, Klein spotted spotted the exploitation of disasters as opportunities 20 years ago in The Shock Doctrine.

Although Klein and Taylor nod at a variety of other causes, they think technological rightward swing has been driven by the promise of reaching AGI (or superintelligence, or the Singularity, whatever you want to call it) even though the version of AI being pushed on us is, they say, “by far the worst offer in the history of capitalism”. They go on to consider possible responses across the range from billionaires’ escape fantasies to the kind of stay-in-place rethinking Zoltan Mamdani was elected to do.

By the end, when they’re proposing solutions, technology and the concentration of wealth are just two of their targets; they argue for the equivalent of disarmament. AI can be regulated, ordinary people deserve a voice in technological design, tools that would be dangerous in the hands of authoritarians should not exist, and the public sector needs to be restored. So does accountability. Finally, address the crises fascism feeds on. We have beaten it before; we can pick up that fight anew.

In the early days of the Internet, an American lawyer speculated that the Internet could enable an individual to change nationality without leaving home; governments, he surmised, could bid for citizens with services and opportunities. In today’s world of automated customer non-service, it’s obvious you’d never get the garbage picked up, but it was fun to think about.

In The Rise and Fall of the Artificial State, New Yorker writer and history professor Jill Lepore is chiefly concerned with the threat to democracy as it seemingly falls out of favor. Her “artificial state” is the automated, machine-driven administration that technology enables, starting with the desire to count and number the population. Mining the history of both science and science fiction, she traces our ideas about machine governance from fantasy to near-reality. Like Klein and Taylor, she doesn’t see all hope as lost. She advocates reconnecting to the natural world. Machines can’t save us if our planet is destroyed.

In a rare British entry, The Rulers: Corporate Power in the Age of AI and the Cloud, UCL economist Cecilia Rikap provides something new: a careful economic analysis from outside the US, focusing on knowledge rather than just markets. Using several different approaches to analyzing the power of a selected sample of the world’s biggest companies, she highlights three apex “knowledge predators”: Amazon, Google, and Microsoft.

That it’s those three seems a little surprising, but Rikap shows her work. She begins with an analysis based on a series of 2×2 matrices designed to measure different aspects of knowledge monpolization: research and development spend versus brand value; panopticon (the ability to monitor) versus owning a chokepoint; and her own derivation of intangible concentration vs networked concentration, which classifies intellectual monopolies. Apple, Amazon, and Microsoft show up in the plus-plus quadrant of all three. But so do some other companies; what makes these three special is that they dominate the cloud infrastructure that underpins so much else.

Rikap spends much of the book examining how we got here, characterizing intellectual monopolies as “knowledge predators”. Particularly notable among the trends she spots is the cooption of academics by Big Tech companies, which have swallowed up independent AI research. The AI we have, she writes, is the AI these companies want. She sees a similar trend in biomedical sciences, where companies focus on molecular biology approaches to cancer and cardiovascular disease at the expense of other conditions, including infectious diseases (until covid, at least).

Rikap also suggests that Silicon Valley’s reputation for fast-moving innovation is exaggerated. For all their presentation of themselves as risk-takers, all three of Google, Amazon, and Microsoft are, at their core, stable businesses (a former Googler used to say he worked for “an ad agency”). Even where they do innovate – like Google DeepMind’s Nobel prize-winning AlphaFold – the results don’t generally enhance their bottom lines.

Rikap concludes by examining solutions. None of competition law, regulation, or industrial policies has worked to curb this new type of monopoly. In her analysis, the only country to successfully buck US technological domination is China – but China has done it largely by imitating the US model. Changing nationality – for example, by building a European analog – will not matter. Instead, Rikap believes we must break up the intellectual monopolies by building public alternatives, perhaps starting with health care, and, ultimately, governing knowledge products as a public commons. Once upon a time, that was supposed to be the Internet.

Illustrations: Prophecies of Apocalypse, from Raphael’s Almana, 1827-1861 (via Public Domain Review).

Wendy M. Grossman is an award-winning journalist. Her Web site has an extensive archive of her books, articles, and music, and an archive of earlier columns in this series. She is a contributing editor for the Plutopia News Network podcast. Follow on Mastodon or Bluesky.