Daniel Mathews

AI debate is full of speculation: how far it can go; how far it will go; how fast its capabilities will improve, or plateau.

How far it can go is a question about the world, an empirical question, and one about which we are learning facts; how far it will go is a social and economic question, limited by the empirical one. As it turns out, you can train an artificial intelligence with the capacity to resolve the Navier-Stokes millennium prize problem, one of the seven most important outstanding problems in mathematics as identified back in 2000. And, more recently, the capacity to produce a further 700-odd papers’ worth, probably at least a dozen Fields Medals’ worth, of breakthroughs: the mathocalypse. These are new facts about the world, and important ones; they deserve our attention quite independently of whether we are interested in mathematics. The further artificial intelligence can go, the more we must pay attention to the various sci-fi type scenarios about superintelligence, and the more we must ask whether it should go as far as it can. Indeed, recent events form a scenario that many would have thought of as science fiction until it happened.

As a graduate student in mathematics at Stanford in the 2000s, and through the 2010s, I recall often hearing from, and reading essays by, people associated with the “singularity” and “rationalism” and “effective altruism” about AI. They seemed to me to mix all sorts of ideas, from the positive and reasonable, through the interestingly weird, to kooky, harmful, and even delusional — together with cultish aspects that would make an actual rationalist in the tradition of Bertrand Russell blush. It frustrated me that they misappropriated the “rationalist” label from the tradition going back to Descartes, just as the “libertarians” misappropriate the label of Emma Goldman. They talked about the world turning to paperclips, artificial intelligences hellbent on gaining resources, and things going “well for AI”, centring AI to the extent of making it a subject and considering technological progress as a matter of welfare for the technology – though that fit with the accompanying transhumanist-extropian ideology-religion.

Often they would ignore, or sometimes even explicitly dismiss, other clear and present harms, such as racial bias, because of their concern with supposedly more important existential risks. It struck me as the same kind of intellectual arrogance, churlishness, and passive cruelty that I sometimes heard from the prestigious mathematicians, dismissing the importance of whole fields of their discipline. Prestige tends to bring with it lesser concern for those of lower status. Neither was a good look.

But Stanford was, after all, a university containing the Hoover Institute, which housed war criminals Donald Rumsfeld and Condoleezza Rice at the time — architects of the Iraq war and the Bush regime torture programme — and adjacent to the rapacious big tech of Silicon Valley, committing mass surveillance, privacy invasion, and algorithmic manipulation for profit. So I never expected much of anybody around there; this was the least of their sins, here in the belly of the beast. As I would tell my friends in the anti-war group there, adapting an adage I learned from Vietnam War-era activism: you go to MIT to learn how to build the bombs; you go to Harvard to learn how to give the orders to drop the bombs; but at Stanford, you can learn both. I was there to learn pure maths, and do what I could usefully do while I was there, which in practice amounted to good deeds with Wikileaks (in 2006-08) and anti-war activism.

It wasn’t that the pure maths was pristine and above the fray; nobody knows what mathematics will find a lethal application. There were students funded on DARPA grants for pure mathematics aimed explicitly at (among other things — there always are) improved lethality. They understood it was wrong. But they were just PhD students, their advisors got the funding and the mathematics they did was pure. There were plenty of great mathematicians. I chose the place partly because of the research interests in the department, but probably mostly because of the Californian weather. I knew its politics enough to know I’d probably not be able to live with myself going there and not resisting somehow. In due course all PhD students were given a warning that we were there to “do math” and not get distracted by other petty pursuits. In practice I dropped the politics when talking science, a formula well known in every authoritarian regime.

I’m enough of a rationalist to appreciate that ideas are independent of the people who espouse them, and in any case the ideas of powerful people can damage the world, so we should at least keep tabs on them. As a result, I wasn’t entirely inclined to dismiss the singularity and AI doomers, although they often presented themselves in a way that could not have been better calculated to invite it. But, I thought at the time, this is a question for down the track, this is an empirical question which will be resolved in due course. I don’t have a dog in this fight. And, I had more pressing matters to deal with: completing a PhD thesis, contributing to promising projects as Wikileaks was then, and keeping the anti-war flame alive — opposing the aggressive war against Iraq, the supreme crime against international law.

How the artificial intelligence story goes, I thought, depends on facts about the world. We will learn some of those facts as computers get bigger, and neural networks get more neurons and synapses and layers. The emergence of artificial intelligences which can win Chess, win Go, calculate protein structures, form ChatGPT, win a Gold Medal at the International Mathematical Olympiad, and solve Millennium Prize problems, has been the story of going down this track. And here we are, still going down, so to speak.

It has surprised me. I thought that developments of this magnitude would depend on understanding scientific questions that are, in some sense, not even yet properly formulated, like the nature of consciousness. Although you can certainly study consciousness in terms of brains and neuroscience, basic questions about the nature of consciousness remain still at least as much the province of philosophy as of science.

It seems to me — I think uncontroversially — as a materialist in the basic sense that the universe runs on physical laws and not supernatural interventions or magic, that consciousness must be describable in terms of physics. We still have essentially no idea what that description is; even the leading theories like Integrated Information seem to me very vague and preliminary, more in the nature of proto-theories.

I think — much more controversially — that quantum mechanics is the only area of current physics that contains any notion even remotely of the type that could explain the phenomenon of consciousness. I say this despite knowing that “quantum consciousness” is the province of many crackpots, and that even the serious approaches in this direction, like those of Penrose, with its objective state reduction, have the current weight of evidence massively against them. Still, I personally can’t see any more plausible way out. Maybe we’ve got it all wrong.

As a result, I tend to think that consciousness is unlikely to come out of an electronic computer. Much less controversially, and in agreement with most specialists, I think it is even less likely to come out of a large language model.

Thinking that probably consciousness is required for high levels of intelligence — here I just mean intelligence in the rough everyday sense of the word — it therefore seemed to me unlikely that pure neural networks, deep learning, pure statistical inference, large language models, reinforcement learning and so on, would lead to high levels of intelligence. Certainly not to the level of resolving a Millennium Prize problem.

Well, I can definitely conclude that something in that chain of reasoning is wrong now. Which of the above steps is wrong, or confused, has major implications. It seems that an AI model can have the “intelligence” to do breakthrough mathematics without consciousness. And questions about consciousness are becoming newly acute — they have always been acute to those whose consciousness has been denied, from animals to oppressed races to human babies — though I think we are still far from machine consciousness now. But who knows.

The state of mathematics and technology today is that, although the mathocalypse papers are long, by all accounts hard to read, not all correct, and will take time for experts in the field to digest, it is not really in doubt that they have produced dozens to hundreds of breakthroughs.

Many of the proofs come with Lean certificates. Lean is a (non-AI) computer language that algorithmically verifies proofs. There are possibilities for doubt with it here: some of OpenAI’s Lean certificates seem to have statements that don’t match mathematical-English statements; Lean code can invoke tricks or hacks; the Lean kernel has had programming errors. But when it is properly used, we can essentially be absolutely certain of the results.

That’s one of the things that drew me to mathematics, from childhood, and it attracts many other mathematicians too: the absolute certainty. It’s essentially the only field where we can make statements that are categorically true. Everything in non-mathematical science is, more or less, falsifiable by experiment or observation. All social or human facts are messy, difficult, hard to verify, subject to interpretation. Maths is not like that, and that is a major part of why I and many others went into it. Knowing things that are true matters. Those things may be useless — most are — or may find applications in a kaleidoscopically many ways, good and bad and otherwise. But they simply are, and they always will be; they always have been. They are abstract, timeless, eternal, analytic truths. They are often beautiful. They are unreasonably effective. So it seems, the universe runs on them.

And now here we are. Far down that track from the 2000s, OpenAI’s 700 AI-written research papers will likely resolve numerous major questions all across mathematics. A small number have been retracted, and who knows how many errors and issues may be discovered, but I think we can be quite confident this is the single biggest mathematical breakthrough in history, by at least two orders of magnitude.

And yet, mathematics is not happy about it. There are exceptions, there is a certain type of excitement, but the general reaction is one of dismay, horror, alarm, or anger.

Why? I will try to disentangle this question, to decipher this mess of science, politics, economics, and philosophy, with reference to my own experience, and history — and say something about what it all means.

And yet, mathematics is not happy about it. There are exceptions, there is a certain type of excitement, but the general reaction is one of dismay, horror, alarm, or anger.

Why? I will try to disentangle this question, to decipher this mess of science, politics, economics, and philosophy, with reference to my own experience, and history — and say something about what it all means.

* * *

Personally, I am, in a certain sense, “excited” about it. I have a philosophical commitment to the notion that knowing more mathematics is a priori good, and so feel compelled to appreciate the progress, to the extent it can be described as such before expert confirmation.

But this is only by ignoring the political and economic reality of the situation — which is, to its great shame, a standard feature of science academia. These realities explain why many of those best placed to love it actually hate it. Just as many people “hate AI”, as a vague generalisation, for any of numerous sufficient reasons, so too do we not appreciate this intervention, in some generalised way. But it behoves us to disentangle why.

The reality is that these mathematical results are not published in the spirit of scientific understanding and progress. The reality is that these mathematical results are published by a rapacious corporation as marketing for commercial gain. The truth and importance of the mathematical statements is completely incidental to the company that published them. The truth and importance of the mathematical statements is only relevant to those companies for reasons of expediency. To the extent their mathematics is true and important, hyperscale AI companies can present their results as trophies, in their marketing, to display the capabilities of their AI models, in order to improve their financial situation, which is woeful.

These companies have hired many mathematicians, and no doubt many of those mathematicians are interested in progress in mathematics. And, no doubt many of the technical employees more generally at these companies are also interested in mathematics — if they get a minute to think about it between the constant pings of breakneck AI model development. It is to the companies as institutions, their shareholders, and their executives, that the mathematical progress is purely incidental. Amidst collateral damage to the environment, climate, democracy, and victims of war and genocide in the AI race, mathematics perhaps uniquely has gained collateral benefit from AI. Yes, generative AI can provide incredible assistance in many matters — but these are benefits to consumers of the AI companies, not outputs of the company itself. Perhaps only biology, through Google DeepMind’s work on protein folding, has seen similar scientific progress from within the companies themselves. But the level of mathematical progress is unique.

Collateral benefit to mathematics, offset against, subtracted from, the shaky finances of an investment bubble. That is the real mathematics that AI companies have in mind.

For more political mathematicians, it presents a new type of violation. Academic pure mathematics, despite its sometimes violent applications, has often been regarded as a “haven of peace”, in the words of Bertrand Russell: abstract, pristine, far away from the wider world of war, oppression, and turmoil. Russell retreated into this haven after discharging his moral obligations, opposing the first World War and winding up in prison. Of course, mathematical life, being a part of academic life, has — for most of us at least — for a long time been less a haven of peace and more a frantic rat race scampering between lectures, tutorials, marking, grants, publications, administration, and committees. But still, the purity of it remains, at some intellectual level. Now even this inner sanctum has been flooded by fossil-fuel powered, authoritarian-enabled, fascist-adjacent, war-enabling, bubble-financed, AI slop. The slop — now, more or less, so it seems, true — precisely because it is probably largely true, has breached the battlements, oozing upwards to fully occupy and overflow the ivory tower.

That is why, despite such enormous objective progress, which in the abstract is something to be celebrated, can only be regarded as “exciting” under the internal duress of prior philosophical commitment. The Grinch still eventually celebrates Christmas.

* * *

They didn’t have to do it this way.

It seems clear — from OpenAI’s own press releases, and from colleagues who have read some of their papers — that many, probably almost all of these papers were not read by a human mathematician before posting them online, certainly not read thoroughly. Only one, apparently, was edited by a human. OpenAI does not have the expertise. They probably, at present, have enough borrowed money to hire enough mathematicians to understand most of the areas on which they published. God knows how many more PhD students graduate than postdoc positions are available, and how low a postdoc salary they will tolerate in present economic conditions. But OpenAI didn’t have the patience, and they didn’t have the inclination. They simply didn’t care.

Moreover, OpenAI defied the recommendations of its own “Advisory Group on Mathematics and Artificial Intelligence” at the Institute for Advanced Study in Princeton, which in the very first paragraph of their guidelines asked frontier AI labs to “stop testing advanced mathematical problems on proprietary models”. I haven’t heard any mathematician report that any of the papers is well written by human standards; they are convoluted, sometimes incomprehensible to read; at the time of writing, OpenAI has retracted 3 of them.

To the extent mathematicians examine and explain these results — processing the slop into something digestible — they are not only expanding knowledge, they are also acting as appendages to OpenAI’s marketing department, which did not bother to produce anything better.

So, the release is a mic drop as much as a slop drop and a drop of academic papers. It’s a flex for investors, science and mathematics be damned. A big fuck you to the mathematical community, look at what we can produce, with nary a concern for producing anything readable. Take this pile of answers to your questions and shove it up your brains. Gangster style, take that, motherfuckers — and now, turning to the investors — give us the money.

It could have been done in collaboration with human experts; the papers could have been reworked until they were readable and comprehensible to experts. That might have meant inviting experts inside the company, or waiting until this AI model was more widely available. It would have meant the papers came out later. It would have diluted the AI’s contribution. It would have slowed them down and cost money — though I imagine many mathematicians would have got on board for free. Instead, some mathematicians are now gathering, bewildered, to try and decipher all this mess.

But it also didn’t have to be this way, in more general and radical senses.

* * *

In this time of polycrisis, the dictum of capitalist realism popularised by Mark Fisher applies more than ever: it is easier to imagine the end of the world than to imagine the end of capitalism. Or, for that matter, to imagine a stabilisation of greenhouse gas concentrations, a long-term liveable planet, a stable secure homeland for Palestinians, or just world leaders actually cooperating to solve some of the world’s problems, or mainstream media giving a reasonable account of the world, or even an edifying social media feed.

We can now add to this sorry list of aphantasiac inequalities: it is easier to imagine the end of mathematics, than the end of AI capitalism. Even an ancient science seems less inevitable than a world of slop.

But it’s socially useful in an age pervaded by the sense of doom to imagine positive futures and visions. And given capitalist-cum-AI-fascist realism, let’s give it a go.

Let’s start from a true fact: there is a computer program that, when asked, can solve mathematical problems that have stumped humanity for decades or more. That is a true fact that, until a few weeks ago, could only have been imagined in science fiction.

Is there a positive vision incorporating this fact?

Of course. We can imagine it easily. In fact, we’ve had supercomputing infrastructure for decades. But such infrastructure is publicly owned and democratically managed through scientific research institutions. Why couldn’t this machine be part of that? In a parallel universe, the news reports:

Following recent scientific breakthroughs, computer scientists and mathematicians are planning to upgrade their supercomputers to build “Large Language Models” that they say can “reason”. Some are sceptical, but leading researchers say this could herald a new era of understanding and knowledge about mathematics and the universe… and possibly even deliver consumer benefits through chatbot assistants. …

Delayed for years because of the pressing need to build out renewable energy infrastructure, and the need to train more mathematicians, the plan is now set to proceed. Recent budget outlays for a buildout of data centres will soak up excess solar energy in the grid, using it to power the chips that train the enormous neural network architecture of the AI models. Local community consultation is now largely complete…

The scientific community waits with bated breath as the model training run commences. Mathematicians are lining up with outstanding problems in their diverse and abstruse research fields to put to the machine. Negotiations are underway with the International Mathematical Olympiad for this year’s problems to be an initial test …

Having blown away the scientific community with a gold medal in the International Mathematical Olympiad, mathematicians are today prompting the model to do its best to resolve one of the most important outstanding mathematical problems of history, the existence of finite-time singularities in solutions of the Navier-Stokes equations…

Even fanciful dreams and science fiction can be useful crutches for the imagination. Indeed, it is roughly “Deep Thought” from the Hitchhiker’s Guide to the Galaxy.

Instead, we have a private company, whose chatbot has caused psychosis, coached users to suicide, revolutionised cheating on homework, enabled industrial-scale disinformation, whose current CEO was previously fired by his own board for dishonesty, and whose immediate and desperate motivation is to turn a profit by causing mass unemployment and poverty. Enmired in debt, it turns to pure mathematics. By solving maths problems, it hopes to convince investors it has the capacity to convince enough bosses to fire enough workers and cause enough social misery that the revenue can cover its debts.

This grim story — beyond the fever dreams of the darkest science fiction; dystopian to the point of murdering our dreams — feels utterly unreal. I can’t quite bring myself to believe it even as I type it. But that is the world we are living in now. We are compelled to face with sober senses our real conditions of life, psychedelically cyber-phantasmagorical as they may be.

* * *

The level of cheating now possible is utterly incredible — where by cheating I simply mean getting a correct answer that you don’t understand by a shortcut. In the last few years, secondary and undergraduate tertiary education have been “revolutionised” (“embracing AI” as their management would say) by the fact of AI chatbots doing students’ homework. Contrary to AI-boom dreams of mass unemployment, it has massively increased the labour required by those of us who have to deal with it at the chalk face.

But now the chatbot can do graduate coursework. It can do PhD theses. It can do breakthrough research. You can even cheat on a Fields Medal: a few prompts, so it seems (if OpenAI can be taken at its word), can in a few hours can return results that would previously have been worthy of many of them. It may not write well, but neither do many humans. It can make mistakes, perhaps always will, given how the technology works; but again, so do humans. Maybe it will improve on this front.

* * *

Though the scale of it might be new, in a certain sense this is not a new phenomenon in mathematics. Though the mythology of genius is often overblown and creates stereotypes ranging from mildly annoying to downright harmful, history presents us with examples of mathematicians who are effectively, for some purposes at least, oracles: propounding miraculous results, correct answers, with minimal or even non-existent explanation, their origins inscrutable. Mathematics professors even at a world-leading institution like Stanford would describe themselves as mere mortals relative to these.

Srinivasa Ramanujan, without any formal mathematical training, was able to produce unbelievably sophisticated equations and formulas, which were often, amazingly, correct — coming from nowhere but his idiosyncratic studies and communion with the gods.

Turning to the subject of my own PhD, symplectic geometry, the figure of Mikhail Gromov looms large. His papers and books are groundbreaking. (Though, I think it is fair to say, outside mathematics his contributions are considerably less oracular). Roughly speaking (and sidelining for present purposes the important work of many others), he reopened a nineteenth-century field of mathematics to powerful new approaches which are now common across vast swathes mathematics and physics. But his papers are terse to the point of unreadability, with enormously sophisticated reasoning hiding behind single phrases and sentences. Following publication of a groundbreaking paper in the 1980s, understanding his work required an entire book to be written simply to create a version for mortals. Now I do not think he is deliberately exclusionary; on the contrary, by all accounts he is eager to explain mathematics as best he can. No doubt he is doing his best; not everyone is a great communicator. And, so I have been told, paper in the Soviet Union was expensive.

But Gromovs are rare; Ramanujans, rarer still. Of course, their pronouncements are no doubt usually the result of extreme effort, intense reflection, and hard work, as well as strokes of insight; but to external observers, including colleagues, they are indistinguishable from magic.

But we are now in a situation where, effectively, similarly oracular statements can be mass-produced. We have now produced machines that can produce breakthroughs — the creativity of which may not be as great as great human mathematicians, though the last few weeks may give reason to doubt that — and are similarly resistant to understanding. Though, maybe they will improve on that front too.

* * *

History often rhymes, and mathematics has a long history and lore, older than civilization. The millennia preceding the (pseudo-)genteel norms of modern academia have endowed mathematics with a unique catalogue of folly. In this context, the latest developments can be seen as an atavism, regressing to the behaviour of centuries past. To decipher all this mess is, indeed, a charged phrase in mathematical history.

In 16th century Italy, mathematicians secretly developed their methods of solving cubic equations and challenged each other to “mathematical duels”. These duels, rather charmingly, were fought not with swords or guns, but by challenges to solve each other’s cubic equations — though they were deadly serious matters of honour and prestige to their protagonists, such as Cardano and Tartaglia. These academics worked in secret, jealously guarding their formulas and methods.

They demonstrated their prowess by displaying their answers, but not the process behind them. So does OpenAI. OpenAI may have published the papers and formal verifications, but jealously guards its model, its prompts, and all but the vaguest of its technical details.

Another duel — now of the classic type, pistols at dawn — figures prominently in the most famous slop drop of mathematical history. It also concerned solving equations.

The French firebrand Évariste Galois, shortly after his release from prison for Republican activities, in 1832 was challenged to a duel, apparently over a woman. He had also proved the insolubility of quintic equations. This stunning combination of politics, science, and idiocy makes Galois’ story legend.

At high school you learn a formula for solving quadratic equations: degree 2 equations. The sixteenth century Italian mathematical duellists were solving cubic equations, degree 3 equations: there is also a cubic formula, bigger than the one you learn at school. If you really want, but you probably don’t, there’s a formula for solving quartic equations, degree 4 equations. The challenge in the early 19th century was to solve quintic equations, degree 5.

But Galois proved the challenge is impossible: he showed no formula exists in degree 5; there cannot be a quintic formula, as there are quadratic, cubic and quartic ones. How on earth could you prove it’s impossible for a formula to exist? How can you guarantee that you just haven’t been ingenious enough, that there might be one if only you had a bigger brain, more time, greater stamina, or a computer? But Galois had a big enough brain, and in his genius proved it. (It had been proved earlier, unbeknownst to him, but his conceptualisation was the most fundamental.) Such is pure mathematics that you can prove such things; you can learn the proof today in undergraduate algebra courses.

But Galois also wrote slop — though his sloppiness is perhaps better characterised as an inability to communicate admittedly extremely sophisticated abstract ideas on the frontier of knowledge at the time. This, combined with an incredible run of bad luck with mathematical elites (or perhaps politically motivated delay), meant he was never understood in his lifetime. The night before his duel he wrote a letter, what we would now call a brain dump, attempting once more to disseminate his results, so that, in his words, “il se trouvera, j’espère, des gens qui trouveront leur profit à déchiffrer tout ce gâchis” — there will be, I hope, some people who will find it to their advantage to decipher all this mess. Shot in the abdomen, he died the next day. He was 20 years old.

As for OpenAI, it is now to their profit for us to decipher all their mess. Leur profit, à déchiffrer tout ce gâchis.

The OpenAI brain dump is no less revolutionary, no less sloppy, no less stupid in its immediate precipitating cause. But it is no less significant or true. Like Galois’ successors, we are left to decipher tout ce gâchis. Like Galois, AI companies know their results are important and true, though unlike him they do not understand them. They too are locked in a duel to the death, a race with other AI companies. Corporate death by financial ruin is quite possible, even likely. And like Galois, they need to disseminate their results rapidly before the reckoning comes.

Galois trapped himself in the dumbest way to die imaginable — especially unforgivable given he had already put his life on the line for a much greater political cause, even having spent time in jail for political offences. But with OpenAI, the stupidity is simply the nature of capitalism. By its own internal logic, the frantic brain-dump slop-drop is perfectly rational. Though describing OpenAI as merely a rational capitalist is probably too anodyne a political description: OpenAI brazenly cozies up to the Trump administration, and placed elites like Jeffrey Epstein confidant Larry Summers on the board in the 2023 restoration of Sam Altman to the throne following his ouster for dishonesty. Whatever category of political turpitude you ascribe to such figures, OpenAI is adjacent to them.

And while Galois’ tale is a tale of tragic, hotheaded stupidity — an insult under a barbaric misogynistic honour code cutting short a life otherwise devoted to high ideals — OpenAI’s tale is simply the latest, fastest, largest, highest-powered iteration of capitalism delivering an insult to the honour of science and rationality itself.

And whereas, had Galois lived, he may not only have advanced mathematics as best he could, he may also have contributed to democracy, liberty, equality, and fraternity; as long as hyperscale AI corporations live, they might continue to advance mathematics as collateral benefit, if it suits them, but they will certainly continue to undermine democracy, ally with destroyers of liberty, accelerate inequality, and dissolve fraternal bonds in chatbot isolation.

The notion of “AI as insult” brings to mind the memorable comment of Japanese filmmaker Hayao Miyazaki on an earlier iteration of AI: “an insult to life itself”.

Such a notion applies even more strongly here. For what is life — at least to those of us of a philosophical or scientific disposition — if not to know, to understand ourselves, the world, the universe? And mathematics is more than what is true in this universe; mathematics is the set of things that are true in all possible universes.

This great human project — this great, existential, more-than-human project — the project, almost, of the universe itself — is to work through these questions. To take such deep questions, cheat on the test and drop the answers without understanding them in order to gain money, money that will be used to cause suffering, seems to me such a profound wrong as to offend the whole spirit of civilization. Even more than the slop art insulting Miyazaki’s opus, does OpenAI’s effort seem to me to come into the category of insult to life, or even surpass it. It is an insult to the universe.

This may be a bit much. Plenty of mathematicians do mathematics for less than noble reasons, from the pursuit of fame and glory, self-aggrandisement and ego, down to petty rivalries and jealousies, all the way through to fraud and plagiarism. The Manhattan project was a much larger insult in many ways, hijacking the study of the quantum world to kill millions. As Russell put it, “Archimedes used mathematics to kill Romans, Galileo to improve the Grand Duke of Tuscany’s artillery, and modern physicists to exterminate the human race”.

But, none of those predecessors have made such enormous breakthroughs: breakthroughs in the service of capitalist selfishness and, if they are successful by their own measures, civilization-scale objective harm.

Switching from high- to low-brow, we can tell them, we’ll take your theorems thank you, and thank you also for creating such demand for mathematicians and our expertise to explain your slop. But you can go and stick your investment bubble up your arse. We hope it pops.

* * *

Well, not quite. When large enough financial bubbles pop, it is not only the perpetrators of the bubble who suffer; they may not suffer at all, as we learned acutely in 2008. Perpetrators may be bailed out while ordinary people lose their life savings, their houses, or worse. As Thucydides wrote millennia ago, the strong do what they can, and the poor suffer as they must.

An astronomical amount of capital has flooded into hyperscale AI companies, and if that capital sees insufficient return and bankruptcies ensue, the consequences will not be limited to them. Indeed, given their political power, the consequences may be limited to others.

Of course, the hyperscale AI companies are enormously powerful, for now at least. They are aligned with the Trump administration. Their executives are touted as titans, divine tech bro kings. Who knows what they may do if the financial tide turns against them: pivot, cannibalise each other, charge more to customers, merge with the military-industrial complex, surveil, advertise, generally enshittify.

We can only hope for a scenario in which the savings of ordinary people, pension and superannuation funds, extract themselves and limit their exposure to a crash.

The data centres are built. They will still be there after a crash. The chips burn out pretty quickly but they won’t be complete lemons. Unlike the whims of financial markets and the debt-fuelled manias on which our economy increasingly irrationally depends, physical infrastructure tends to endure.

In the immortal words of Ursula K Le Guin — once more turning to the world of science fiction to explain science fact — the power of capitalism seems inescapable. So did the divine right of kings. May we one day look back at tech bro CEOs the same way.

* * *

Returning to the history, perhaps the event that shocked the mathematical community into realising the mathematical capabilities of AI models was the 2025 International Mathematical Olympiad, the IMO. The 2025 IMO was held on the Sunshine Coast, the first time it had been held in Australia since 1988, part of the bicentennial.

I was there, a member of the Problem Selection Committee. I had been involved as a student back in the day, even deputy of the Australian team for a few years; I still help to set the Australian national competitions. But I was out of practice and out of touch with two decades’ worth of developments at the IMO. Nonetheless, organising an IMO requires the involvement of so many local people that my services were called upon.

The IMO is a competition for high school students. It consists of two exams, each 4.5 hours long with three problems. The problems are designed not to use anything more than “elementary” concepts, roughly the standard high school curriculum appended with various specialised topics. To solve the problems requires extraordinary problem-solving skills — judgment, calculation, endurance, tenacity, knowledge and application of a kaleidoscope of approaches and perspectives — but also creativity and ingenuity at levels ranging from talented to preternatural. The problems range from the merely very hard — and students who have trained on enough problems will often recognise patterns in problems and approaches that might work — to extreme. Despite hundreds of attempts by the best secondary school student mathematicians from around the world, the hardest question is often solved by less than a dozen.

With AI companies turning to mathematics as a means to an end — to demonstrate the capabilities of their models — the IMO became a perfect testing ground. Correct mathematics being verifiably true, it cannot be dismissed as just more hype. And, also because mathematics can be verifiably true, it is a perfect case for reinforcement learning techniques on AI models.

Even better, the IMO awards medals. If you score highly enough, you get a Bronze medal; higher again, Silver and Gold. What better press release could there be for an AI company than to say it could win a Gold Medal in mathematics?

* * *

It was at the previous Australian IMO, Canberra 1988, that Prime Minister Bob Hawke presented a young Terry Tao — now often regarded as the greatest living mathematician — with a gold medal. It has become an iconic image.

It perhaps symbolizes the best of Australia. As a thoroughgoing internationalist, I have absolutely no belief that the nation I was born in is intrinsically better than any other. But if we Australians want our society to be good, we should promote the best of it. And for a positive image of the nation, we could do no better than this one: a uniquely charismatic Prime Minister, former trade union leader, recognising scientific brilliance by a young Australian of Chinese heritage. The picture has aged well. What better picture of a multicultural social-democratic society nurturing the highest levels of scientific achievement?

In 2025, at the corresponding ceremony, various officials presented the medals, including myself. Again, Australia won Gold, awarded to two members of the 6-strong Australian team. But the media barely covered it. Prime Minister Albanese was absent. No member of Cabinet was present. No Senators, no MPs, not even the local member. Not Queensland Premier Crisafulli, no member of State Cabinet or the Queensland Parliament either. The highest ranking political official in attendance was the Deputy Mayor of the Sunshine Coast, God bless her soul.

The reason? Not AI, but not entirely separate from it either.

* * *

When Russia invaded Ukraine in 2022, many sports federations declared sanctions against Russia. Following the International Olympic Committee, sports from Badminton to Taekwondo immediately became high-flying defenders of human rights and international law. So too did Chess – and Olympiad mathematics followed suit.

The International Mathematical Union (IMU) condemned the invasion as “a violation of international law, with the most terrible consequences for millions of innocent people affected by this aggression”. Its premier conference, the quadrennial International Congress of Mathematicians, which was shortly due to be held in St Petersburg, was promptly moved.

The IMO, which is completely distinct from the IMU, took a less grandiloquent approach, but came to a similar conclusion. We all became used to seeing Russians competing under a neutral flag in all manner of sports, and this was also true at the IMO.

I think sports sanctions are, in principle, a good thing. Sanctions against apartheid South Africa are now seen as part of the political pressure that contributed to the end of apartheid. The Black Power salute by Tommie Smith and John Carlos at the 1968 Olympic games is a defining moment in sporting history. Peter Norman, the Australian athlete who supported them on the Olympic dais, is now commemorated by a public statue in Melbourne.

There are some crimes which so shock the conscience that we feel compelled to do what we can to oppose them. Sometimes other remedies are not possible; sports sanctions are highly visible and have strong symbolic value.

As many pointed out at the time, banning Russia for its international crimes is all well and good, but Russia was an international pariah, which made the ban politically easy. The real test, as many of us noted at the time, would come when another State did something similar, and consistency required sanctions that were not so easy. No doubt there would be a time when this was tested, and a choice would arise between courage and cowardice, between consistency and hypocrisy. That choice came for the IMO in 2025.

Consistency would require sanctions against any other country engaging in similar behaviour to Russia. And there is perhaps no professional group or discipline so ontologically committed to consistency as mathematicians and mathematics.

So, after the October 2023 escalation of violence in Israel-Palestine, as Hamas militants and others broke the walls of their Gaza prison and went on a terrorist rampage of massacres, and Israel proceeded to obliterate the Gaza Strip — with a level of destruction for which the only appropriate noun in everyday English is genocide, and for which many legal bodies have found the label is juridically appropriate — the only surprising thing about the efforts at the 2025 IMO to sanction Israel was why they took so long.

* * *

As has been widely documented, AI systems have been used extensively by the IDF in Gaza.

One AI system “the Gospel” used machine learning to recommended targets for bombing, much faster than any human intelligence analyst. In previous Gaza wars — if “war” is even the right word given the mismatch of forces; “mowing the lawn” in the vile rhetoric of some Israeli strategists and politicians — the Israeli air force had run out of targets to bomb. Thanks to AI, this problem was eliminated, along with many thousands of Palestinian children.

Another AI system “Lavender” recommended individuals to bomb, with humans providing a stamp of approval, according to those who approved it.

And a third AI system “Where’s Daddy?” waited for militants to return home, when they could be exterminated along with their families, down to as many generations as happened to live together —along with whoever else happened to live nearby.

* * *

The IMO is governed by its Jury, something like a localised UN General Assembly, and Board. Every participating country receives one vote in the Jury. I was not a member, though I attended a couple of sessions as they set the exam papers and addressed the jury on number theory problems.

For mathematicians facing the question of sanctions — or really any question whatsoever — the preferred outcome would be that the question could be answered by applying some general principle. But any general principle other than the null one — nobody gets sanctioned — requires some thought. Where to draw the line? Genocide? War? All wars? Which wars? Which types of violence, or oppression, deserve sanctions, and which escape them? The question ramifies immediately.

Mathematicians, being intuitive seekers of abstract principles, instinctively arrive at that question. They are also uniquely placed to think of difficult examples and edge cases, and uniquely unqualified to classify them. Such a classification of the very worst things human beings can do to each other — a taxonomy of failures of the human spirit — is not something that mathematicians are familiar with. It is part of the messy, human world, a world without theorems and axioms and usually without clean logical deductions.

But such a classification exists. It is called international criminal law. The International Criminal Court (ICC) applies it, as codified in the Rome Statute. Genocide and aggressive war are the two biggest crimes in the Rome Statute book. At the time, the ICC had outstanding warrants for precisely two sitting heads of state, namely those of Israel and Russia. The ICC had long been criticised for its selective application of international law, disproportionately against poor, developing and African countries — but its warrants against Putin and Netanyahu had suggested things could be otherwise. The US, for its part, has a law authorising an attack on The Hague should any US defendants ever face justice there.

However, not many mathematicians know international criminal law. So far as I know, international law did not arise in the jury’s deliberations.

The IMO has a President. Together with the IMO board and its “ethics committee”, he advocated that sanctions should only be considered for infractions like cheating. He argued that sanctions are bad for business: sponsors might be deterred if the organisation were seen to be “political”.

So it was that, in the midst of an AI-enhanced genocide, faced with a motion to remain consistent with a previously expressed stand for human rights, the IMO Jury voted. By 62 to 23, they voted to remove sanctions against Russia.

* * *

With the exams over, medals decided, and Russia fully reinstated, all that remained at the IMO were the closing festivities.

We can now see why the highest ranking political official in attendance at the closing ceremony was the local deputy mayor: no other politician would go near it.

Even had the Jury voted to extend sanctions consistently, the closing ceremony would have been no different. All parties in the Jury were clear that, whatever the outcome, the Israeli team was welcome until any ban took effect in a subsequent year; that they should not be treated any differently from others; even under sanctions they would still be welcome to compete under similar terms to Russia; and of course the country’s maths team were not responsible for the actions of their government. Mathematicians are too smart for any nonsense to the contrary. Indeed, one of the Israeli team members was interviewed in the press supporting sanctions against their country.

But Australian politicians bolted in panic. Even though no country was sanctioned — in fact, all sanctions in place were dissolved — and even though the Jury explicitly voted to take the most apolitical line possible, they ran for the hills. The mere hypothetical possibility of some controversy around Israel-Palestine, which never eventuated, and which was in the final event explicitly disavowed, was enough to make every official of higher rank than deputy mayor disappear without a trace.

As a result, Australia at large treated the IMO as a non-event. Media coverage was almost non-existent. The country’s leaders deprived themselves of any opportunity to promote science, of any chance to celebrate the world’s best young mathematicians, and of any possibility of a future iconic moment like the Hawke-Tao encounter.

* * *

AI companies, however, were waiting in the wings, seeking medals for profit. In fact, the IMO President, prior to his successful jury motion, had successfully irritated organisers with his eagerness to meet AI company executives who had flown in for the event.

A Gold medal in the IMO requires a sufficiently high mark: in 2025, the cutoff was 35 out of 42.

Marking an IMO is not an easy process. It is not a simple matter of getting the right answer. Solutions are proofs, written by students with pen and paper; each problem is marked out of 7. The Problem Selection Committee develops intricate marking schemes, attempting to cover as many possible approaches as possible. But the problems often allow many creative approaches, and student solutions can be incomplete or problematic in many different ways, so deciding marks is often far from easy. The leaders of each team — usually academics or former Olympians — negotiate with marking coordinators working under the problem selection committee to agree on marks for their team. The process is laborious and labyrinthine: dozens of coordinators — academics, graduate students, former Olympians, local and international — schedule meetings with every single team’s leaders until they agree on every single solution from every single student.

Anyone can try the IMO problems from a few minutes after the exam ends, as they appear on the internet essentially immediately. The AI companies at the gates did so. The question for them was how to grade their AI-generated solutions.

Some companies, like OpenAI, simply marked the problems themselves. All these companies have several former IMO participants and medallists on staff, so this is perhaps less of a cheat than it sounds, but the self-interest and bias is clear enough. Nonetheless, if a solution is clear enough, it’s 7 out of 7, and this is what OpenAI and Google DeepMind both claimed for 5 of the 6 problems.

The AI companies who came to the IMO, including Google DeepMind, tried to take a more “official” route. The IMO President thought he could negotiate a deal with them, with the event already in progress, and then we markers would mark them — which was also, of course, AI marketing.

Unsurprisingly, some of us doing the marking had some concerns about such an arrangement — quite apart from the increase to the already-backbreaking workload. The IMO is about celebrating student achievement, not AI; we were working as volunteers but being asked to do marketing work for companies not contributing financially to the IMO; the parameters and usage of the AI models were not transparent. Couldn’t the announcement of AI results at least wait a week, and give the students time to shine? In any case, we were not officially tasked to mark AI scripts.

But Google, who had sent employees all the way to the Queensland antipodes for an official IMO stamp of approval, was panicked by the prospect of being scooped by OpenAI, making press releases about their self-marked scripts from afar.

As a result, Olympians were treated to the spectacle of Googlers wandering the IMO after party armed with laptops, trying to find markers to certify their AI scripts. They didn’t find me, and some markers they did find declined to participate in their marketing. But they eventually found enough willing markers to claim in their press release that their solutions were “officially graded and certified by IMO coordinators”.

Google waited and made their announcement on July 21. OpenAI scooped them with a press release on July 19, an hour after the closing ceremony.

One team runs helter skelter amidst markers finally trying to relax after an enormously stressful week, imploring them to mark their laptops. The other team marks their own papers and steals the limelight from a high school maths competition via press release one hour after their medals are awarded. This is the face, and the farce, of the AI race; the companies being handed trillions and given free rein over the future of our economy, whether by debt-bubble-crashing failure, or mass-unemployment-inducing success.

The latter team turned out to be the ones who a year later gave us the mathocalypse. Given what they did a year earlier, it is no surprise.

* * *

And that brings us to the last few months. Increased power and capability seem to have brought not a sense of responsibility and higher purpose, but the willingness to abuse it.

When the Navier-Stokes results came out, OpenAI refused to engage or collaborate with any work that might have included an Anthropic employee. But by then their attitude had turned sinister. When Tristan Buckmaster, one of the humans scooped by OpenAI, refused their offers sidelining the Anthropic employee, the OpenAI representative’s reply was “If you don’t want me to be nice, then I don’t have to be nice.”

Take those papers and stick them up your brains.

* * *

And here we are, with all this mess, slop oozing and overflowing the tower.

In some less-informed quarters, there is no shortage of claims that mathematics is solved, mathematicians are now obsolete.

Nothing could be further from the truth. Given these 700 papers that seem to be terribly written but full of breakthroughs, who is going to evaluate them, understand them, explain them? Mathematicians. In doing so, they will be contributing to the advance of knowledge, understanding new breakthroughs in the process. It is a new mode of scientific progress, but clearly produces valid knowledge despite its dystopian provenance.

With the enormous quantities of mathematical verbiage that machines can now produce — and a slopocalypse of hundreds of major breakthroughs — the need for mathematicians is now greater than ever. We need more researchers, we need to train more students, we need more people to explore the universe of mathematics, whose accessible regions have expanded almost unimaginably rapidly.

It is a second ironic boon, of a sort, to mathematics departments. In its quest to convince investors it can turn a profit by getting workers fired, AI companies first created a vast demand for teaching labour — to redesign teaching and assessment to avoid AI cheating by students. Now they have created the demand for massive numbers of research mathematicians. Perhaps one day this demand can be met by a sufficient supply of teaching and research staff.

Even the very idea that mathematics can end, or be solved, is a misconception.

It can never end: every question answered creates a dozen more; every landscape understood and mountain climbed opens up the next landscape in the valley beyond. In the image of Jordana Cepelwicz, we have been teleported to the top of hundreds of mountains, without knowing how we got there or what lies beyond. Not only do we need to understand how we got there, we now have whole new countries to explore.

In his classic 1930 radio address — possibly the most famous radio address by a mathematician — David Hilbert declaimed “We must know — we will know!”

And now we have the technology — we can know! We know how to know!

Humans, assisted by machines, can now push mathematical knowledge beyond the wildest dreams of the world’s greatest minds, as of only a few weeks ago. Of course, not everyone may want to use the machines as they are — I certainly don’t. Their business model is a cluster bomb of social harms.

But there is no reason that existing arrangements are inevitable; there is no reason that the existing compute cannot be powered by renewable energy, governed democratically and used for social benefit, run as a public utility, its usage appropriately prioritised among other important social goals such as avoiding climate breakdown. These large language models, after all, are trained on the collective work of all of humanity, including the accumulated genius of the history of mathematics. Humanity’s collective intelligence powers the technology, and humanity should collectively decide how the technology is used. It is just the current social reality that makes it a dystopian nightmare.

Utopian possibility in a dystopian reality: this is not just mathematics, this is the essential state of the human present. Our job, to the extent possible, is to lean on the scale, as best we can, to improve the chances.

* * *

The immediate effect of the mathocalypse is to produce a gold mine of poorly understood papers which probably contain a vast quantity of scientific breakthroughs. Or, perhaps more accurately, a slop mine where the slop can be refined into well-understood mathematical gold.

In doing this refining work, mathematicians will also be doing OpenAI’s marketing work for them — except when the results turn out to be wrong. In recent days I have seen several papers posted, along the lines of “A readable version of OpenAI’s terrible proof of a theorem, which by the way was also way more complicated than necessary”. But even such papers validate an OpenAI breakthrough.

As Cory Doctorow has noted, AI can be used to create both centaurs and reverse centaurs: a human using a machine, or a machine using a human. In verifying OpenAI’s proofs, mathematicians are acting as appendages to their marketing department, humans augmenting the corporate machine.

When mathematicians use AI under their own control, whatever we might think of it ecologically, socially, politically or philosophically, they are acting as centaurs. Although there are certainly risks of reliance on the machines, from laziness through to full cognitive surrender, judicious and self-controlled use may augment their own brains, their own capacities, using a powerful tool.

Perhaps the most directly politically crushing aspect of the mathocalypse is that to engage with it, advancing knowledge in the process, is to become OpenAI’s reverse centaur. But other hyperscale companies are little better, and as long as they have a monopoly on the most advanced AI models, this is unavoidable. It is all the more reason to build alternatives.

* * *

And there are alternatives, and there will be more. It is possible that soon there will be nothing but alternatives to the existing hyperscale AI companies.

Although a revolution in mathematical technology is clearly happening, the AI companies’ case for viability is still far from clear. They have borrowed astronomical amounts of money to build their data centres, and these debts will come due. To pay those debts and turn a profit, they need their software to replace an astronomical number of workers — although, as Cory Doctorow also notes, AI does not necessarily need to be able to replace those workers, just good enough to convince their bosses to replace the workers, and for the bosses to win the ensuing industrial relations struggle. It is not at all clear that pure-mathematical capabilities affect that overall viability substantially.

Even though the capabilities in mathematics are extraordinary, the capability to write breakthrough pure maths proofs is not one itself that will convince many bosses to replace many workers. There are not many bosses who need this skill. And even in mathematics, as already noted, this capability creates demand for mathematicians, and possibilities for more research and knowledge, rather than rendering them obsolete.

The best argument for the hyperscale AI companies’ pursuit of mathematics — marketing aside — is that mathematical capabilities indicate broad competence, on the road to “general” or “super” intelligence that can replace enough workers to inaugurate profit for themselves and catastrophic unemployment for the rest. But pure mathematics, despite its unboundedness, is a very limited domain of the world. It is purely formal, can be defined by axioms, and has binary notions of correct and incorrect, amenable to reinforcement learning techniques. This is precisely why it usually has so little to say about the real world, and why many mathematicians like it.

As Bertrand Russell wrote:

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true… Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

The economic world, the world of business operations and institutional organisation — the world in which AI must achieve superhuman capability to achieve profitability — is an entirely different world, teeming with tacit knowledge: nebulous, indeterminate, inchoate. This is why many mathematicians dislike it, and maybe AI too. Even astonishing capabilities in the formal domain of the empty assertions Russell describes does not seem to substantially alter AI’s overall capacity to replace workers.

Of course, that said, the history of predictions of AI capabilities is a history of underestimation. The AI models will no doubt gain more capabilities as time goes on.

But even replacing all the mathematicians, along with other likely marks such as commercial illustrators, coders, truck drivers, and so on, does not seem to be enough. Where will they find a big enough market for their capabilities?

The bubble cannot go on forever. Whether a crash is inevitable or not, an eventual shock and some sort of crisis seems to be very possible, even likely. At the very least, we should best be prepared for it. And if hyperscale AI companies go bankrupt, the computing infrastructure will still be there.

Naomi Klein, in her book The Shock Doctrine, discusses the imposition of neoliberal ideas on the world. The public being resistant to them, they could only be imposed in times of shock. As Milton Friedman schemed — and implemented, for instance, through his friends in the Pinochet Regime:

Only a crisis—actual or perceived—produces real change. When that crisis occurs, the actions that are taken depend on the ideas that are lying around. That, I believe, is our basic function: to develop alternatives to existing policies, to keep them alive and available until the politically impossible becomes politically inevitable.

If the bubble pops, if God forbid there is a devastating crash, if the data centres are up for grabs, what ideas will be lying around?

* * *

The idea of a public utility AI, used by humanity in the public interest — for the things we actually want, and not for the things we don’t — is not at all a distant one. The thing itself exists. It’s just that the social and economic relations are all wrong.

There is an investment bubble. At least some hyperscale AI companies will likely go bankrupt. The physical infrastructure they are using will not disappear. For better or worse — probably worse, given all the renewable energy projects that could have been built instead — it can be put to use.

It is to our advantage to decipher all this mess before the bubble pops.

In the 2008 financial crisis, the UK Government nationalised several banks. They nationalised Bradford & Bingley. They nationalised Northern Rock. They bought 84% of the Royal Bank of Scotland. It cost them hundreds of billions of pounds.

What should governments do if AI companies find themselves in a similar situation?

“Lemon socialism” describes the buying up of failing companies into public ownership. But AI companies, if and when they fail, are only lemons for the purpose of replacing workers and making profits. They are astonishingly good for many other purposes, like mathematics. Why not make some lemonade?

* * *

Of course, it would be grotesquely polluting lemonade. AI models, as they are currently built, require enormous physical infrastructure. Perhaps these models do not need all the chips we throw at them, but maybe they do.

Whether we build all those chips, all those computers, all those data centres, or whether we build something else — like a renewable energy buildout, like retrofitting infrastructure to adapt to climate change — is a choice for society at large. It should not be a choice for tech bros, fascist venture capitalists, and irrational investors chasing bubbles.

But it is not even a serious question. Which first? Averting planetary crisis by building renewable energy? Or adding to the crisis by building data centres everywhere with the energy requirements of major cities? The question answers itself. Humanity, given the choice, would answer it accordingly.

But humanity is not answering it. It has not been given that choice. It has, for some reason, produced a situation where the power and authority to make those decisions lies with some of its worst specimens, aided by — produced by — exploitative and undemocratic economic and political systems.

Most people now see much more AI slop than they need or want. Even we mathematicians have enough papers with enough breakthroughs to set us on our way for years.

Climate activists have remarked that, even under relatively progressive conditions, business and government never quite seemed to find enough money for the urgent renewable energy buildout that science tells us is required to avert climate breakdown. Yet somehow, those barriers all disappeared for the, so it seems, much less profitable AI data centre buildout. We can build a lot of physical infrastructure when we really want to.

So, let’s do that first. When the economy hands us AI lemons, we can make the lemonade. In the meantime, we have other important work to do as well. Doing that might even bring us the lemonade sooner.

* * *

If AI turns out to be a normal technology, then a crash or crisis is likely and public ownership a desirable outcome. Of course, public ownership can take many forms, from incorporation into the military-industrial complex, through to democratic ownership under popular control, and the operation of public scientific research institutions. The details are precisely the policies that we must develop and keep alive, Shock Doctrine-style, until the politically impossible becomes inevitable.

But if, on the other hand, it turns out to be true that AI is capable of replacing most human workers — the sci-fi scenario, the dream of the hyperscale AI companies, and possibly their only route to profitability — we arrive at a similar conclusion. There would ensue a civilizational catastrophe of unemployment and poverty. But it is a catastrophe only under certain economic conditions, namely the ones we inherit today.

Unemployment is catastrophe in a capitalist economy because people need income from employment to survive. In the sci-fi AI scenario, very little work and very little income will be disastrous. A universal basic income, the preferred solution of the tech bros, is insufficient, precisely because it is only basic. It is not an come to live on; it is not a living wage. For professionals across the working and middle classes, reduction to a mere basic income is cold comfort. Do you think you are basic enough for a basic income? And why shouldn’t you get a living wage under conditions of overall wealth and luxury? It’s because of capitalist property relations: you are not an owner of AI, so you do not get a share of the profits.

Either way, we reach a similar conclusion. Whether the normal technology or the sci-fi scenario plays out, public ownership becomes not just a utopian prospect, it becomes the natural escape route to a liveable world under changed technological circumstances. Capitalism simply fails to distribute labour so that increased wealth and productivity can be experienced as freedom and leisure.

This failure of capitalism to improve working hours is well known. It is now almost a century ago that Keynes wrote, in Economic Possibilities for our Grandchildren, that

the economic problem may be solved, or at least within sight of solution, within a hundred years. This means that the economic problem is not — if we look into the future — the permanent problem of the human race.

He predicted overall economic growth over that century with great accuracy. We are as much better off, roughly speaking, overall, in the economists’ way of thinking, as Keynes predicted. But he predicted a 15-hour work week in the coming age of leisure. Now working hours are highly contingent, the subject of struggle at levels of workplaces, classes, industries and ideologies; they are by no means determined entirely by economic institutions. But, a century later, it seems to be a fairly safe conclusion that capitalism, even tamed by such social-democratic reforms as we have achieved, is bad at producing freedom and leisure.

So perhaps we should go further in the direction of that utopian socialism. In a rational economy, democratically and participatorily planned for the public good, people could democratically choose how much they want to work, and how much income they have. In the sci-fi AI scenario, the choice of very little work and great income will be possible. In the normal scenario, the choice is just as good, maybe even better for those of us for whom productive work gives us meaning. AI might even help with the planning.

In many ways, the story of AI development is the story of humanity developing technologies it is not yet evolved enough to handle. The race to AI is also the race to develop an economic system, and a society, which is ready for it.

But, if we can lean on the scale enough, develop that system, and avert the worst of our suicidal tendences, we have enough for the leisure Keynes dreamed of. We are the grandchildren of his dreams — and also, for that matter, the immortal dreams of the condemned anarchist Bartolomeo Vanzetti:

I sought my liberty and the liberty of all, my happiness and the happiness of all. I wanted a roof for every family, bread for every mouth, education for every heart, light for every intellect. I am convinced that human history has not yet begun, that we find ourselves in the last period of the prehistoric. I see with the eyes of my soul how the sky is diffused with the rays of the new millennium.

For the mathocalypse to be a ray of the new millennium, much must go right: the sky must be cleaned of the pollution diffusing its rays; its benefits must be taken from the oligarchs and put into democratic control, given to every family, every heart, every intellect; and its destructive powers to control, corrode, divide, disempower, stupefy, alienate and kill us must be curtailed. Our dreams, as ever, remain.