The slow unspooling
On mathematics, meaning and the machine in the ivory corridor
There is a particular quality of light in Cambridge when the winter is struggling not to give way to spring knocking at the door, a kind of golden restraint that falls upon the ancient stone and makes one feel, momentarily, that the place exists outside of time. It was in such light, crossing a courtyard strewn with damp leaves, that a colleague from engineering, a man who builds things, who believes in the solid and the verifiable, offered a pronouncement with the easy confidence of one delivering news of a death. “But we know the ivory tower hates the large language models,” he said. He meant it as a settled fact, a piece of common knowledge as unremarkable as the dampness of the leaves. And for a moment, the phrase hung there in the thin, cold air, a small, convenient lump of received wisdom.
It is a potent image, to be sure. It conjures a sequestered elite, peering down from a Gothic fastness upon the muddy, complicated business of the modern world, recoiling in horror at the arrival of a new and unsettling technology. The large language model, in this telling, becomes a kind of Trojan goat. Our usual reluctant curiosity is held in check as it is met with the frantic barring of gates and the sharpening of antiquated implements. The accusation is that the academy as the great sprawling organism dedicated to the pursuit of new knowledge, has welcomed the latest tool for generating and manipulating knowledge with nothing but a reflexive and petulant hatred.
This is, I have come to believe, a diagnosis that mistakes the symptom for the disease and the fever for the patient’s true nature. It is a story too simple, too dramatically satisfying, to be entirely true. From where I sit, which is to say, at a desk overlooking the Cam, cluttered with the overlapping proofs of mathematical intuitionism, the dense prose of critical theory and the brittle, yellowed pages of New Journalism, the situation presents itself as something far more interesting, far more nuanced and ultimately, far more human than a simple tale of Luddites and innovators.
Let us first extend the accusers their due, as the perception of hatred does not emerge from a vacuum. The initial encounter between academia and the large language model was, to be charitable, a collision rather than a conversation. The technology, initially presented in the polite guise of a research proposal or a subject for a seminar, arrived as a kind of digital poltergeist, wreaking its most immediate havoc in the one place the academy holds most sacred: the mechanisms of assessment. Overnight, it seemed, the undergraduate essay as the venerable workhorse of a liberal education, was rendered profoundly suspect. The carefully crafted argument, the dutifully cited source, the elegant turn of phrase, all could now be conjured by a machine in a matter of seconds. The initial response was not hatred, I think, but a more primal and understandable emotion: fear. It was the cold, creeping fear of a goalkeeper watching the ball curve in an impossible trajectory, the fear of a system realising that the rules of the game had been fundamentally and perhaps irrevocably altered. The cry that went up was not so much a condemnation of the machine as a desperate plea for the protection of a cherished and fragile process, the slow, painful and essential process by which a mind learns to think by being forced to articulate its own thoughts.
This fear bleeds into a second, more profound source of friction. The academy, at its best, is an institution built upon a kind of sacred trust in the verifiable. Its currency is the citation, its law is peer review, its highest virtue is the original contribution. The large language model, by its very nature, presents a challenge to all three. It is a master of pastiche, a weaver of plausible fictions from the vast tapestry of human expression. It does not cite in the way we understand citation; it absorbs, synthesises and re-presents, often with a terrifying fluency that masks a profound and sometimes dangerous ignorance. Its tendency to hallucinate, to invent sources, to fabricate facts, to construct arguments of elegant nonsense, is not a bug to be fixed so much as a feature of its fundamental mode of operation. It is a confidence artist of the highest order and the academy, an institution built on a deep and abiding suspicion of the confidently unverifiable, was bound to view this new arrival with a deeply sceptical eye.
Beneath these institutional anxieties lies something even more personal, more existential. After having spent a decade, perhaps two, climbing the narrow and treacherous path to become the world’s foremost authority on the role of the null subject in 14th Venetian accounting ledgers and then witness a machine generate a passable, if superficial, summary of the field in the time it takes to pour a cup of coffee, we experience a peculiar and unsettling form of vertigo. It is the fear of being devalued, of having the hard-won specificity of a life’s work rendered suddenly and terrifyingly generic. The “hatred,” in this light, is simply grief. It is the mourning for a past in which expertise was a rarer and more precious commodity, our history that is, perhaps, slipping away from us with every new iteration of the underlying model.
To stop here, to accept this narrative of institutional paralysis and existential dread, would be to miss the larger and far more interesting story. The academy, for all its Gothic stone and antiquated ritual, is not a museum of dead ideas. It is a living, breathing and remarkably adaptive ecosystem. The initial shock has passed and the real work, the slow, patient and intellectually rigorous work of understanding, has begun. The question is no longer how to banish the machine, but how to live with it, how to train it, how to make it useful without being made useless by it. We are, as we can observe in a daily basis, in the process of learning how to handle the tools.
This process of learning is playing out in classrooms and lecture halls across the globe and this process is far more subtle and inventive than any simple prohibition. The conversation has shifted from the policing of dishonesty to the re-imagination of pedagogy itself. If a machine can write a competent five-paragraph essay, then perhaps the five-paragraph essay has outlived its pedagogical usefulness. The challenge, as many of my colleagues are discovering, is to design assignments that the machine cannot do, that require the very things the machine lacks: a lived experience, a personal stake in the argument, the ability to synthesise disparate ideas from a seminar discussion into a novel and personal insight. This might mean a return to the in-class timed write, a form as old as the examination hall itself. It might mean placing a new and profound emphasis on the process of writing, the drafts, the revisions, the messy, generative struggle with language, rather than the final, polished product. It means teaching students not just how to write, but how to think about writing and in doing so, how to think about thinking. The machine is then no longer a threat to be avoided, but a foil against which to define a more robust, more genuinely human, conception of intellectual work. It forces a question we should have been asking all along: what is education for, if not to cultivate capacities that no machine can replicate?
And what are those capacities, precisely? This is where my own intellectual preoccupations, the tangled roots of mathematical intuitionism and the long shadow of a certain Dutch mathematician, offer a way forward. At the heart of intuitionism lies a deceptively simple and radically disruptive idea: that mathematical truth is not discovered in some pre-existing Platonic realm but is created in the mind of the mathematician. A mathematical object exists only insofar as it can be constructed, step by step, in a series of mental acts. The law of the excluded middle, as one of the mainstays of classical logic which insists a proposition is either true or false, is rejected because it allows for the existence of things that cannot be constructed. For the intuitionist, to exist is to be constructed, to be built in the active, intentional consciousness of a thinking subject.
This framework, developed a century ago in response to a crisis in the foundations of mathematics, now seems to me a surprisingly apt lens through which to view our current predicament with the machine. What the large language model presents us with, above all, is a triumph of output without a corresponding process of inner construction. It can generate a proof, but it has not experienced the creative leap, the sudden, illuminating insight, the slow, painstaking work of groping towards a solution that characterises the mathematical act. It can write a sonnet, but it has not felt the thing the sonnet describes. It can produce a philosophical argument, but it has not wrestled with the doubt, the uncertainty, the existential weight that gives the argument its force and its meaning. The machine produces the what with astonishing fluency, but it is entirely ignorant of the how and, more importantly, the why. It is all buldings and no architect, all text and no subtext, all answer and no question.
The machine, in its essence, is a perfect mimic of the products of thought, but it is a stranger to the process of thinking itself. And it is precisely that process, that slow, difficult and glorious act of inner construction, that the academy, at its best, exists to cultivate and to celebrate. We are not, in the end, in the business of producing text. We are in the business of producing minds capable of producing meaning from text. The machine, by so perfectly mimicking the final stage of that process, performs an unexpected and invaluable service: it throws into sharp relief the value of everything that comes before. It clarifies, by its absence, the importance of the constructing subject, the lived experience, the intentional consciousness that is the true author of any genuine thought. We do not hate the machine for what it can do. We value it for showing us, more clearly than ever before, what it cannot.
This perspective allows us to move beyond the crude binary of hatred and embrace and into a more productive engagement with the tool, because a tool it most certainly is and a remarkably powerful one at that. My own work, which sits at the uneasy intersection of mathematical foundations and non-scientific philosophy, requires a voracious and promiscuous reading habit. I must move from the technicalities of Brouwer’s proof of the fan theorem to the cultural criticism of a certain German philosopher of cynicism and enormous glass houses, from the dry analytics of structural realism to the luminous, crystalline prose of a British essayist who taught us how to look at the places we live. The large language model, used with discretion and a healthy dose of scepticism, becomes a kind of super-powered research assistant, a tireless reader capable of summarising a dense argument, generating a bibliography on an obscure corner of the literature or translating a particularly thorny passage from the German. It does not think for me, but it can certainly read for me, clearing the undergrowth so that I might better see the shape of the forest.
There is a distinct and peculiar pleasure in this collaboration, a dry, whimsical delight in treating the machine as a kind of infinitely patient and uncomplaining junior colleague, one who never sleeps, never asks for credit and never points out the inherent absurdity of the questions one poses to it. I learn its quirks, its habits, its strange and wonderful capacity for both profound insight and breathtaking nonsense. It is, in a strange way, like training a very clever, very literal-minded and slightly unstable graduate student. You learn to phrase your questions with precision, to check every source it provides and to never, ever trust it on a matter of fact without independent verification. It is a tool that demands, above all, a heightened state of critical awareness from its user. And that, surely, is no bad thing for an academic to cultivate.
This critical awareness is the key that unlocks the door to a future in which the machine is not our enemy, nor our master, but a partner in the endless, fascinating project of making sense of the world. The academy is uniquely positioned to lead this partnership, precisely because its core values, scepticism, verification, the patient construction of argument, the celebration of original thought, are the very values that guard against the machine’s seductive but shallow fluency. The task before us is the teaching of a new kind of literacy, a literacy of the algorithm. We must teach our students and ourselves, not just how to use the machine, but how to interrogate it, how to understand its biases, its limitations, its fundamental otherness. We must learn to see the seams in its apparently seamless prose, to detect the hallmarks of its confabulations, to distinguish the elegant simulacrum from the genuine article.
This is, in a sense, a return to a very old calling. The academy has always been in the business of teaching people how to navigate a world saturated with information, how to separate the signal from the noise, the true from the false, the meaningful from the merely plausible. The large language model is simply the latest and perhaps the most sophisticated, source of that noise and the most seductive purveyor of that plausibility. It is a test of our fundamental capacities, a challenge to our most deeply held assumptions about what it means to know and to create. The initial fear, the defensive posturing, the cries of hatred, these were the understandable reactions of a body confronted with a sudden and unexpected invasion. But the body is resilient and adaptable. The antibodies are forming. The real work of incorporating this new element, of rendering it safe and useful, has begun.
The ivory tower does not hate the large language model. It is engaged in the long, slow and necessary work of digesting it. This process will take years, perhaps decades and it will leave both the tower and the machine irrevocably changed. The final shape of that change is not yet written, but the direction is clear. It lies in avoiding rejection and a quest for integration; not in fear, but in understanding; not in a retreat from the world, but in a deeper and more critical engagement with its newest and most unsettling creations. The light in the courtyard will continue to fall with that same golden restraint, but the work being done in the rooms that open onto it will be different. It will be work that acknowledges the presence of the machine, that uses its power and is wary of its limitations, work that is, in the end, more human for having to define itself against the ghost in the digital machine. The tower stands, but its windows are open and the cold, fresh air of a complicated century to come is blowing through.