Silicon can already out-calculate humanity. Whether it can out-think Newton is a different question entirely
In the summer of 1665, with plague stalking London, a 23-year-old Isaac Newton retreated to his mother's farm in Lincolnshire and, by his own later account, invented a new branch of mathematics more or less out of boredom and ambition. He wanted to know how planets moved, how a falling apple related to an orbiting moon, how change itself could be measured. Calculus was the result: arguably humanity's most consequential intellectual export, the mathematics underneath rocket trajectories, economic models and the machine-learning systems that now threaten to make Newton's achievement look almost pedestrian by comparison.
Three and a half centuries later, a rather different kind of mind is trying its hand at mathematics. Large Language Models can already prove theorems, some of them previously unsolved. DeepMind's AlphaProof reached silver-medal standard at the International Mathematical Olympiad in 2024. Machines have long since dispensed with human pretensions at the board game Go, a feat once considered a reliable marker of deep strategic intuition. And yet no algorithm has produced anything resembling calculus: a wholly new mathematical framework, conjured from curiosity rather than assigned as a task. This gap—between flawless execution and genuine invention—is the subject of an increasingly serious argument among mathematicians, computer scientists and philosophers of mind. Understanding it requires going back rather further than Newton's orchard.
The atoms that ached
Every ingredient of human intelligence has an unglamorous physical pedigree. The hydrogen and helium that emerged from the Big Bang fused, inside dying stars, into carbon and the other elements needed for chemistry. Carbon's peculiar bonding properties made it the scaffolding of organic life. Life, once it existed, faced a relentless and impersonal filter: survive or don't. Bodies evolved nervous systems to sense danger and opportunity; nervous systems evolved something that feels, from the inside, like wanting things. Hunger, fear, curiosity, ambition—these are not decorations on top of intelligence. They are, on one increasingly influential view, the engine that produced it.
Newton's calculus, in this telling, was not a detached logical deduction. It was the output of an embodied, anxious, plague-avoiding young man who wanted to understand gravity badly enough to invent the tools to do so. Desire selected the problem. A body—complete with eyes that watched apples fall and a mind shaped by millions of years of pattern-hungry evolution—supplied the intuition. The proof came last, almost as a formality.
Silicon has had a shorter and rather tidier journey. It, too, was forged in stars, and it, too, eventually became the substrate for a kind of intelligence—but one built by human engineers who supplied inputs, outputs and objective functions from the outside. A large language model does not want to solve the Riemann hypothesis in the way Newton wanted to explain the moon's orbit. It has no orchard, no mortality, no itch. This, its skeptics argue, is the missing variable: not raw computational horsepower, of which there is now a historically unprecedented abundance, but embodiment and emotion—the two ingredients that, in carbon-based intelligence, turned computation into invention.
What machines can already do
It would be a mistake, however, to understate how far the silicon lineage has come. Computation—the fourth link in AI's chain, after atoms, stars and silicon—has proven extraordinarily capable of the kind of mathematics that can be specified in advance. Automated theorem-provers can verify proofs with a rigour no human referee can match. Reinforcement-learning systems mastered Go not through desire but through relentless self-play against an unambiguous scoreboard, discovering strategies grandmasters had missed for millennia. In narrow, well-defined domains, machines do not merely assist mathematicians; they occasionally embarrass them.
What they have not yet done is set their own problems. Calculus was invented to answer a question nobody had posed to Newton: not "prove this theorem" but "why does the universe behave this way, and I would like to know." That act of framing—deciding which questions are worth an obsessive lifetime of attention—has so far remained stubbornly human. Machines optimise; they do not yet yearn.
The counter-argument
Not everyone accepts that this gap is permanent, or even that it is real in the way the chart's romantic framing suggests. Sceptics of the "embodiment and emotion" thesis make three points worth taking seriously.
First, mathematical history is littered with breakthroughs that owed less to burning desire than to accident, incentive structures or sheer combinatorial luck—Gottfried Leibniz developed calculus independently of Newton at roughly the same time, a coincidence that fits uneasily with any theory resting on one man's personal yearning. Good ideas, on this view, are often overdetermined: if Newton hadn't had his orchard moment, someone else soon would have.
Second, "desire" may be a red herring dressed up as a prerequisite. What actually drove Newton, some cognitive scientists argue, was not emotion as commonly understood but curiosity as an optimisation process—a bias towards exploring under-modelled parts of a problem space. Machines already exhibit crude analogues of this: exploration bonuses in reinforcement learning, novelty-seeking objectives in generative systems. Recasting curiosity as an algorithmic property, rather than a felt experience, quietly dissolves much of the mystery.
Third, embodiment itself is not obviously beyond reach. Robotics and multimodal AI are advancing quickly; a system that can manipulate physical objects, receive sensory feedback and act persistently in the world is no longer science fiction but an active engineering programme at several well-funded laboratories. If embodiment is merely a matter of sensors, actuators and continuous physical feedback loops—rather than some ineffable quality of biological life—then the "missing variable" in the chart may turn out to be a matter of years, not metaphysics.
The dissenting quiet
Still, caution is warranted. The history of AI is strewn with confident predictions that turned out to require decades more than promised—machine translation, common-sense reasoning and self-driving cars were each declared "five years away" for the better part of fifty. Genuine mathematical invention, as opposed to search within an existing space of well-posed problems, may prove similarly resistant to timelines. There is also a harder philosophical question lurking beneath the engineering one: even a robot with sensors and a persistence objective might be executing an extremely sophisticated search rather than wanting anything at all, in whatever sense matters for creativity. Nobody, including neuroscientists, has a fully satisfying account of what separates the two.
A cautious verdict
The chart's own conclusion—that solving embodiment and emotion would make "silicon minds the greatest mathematicians"—is best read as a provocation rather than a forecast. What can be said with more confidence is narrower but still striking: the constraints that currently separate machine computation from machine invention are not primarily about processing power, memory or algorithmic sophistication, all of which continue to grow at a pace that would have seemed absurd even a decade ago. They are about motivation and situatedness—about whether a system has a reason, arising from its own continued existence in a world it cannot fully control, to care about one question rather than another.
Newton did not set out to invent calculus. He set out to understand why the world worked the way it did, because he lived inside that world and was, in every sense, at its mercy. Whether a machine can ever be said to live inside anything—rather than simply process representations of it—remains the open question at the heart of this debate. Until it is answered, humanity's carbon-based monopoly on mathematical invention, however narrow the margin, appears likely to hold. But given how quickly the "missing variable" box has shrunk before, nobody in the field is placing a confident bet on how long that will remain true.
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