The cycle that began with [YOU] on AI asks what remains distinctively human as the machines advance. Du Sautoy answers not with a list of capacities but with a test and a taxonomy. His Lovelace test—named for Ada Lovelace, who first asked whether a machine could originate anything—refuses the soft question of whether AI output impresses us and insists on the hard one: does the output belong to the system rather than to its makers? The test converts a metaphysical argument into something closer to an empirical one, and it is the most rigorous instrument the cycle possesses for distinguishing genuine machine creativity from sophisticated imitation.
His diagnosis of the three types of creativity maps precisely onto the cycle’s central concern. Exploratory creativity—finding what the rules permit but no one has yet discovered—has been, du Sautoy argues, decisively taken by the machines. The extraordinary move made by AlphaGo in the second game of its 2016 match against Lee Sedol, a move two and a half thousand years of human play had never found, is his clearest exhibit. That move was new, surprising, and of value, and it did not come from any programmer. The machines have passed the Lovelace test at that level. What they have not yet shown is the capacity to change the game itself—to perform the transformational act that drops a rule everyone treated as essential and opens a new territory on the other side.
Du Sautoy also introduces a dimension the cycle treats as foundational: the question of understanding versus production. His deepest claim is that the machines can produce a proof, a melody, a winning move, without understanding what they have made—without the illumination that, for a mathematician, distinguishes a proof that compels assent from one that brings genuine comprehension. Where Judea Pearl locates the machine’s limit in its inability to reason about causation, du Sautoy locates it in the gap between generating a result and grasping why it is true. Both diagnoses converge on the same conclusion: the machines are astonishing on the first rung of intelligence and still on the near side of the threshold that matters most.
The collaborative picture du Sautoy sketches complements what the cycle insists throughout. The machine explores; the human judges significance. The machine searches a vast space; the human recognizes which discovery is worth calling a discovery. This is not a division of labor that diminishes either partner, but it does insist—exactly as the cycle insists—that the human must remain genuinely active, genuinely present, genuinely responsible for the understanding that the machine cannot supply. The danger he names is not conquest but surrender: the quiet abdication of the creative act to a system that can perform its outward form without performing its inner function.
Du Sautoy grew up in London and was drawn to mathematics in his teens by a teacher who showed him that the subject was not calculation but discovery—an encounter with structure and pattern that felt, he has said, more like finding something that already existed than inventing something new. He read mathematics at Wadham College, Oxford, and pursued a doctorate and subsequent research career in group theory and number theory, specifically using the tools of one discipline to illuminate the other in ways that exemplify the combinational creativity he would later anatomize. He was elected to the Royal Society in 2016 and holds the Simonyi Professorship previously occupied by Richard Dawkins, bringing to it a temperament as interested in the philosophy of knowledge as in its public communication.
The question of machine creativity became urgent for him when he watched the machines begin to write, paint, and compose at a level that required something more than dismissal. His books trace his investigation in real time: The Music of the Primes (2003) establishes his feel for the deep creativity involved in mathematical research; Finding Moonshine (2008) maps the architecture of symmetry; What We Cannot Know (2016) arrives at the limits of formal systems through Gödel’s incompleteness theorems; The Creativity Code (2019) directly addresses whether the machines can be creative; and Thinking Better (2021) examines the shortcut—the structural insight that collapses an enormous task into a small one—as the signature of mathematical intelligence. Across these books the same question recurs: what is actually happening when a mind produces something genuinely new, and can the machines be said to do it?
He reached for Boden’s taxonomy as the sharpest instrument available for making the question precise, and the adoption is characteristic. Du Sautoy does not build walls against the machines or wave them in. He looks for the most demanding definition he can find and asks honestly which side of it the systems fall on. His answer has hardened over time—the machines are more creative than he initially expected in the exploratory mode, and the transformational mode remains the contested frontier—but it has never been dishonestly resolved in either direction.
The Lovelace Test. Du Sautoy’s criterion for machine creativity requires that an output be new, surprising, and of value, and—crucially—that it not be explainable as a mere consequence of the programmer’s intentions. The fourth condition is the teeth of the test: it forces a question about attribution, about whether the act belongs to the system or to the humans who designed it. He holds this standard high deliberately, because he wants a criterion that resists wishful thinking in both directions, and because modern machine learning’s opacity makes the standard genuinely hard to adjudicate rather than trivially satisfiable.
Move 37. The thirty-seventh move of AlphaGo’s second game against Lee Sedol in March 2016 is du Sautoy’s clearest exhibit of a machine satisfying the Lovelace test. That move—on the fifth line in a position where every human master would have played more conservatively—was new, genuinely surprised the professional commentators, and contributed to a historic victory. No programmer authored it; the system’s self-taught intuition, built from millions of games against itself, had found something two millennia of human play had not. Du Sautoy calls it an act of exploratory creativity and means the assessment as praise, not consolation: the machines have entered real territory.
The Creativity Code’s three modes. Borrowing from Margaret Boden, du Sautoy uses combinational, exploratory, and transformational creativity as his diagnostic framework. Machines are formidable at exploratory creativity and increasingly capable at combinational. Transformational creativity—changing the rules rather than playing them, producing what the existing distribution could not have predicted because it belongs to a distribution that did not yet exist—remains the holdout. This is where he locates the frontier.
Understanding versus production. Du Sautoy’s deepest claim, grounded in his experience of mathematical research, is that understanding is more than the most sophisticated kind of production. A proof that illuminates is different in kind from a proof that merely compels assent through verified steps. A melody that is about something is different from a melody that resembles something. Whether the machines understand, in this sense, is the question that Gödel’s incompleteness theorems sharpen to a precise point: truth outruns formal proof, and whether human mathematicians reach truth by some non-formal act of insight is the question the machines force us finally to take seriously.
The shortcut as creative act. In Thinking Better du Sautoy argues that the shortcut—the structural insight that makes a class of problems suddenly tractable by revealing a hidden pattern—is creativity made operational. A machine that solves a problem by exhaustive search has not found a shortcut; it has substituted speed for insight. The transformational creative act is precisely the shortcut that changes the game: it reveals a structure no one knew was there. Whether this is computable is, for du Sautoy, the same unanswered question approached from a concrete direction.