Transformative Creativity

Sources#

Summary#

Does more intelligence imply more creativity? The "From AGI to ASI" report uses Margaret Boden's framework to give the question structure and to locate where current AI sits. A creative product must be novel, surprising, and valuable (Boden 2004) — and the report argues today's celebrated AI achievements are predominantly exploratory creativity within human-provided conceptual spaces, while transformative creativity (creating entirely new conceptual spaces) may be the hallmark requirement of true ASI.

Boden's three levels#

Combinational — unfamiliar combinations of familiar ideas (poetic imagery, analogies, recombining engineering modules).
Exploratory — finding new elements within an existing conceptual space (a new piece in an established musical style; a novel move in a known game).
Transformative — creating entirely new conceptual spaces or ways of thinking (quantum theory, relativity, Cubism, inventing a new kind of game).

Novelty splits into P-creativity (psychological — new to its creator) and H-creativity (historical — new to humanity). Surprise ranges from statistical unlikelihood to "previously seemed impossible." Value is contextual and may only be recognized retrospectively.

Where AI sits today#

AlphaGo's Move 37 (2016) — the canonical example: a statistically-unlikely, expert-surprising, effective move. Lee Sedol: "Surely AlphaGo is creative... a really meaningful move." But it is exploratory — a novel move in a known game.
AlphaFold (novel protein structures) and automated theorem-proving — also predominantly Boden levels 1–2: profound exploratory creativity within well-defined, human-provided conceptual spaces (see AI-Driven Formal Proof Search).
Today's systems augment human ideation in math and physics, boosting the creativity of human–AI collaboratives in subtle ways.

The transformative test for ASI#

Reaching Boden's third level — inventing scientific theories that trigger Kuhnian paradigm shifts — would firmly satisfy the criteria and is offered as a "true test" for ASI. Demis Hassabis's formulation:

"If we went back to the time of Einstein in 1900... could an AI system actually come up with general relativity with the same information Einstein had at the time? And clearly today, the answer is no... there's still something missing."

This is the creativity-framing of the The Abstraction Barrier: transformative creativity is grounded discovery of novel conceptual primitives. The report also distinguishes scientific creativity (value grounded in predictive power / empirical truth) from artistic creativity (value is subjective, set by dynamic social systems of artists/audiences/critics) — transformative artistic creativity would require deep grounded understanding of human culture and its emotional trajectory, not just raw optimization power.

A conceptual space you can print (August 2026)#

Everything above locates AI at Boden level 2 by arguing from outputs — Move 37 was a new move in a known game, AlphaFold folded proteins in a space biology had already defined. Idea Search (Xuefei Julie Wang, Hao Cui, Michael P. Brenner & Subhashini Venugopalan — Caltech / Google Research / Harvard, arXiv 2608.08958, 2026-08-09, empirical) is the first source in this corpus where the conceptual space is not inferred from behaviour but shipped as an inspectable artifact: a literal list of atomic "ideas" that a Tree Search samples from, one per code mutation, printed in full in the appendix.

The system decomposes ten expert scRNA-seq batch-integration methods (BBKNN, ComBat, Harmony, LIGER, SCALEX, Scanorama, TabVI, fastMNN, mnnpy, scVI) into 30 atomic ideas — "condition decoder on batch ID", "merge per-batch nearest-neighbor sets", "use empirical Bayes to stabilize gene corrections" — then samples one into each mutation prompt, scores every solution with the OpenProblems v2.0.0 metric, and feeds new ideas back by decomposing whatever the search produced.

The result, with its uncertainty attached. Against a pure Tree Search baseline that plateaus around 300 nodes at 0.678 ± 0.011 (max 0.694), idea injection breaks the plateau around 500 nodes and reaches a mean of 0.697 under both samplers (random 0.697 ± 0.012, bandit 0.697 ± 0.008) with a best single solution of 0.728. The gain is roughly 0.02, and the paper states plainly that this is comparable to the 0.008–0.018 trial-to-trial standard deviation across its 5 trials — "the practical signal sits in the best-of-n solution more than in the average run." One task, one backbone (Gemini 2.5 Pro), validation split, no claim against the held-out leaderboard. Read it as a distribution reshaped (heavier upper tail), not as a calibrated effect size.

Level 2 by construction, not by observed limitation#

The interesting thing is not the score. It is that this architecture cannot reach Boden level 3, and you can see why from the design rather than from the results — the argument below is wiki-derived, not the authors':

The space is enumerated before the search starts. Boden level 2 is "finding new elements within an existing conceptual space." An Idea Bank is that space, written down, with a cardinality. A run's reachable methods are combinations of bank entries; the search's job is explicitly to "mix and recombine" them.
Value is fixed by a scorer the search cannot revise. The OpenProblems metric defines what "better" means for the entire run. Transformative creativity in the scientific sense means changing what counts as a good answer — Kuhnian, in this page's framing above. A hill-climb against a frozen metric is definitionally barred from it.
Bank growth is closed under recombination. New ideas enter only by an LLM decomposing solutions that were themselves generated from bank ideas plus the model's own priors. The space can grow; nothing in the loop can transform its rules.

The 49 brainstormed ideas are the level-3 test — and they fail it#

The sharpest test the paper offers is its Augmented Bank: the 30 expert-derived ideas plus 49 more generated by asking Gemini 2.5 Pro to "brainstorm and suggest more relevant ideas." If an LLM asked to expand a conceptual space ever leaves it, this is where it would show. Appendix A.2 prints both banks verbatim, so the check is direct — and every added entry names a pre-existing, already-published technique transferred in from adjacent machine-learning literature: normalizing flows, cycle-consistent GANs, Gromov–Wasserstein optimal transport, hyperbolic embeddings, topological data analysis, conformal prediction, Siamese networks, ADMM, sparse PCA, federated learning. Not one is a new primitive; each is a known tool pointed at a new application. In Boden's terms that is combinational (level 1) creativity operating inside an unchanged level-2 space — the The Abstraction Barrier made into a data structure, since the bank contains exactly the concepts humans already extracted and nothing else.

Two smaller observations sharpen it. The printed Augmented Bank contains at least two verbatim self-duplicates ("minimizing mutual information between latent space and source ID"; "regressing out the source ID from principal components" each appear twice), so the "49 additional ideas" are not 49 distinct ones. And the measured effect of adding them is not novelty but sampler-dependent noise: augmentation helps bandit sampling (0.692 ± 0.007 → 0.703 ± 0.007) and hurts random sampling (0.712 ± 0.012 → 0.698 ± 0.018), while the augmented-plus-random arm nonetheless produced the single best solution in the paper (0.728). Whether more ideas help depends on the selector, not on the ideas.

What would count as evidence the other way, stated so the next source can be graded against it: an entry appearing in the bank that (a) names no technique in the prior literature and (b) requires a quantity the OpenProblems scorer does not measure in order to be evaluated at all. The first condition is about the space; the second is what makes it transformative rather than merely unfamiliar. Nothing in this paper meets either.

The honest scope limit#

This is one automated-discovery system on one benchmark, so it settles the AlphaGo→AlphaFold question only for its own class. What it does is convert the question from an interpretive one into a checkable one: any system that makes its conceptual space explicit can be audited for level-3 content by reading the space. That the first such audit returns "level 2 by construction, level 1 for the LLM's own contribution" is a datum, not a proof — but it is the first one this page has that isn't an argument from a demo.

The practitioner's version of the same boundary, from inside a lab (September 2026)#

Every source above reaches Boden's level-2 verdict by argument — from outputs (Move 37, AlphaFold), from a printed conceptual space (Idea Search), or from Hassabis's general-relativity thought experiment. Brown (Dwarkesh Podcast, 2026-09-17, practitioner-opinion) states it as a working observation about models that have just solved a Millennium Prize Problem, which makes it the strongest-capability case the boundary has yet had to survive:

"They're clearly exceptional in some ways, but they are weaker than human mathematicians in other ways… They're not very good at posing new problems. They're not really good at understanding what directions, what whole branches of mathematics are worth exploring or developing."

Both halves of that sentence are this page's level-3 criterion in the practitioner's vocabulary. Posing new problems is creating a new element of a conceptual space's question-set; deciding which branches are worth developing is revising the space's own value function, which §"Level 2 by construction" above identifies as the thing a hill-climb against a frozen scorer is definitionally barred from. So the corpus now has the level-2 verdict reached three independent ways — theory (Boden via the DeepMind report), architecture (Idea Search's enumerable bank), and observation at the frontier (Brown) — and they agree.

(2026-09-21: the first-party announcement of that result is now compiled as The Navier–Stokes AI Claim, vendor-claim and disputed — so "models that have just solved a Millennium Prize Problem" is OpenAI's claim rather than an established fact. It does not weaken Brown's observation, which is about a boundary he says the capability has not crossed, and it adds one supporting detail: the problems were posed by the Clay Institute, the problem variants were assigned to agent groups by humans, the pivot to Navier–Stokes was a human decision, and the winning group was steered by Codex-consolidated insights. Every act of problem selection in the campaign was human.)

What makes it a harder datum than the other two is the capability level it holds at. Idea Search's system is a Gemini 2.5 Pro tree search on one benchmark; Move 37 is a decade old. Brown is describing a system that produced a result he himself had projected for 2028 at the earliest, and the solving capability is what moved while the posing capability, on his account, did not. That is the cleanest available evidence that the two are separate axes rather than one capability at different maturities — which is precisely what the abstraction barrier predicts and what "just another capability AI fails at then masters" predicts against.

The counter is in the same breath and should be carried with it. Brown does not treat the boundary as permanent: "the things where they're far behind humans, they're going to be less behind humans at. Over time, it is possible that they're just better across the board. Now, I don't know how long that takes. It depends on how long the long tail is of things that they're bad at." So this is a current separation with no claim about its durability — an observation of where the frontier sits in September 2026, not a ceiling argument. What it adds to this page is a dated marker on a line that otherwise has none.

It is also, read against Anthropic's ~80% blinded hypothesis preference, the corpus's sharpest live disagreement about where taste sits. The two are reconcilable — generating a molecular-biology hypothesis inside a defined problem area is exploratory work in a given space; deciding that a new branch of mathematics is worth developing is not — and that reconciliation is exactly the level-2/level-3 distinction doing real work rather than being applied retrospectively, which is the first time on this page it has.

The same line, drawn by philosophers of mathematics (2026-09)#

Boden's level-2/level-3 boundary gets an independent restatement from outside this literature, in vocabulary worth keeping. De Toffoli and Duede (After Math, practitioner-opinion) distinguish an answer — a result, even a formally certified one — from a solution, which additionally supplies "an intelligible mathematical argument that allows the result to become part of mathematics as understood and practiced by mathematicians." Read against Boden: an answer is a search result inside a conceptual space; what makes a solution fruitful is that other mathematicians can take its ideas up, which is how a conceptual space gets changed at all. Their example is OpenAI's Navier–Stokes announcement, which they place on the answer side "at this moment" while explicitly leaving the other verdict open. Full treatment on Logical vs Intelligible Proof.

Two reasons this is a reframing rather than evidence. It contains no measurement, and it is not about creativity — the authors are arguing about what proof is for, and the mapping onto Boden's levels is this wiki's. But it converges with the corpus's practitioner source from the other side: Noam Brown's concession, quoting Tao, that these systems are "solving a lot of these problems" without "coming up with new insights or formulating insightful new questions and new modes of theory." An advocate and a critic describing the same gap in different vocabularies is the closest thing to triangulation this page has on a question no one can measure.

A survey that refutes level 1 and concedes level 2 (2026-09-23)#

Jedlička's survey (arXiv 2608.17970, 2026-08-18, practitioner-opinion; full treatment on Autonomous Scientific Discovery) makes two moves that land on opposite sides of this page's ladder, and it is worth keeping them apart because the paper runs them together.

It retires the strongest form of the stochastic-parrot thesis, which is a level-1 claim. Against Bender et al. (2021) — that language models "do not possess genuine understanding but merely recombine linguistic patterns encountered during training" — the survey holds that the mathematical and scientific results it reviews "refute the strongest versions of the claim that state-of-the-art systems function only as mechanisms of recombination," and that "at a minimum, they suggest that such systems can now produce outputs that satisfy ordinary standards of novelty." Read against Boden, that is an argument that the systems are above level 1 (combinational). It says nothing about level 3, and the survey is careful to say the examples "do not settle the broader philosophical debate about understanding or originality."

And in the same paper it concedes the level-2 ceiling explicitly. §8: AI "has not produced paradigm-changing discoveries comparable to the most transformative ones in the history of science"; the successes are "highly specific problems, which however already existed within established scientific frameworks"; the systems work best "as powerful cognitive tools within existing research programmes designed and directed by human scientists." Level 2 in plain language, from a philosopher of science with no stake in either lab — the third independent statement of this page's boundary after Brown's and the De Toffoli–Duede one, and the only one that reaches it by surveying all the disciplines rather than mathematics alone.

The inversion in its last pages is the part this page does not already hold. If future systems do differ qualitatively, the survey argues, the binding constraint moves from the generator to the reader: machine-generated hypotheses and frameworks may look "implausible, unintelligible, or hallucinatory from the perspective of contemporary scientific paradigms, despite containing genuine insight," so "human cognitive limitations could therefore become a significant obstacle to the assessment of increasingly sophisticated machine-generated knowledge." Its positive version is the 'alien space of science' hypothesis (Artiles et al., arXiv 2603.01092, 2026): that research communities systematically miss directions for which they lack the conceptual tools, and that AI could sample them. On this page's ladder, that is a level-3 claim relocated — the new conceptual space is not one the system creates but one humans cannot currently occupy, and the test of whether it was reached would be run by the people least equipped to run it. Neither source offers a way to distinguish a cognitively-unavailable insight from a confident error, which is why it stays a hypothesis here rather than evidence.

Connections#

Logical vs Intelligible Proof — the answer/solution distinction, which runs parallel to the level-2/level-3 line: a certificate is a result inside a fixed space; a fruitful solution is one whose ideas other mathematicians can take up
Terence Tao — the source of the "solving problems without new insights" objection that Brown concedes, and the venue of the answer/solution argument
The Navier–Stokes AI Claim — the result Brown's observation is held against, now compiled first-party: the problems were posed externally and every selection in the campaign was human, so nothing in it crosses the level-3 line
Noam Brown — the practitioner source for the problem-posing and branch-selection boundary, observed at the capability level that produced a Millennium Prize result, and hedged by him as current rather than permanent
Why AI Lags at Design — the novelty-premium reason borders the harder claim that new-concept generation is a real ceiling
The Abstraction Barrier — Boden level-3 is the creativity-language for exactly what the abstraction barrier says AI may be unable to do: form genuinely novel primitives
Artificial Superintelligence (ASI) — transformative creativity is offered as a hallmark requirement / "true test" of ASI
Research Taste as the Human Bottleneck — judging which novel directions are valuable is the taste dimension; transformative creativity is taste at the frontier of concept-space
Autonomous Scientific Discovery — June 2026 wet-lab AI results are the live test of whether AI is climbing from exploratory toward transformative creativity, or still operating within human-defined spaces
AI-Driven Formal Proof Search — new theorem-proving is placed at Boden levels 1–2 (exploratory within Lean's formal space)
Automated Conjecturing — the corpus's second system whose conceptual space is a printed artifact, and the cleaner of the two: a linear grammar over 45 named invariants and 16 named predicates, filtered against 559 named theorems, with nothing in the pipeline able to propose a term outside those lists
Jagged Intelligence (Ghosts, Not Animals) — "creativity might be just another capability AI fails at then masters" mirrors the joke/theory-of-mind precedent
Context Advantage, Not Taste — the limit Andrew Ng's frame doesn't reach: Boden level-3 creation of a new conceptual space is not a missing fact that better context transfer supplies
Open-Ended Discovery Harnesses — the same idea-space question asked as harness engineering rather than as creativity theory, and the corpus's direct disagreement about it: SwarmResearch forbids its orchestrator from prescribing ideas to preserve diversity, Idea Search prescribes one at every mutation and breaks a plateau
Intelligence Explosion Dynamics — the search-side reading of the same result: what a fixed model plus test-time search can reach is bounded by the space the search is given, and turning the sampler's exploration dial up made it worse
Large-Scale Test-Time Compute — where the Idea Search numbers sit as a budget-shaping result rather than a creativity one: exploration injected at the prompt beats exploration injected at the sampler

Open Questions#

Does increasing intelligence inherently produce increasing creativity, or do transformative leaps require something (grounded discovery) the current paradigm lacks?
Is the AlphaGo→AlphaFold class strictly exploratory, or are there early signs of transformative (new-conceptual-space) creativity? Partially answered (2026-08-12): Idea Search supplies the first case where the conceptual space is an inspectable artifact rather than an inference from outputs, and it is level 2 by construction — the space is enumerated before the run, value is fixed by a scorer the search cannot revise, and bank growth is closed under recombination. The LLM's own 49 "brainstormed" additions are all pre-existing named techniques (Boden level 1, combinational), with two verbatim self-duplicates. This settles the question for one automated-discovery system, not for the AlphaGo→AlphaFold class as a whole; what generalizes is the audit method — a system that prints its conceptual space can be checked for level-3 content by reading it. Second instance, 2026-09-21: AutoGraphForge: Towards Automated Graph Theory Discovery applies that audit method to automated mathematical conjecturing and reaches the same verdict by a sharper route. Its conceptual space is not merely inspectable but exhaustively enumerated in the source code: a linear grammar of halfspaces over 45 numeric graph invariants, with 16 boolean predicates as the only admissible hypotheses, screened against a table of 559 named classical relations. No mechanism in the pipeline can introduce an invariant that is not already a column or a class that is not already a predicate, so level-3 content is impossible by construction, not merely absent in practice. The output backs that up: of the 100 highest-ranked survivors from a 1.22 CPU-year run, 49 are rediscoveries of known theorems, 2 are subsumed by other survivors, 1 has a hypothesis that does no work, and the two the author singles out as genuinely interesting both reduce to three-line combinations of Gallai, Kőnig and Pepper — Boden level 1, combinational, at their most novel. Two systems, two domains, one shape: where the conceptual space is printed, what comes out is recombination within it. The caveat is that this is a single-author workshop-track paper, so weigh the architecture claim above the scale numbers.
Could transformative artistic creativity ever emerge from optimization power without lived cultural grounding?

Sources#

From AGI to ASI — Section 6 ("Is superintelligence super-creative?"); Boden (2004), Hassabis (2025)
On the Navier–Stokes Millennium Prize Problem — OpenAI (no byline), openai.com, 2026-09-08 with a 2026-09-10 update, ~1,900 words, vendor-claim. Cited here only to mark the result Brown's observation is measured against as a disputed first-party claim, and for §"How we found the proof" on the human problem-selection acts in the campaign. Full treatment on The Navier–Stokes AI Claim
Noam Brown – Agent swarms, alignment, & recursive self-improvement — Noam Brown (OpenAI) with Dwarkesh Patel, Dwarkesh Podcast, 2026-09-17 (practitioner-opinion). §00:22:02 only: the jagged-in-maths reading, the problem-posing and branch-selection boundary, and the across-the-board caveat. An unmeasured practitioner observation about an unreleased model — no eval, no rate, no comparison group — and the mapping onto Boden's levels is wiki-derived; Brown never mentions Boden or creativity theory
AutoGraphForge: Towards Automated Graph Theory Discovery — AutoGraphForge: Towards Automated Graph Theory Discovery, Ján Pastorek (Comenius University in Bratislava), arXiv 2609.03478, 2026-09-03, 17pp, ITAT 2026 submission, empirical. Cited here only for §3.2/§3.3 (the generation grammar, the 45 numeric targets, the 16 Sophie predicates, the 559-relation novelty table) and §4.2 (the top-100 audit and the two hand-proved bounds). The Boden-level reading is wiki-derived — the paper never mentions Boden or creativity theory, and makes no claim about the creative status of its output beyond "neither of these is a deep new theorem." Single author, workshop track, no independent replication. Full source treatment on Automated Conjecturing
Idea Search: Guiding Tree Search with Ideas to Explore Diverse Scientific Methods — Wang, Cui, Brenner & Venugopalan (Caltech / Google Research / Harvard), Idea Search: Guiding Tree Search with Ideas to Explore Diverse Scientific Methods, arXiv 2608.08958, 2026-08-09, 14pp, empirical. §3 the Idea Bank / mutation / dynamic-update loop; §4.1 the scRNA-seq testbed, CZ CELLxGENE data and the ten expert methods; §4.3 the 30-idea Expert-Only and +49 Augmented banks; §5.1–5.2 the baseline plateau and augmentation results; §5 "Scope of the results" and §6 Limitations for the effect-size caveat; Appendix A.2, which prints both banks verbatim — the primary evidence for the Boden-level reading above. The paper has zero tables; every number quoted here comes from prose, and the figures were read under the image two-pass rule. The level-1/level-2/level-3 mapping, the closed-under-recombination argument and the duplicate count are wiki-derived, not the authors' claims — the paper never mentions Boden or creativity theory.
After Math — De Toffoli & Duede, "After Math", guest post on Terence Tao's blog, 2026-09-12, ~2,000 words, practitioner-opinion. Cited here only for the answer/solution distinction and the aims-of-mathematics list it rests on (Tao 2026, arXiv 2608.16753, not in this corpus). No measurement, no Boden, no creativity claim — the mapping onto levels 2 and 3 is this wiki's, not the authors'. Full treatment on Logical vs Intelligible Proof
Quo Vadis? Scientific Discovery in the Age of Artificial Intelligence — Petr O. Jedlička (Institute of Philosophy, Czech Academy of Sciences), Quo Vadis? Scientific Discovery in the Age of Artificial Intelligence, arXiv 2608.17970, 2026-08-18, 40pp, practitioner-opinion. Cited here for §6.1's stochastic-parrot passage and §8's conclusion only. The mapping onto Boden's levels is this wiki's, not the author's — the survey never mentions Boden. Artiles et al. (arXiv 2603.01092) is not in this corpus; it is carried as the survey characterises it. Single-author review, no original measurement; PDF-derived, 0 tables, quoted from prose re-read against pdftotext -layout. Full treatment on Autonomous Scientific Discovery