The New Act of Creation: AI, Creativity, and the Future of Science

From Arthur Koestler’s theory of bisociation to AI-generated mathematical discoveries, synthetic science, and machine-assisted invention: what happens when creativity is no longer exclusively human?

October 21, 2026 | Approximately 17–19 minutes of reading

Key Takeaway: Artificial intelligence is moving beyond solving problems toward making original mathematical discoveries, designing new drugs, and generating technological inventions. Revisiting Arthur Koestler’s The Act of Creation, I explore whether his concept of bisociation—the unexpected intersection of previously unrelated ideas—can help us understand machine creativity, and what this transformation means for science, consciousness, and human originality.

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In 1994, during my first stay at the University of Paderborn in Germany, I came across a quotation in the office of my academic advisor, Professor Spaeth, that I have never forgotten:

“Theory is when you know everything, but nothing works. Practice is when everything works, but nobody knows why. When theory and practice come together, nothing works and nobody knows why.”

The quotation, of unknown authorship and frequently attributed to Albert Einstein, remains, to me, one of the most amusing descriptions of the difficulties of scientific research. More than thirty years later, in light of the paradoxes introduced by artificial intelligence, its irony seems to have taken on an entirely new meaning.

1. When Machines Begin to Discover

For centuries, scientific discovery has been associated with extraordinary individuals who dedicated years, sometimes entire lifetimes, to solving difficult problems. From Newton and Euler to Hilbert and Einstein, the history of science has often been told through exceptional minds capable of recognizing connections that others had overlooked. Yet we may be approaching a period in which the production of original mathematical results becomes increasingly automated, raising uncomfortable questions about the nature of intellectual creativity and the future role of human scientists.

On October 6, 2026, OpenAI released an extraordinary collection of 722 mathematical manuscripts, organized into 372 families of results, generated by an internal frontier AI system. The collection addressed research problems across number theory, geometry, algebra, mathematical physics, and theoretical computer science. Three manuscripts were subsequently withdrawn following the identification of a mathematical error, while others required corrections. The public repository currently lists 719 manuscripts, with approximately 42% of its principal results accompanied by formalizations in Lean, a system that checks whether mathematical arguments follow rigorously from specified axioms and assumptions.

These figures are impressive, but they require careful interpretation. The manuscripts contain claims at different stages of verification, not hundreds of discoveries already accepted by the mathematical community. A formally checked proof establishes logical consistency within a specified framework; it does not automatically establish originality or scientific importance. Nevertheless, the scale of the achievement suggests that artificial intelligence is moving beyond solving textbook problems toward participating in original mathematical research.

More importantly, evidence of these capabilities now extends beyond announcements made by AI laboratories themselves. Independent evaluations and human-verified mathematical discoveries are beginning to provide a clearer picture of what advanced AI systems can accomplish. Some of these results are remarkable not merely because they solve difficult problems, but because they reveal unexpected connections between areas of mathematics that had previously appeared unrelated.

The possibility of artificial creativity fascinates me for reasons that go far beyond technological performance. What, exactly, does it mean to create something new? Does genuine creativity require consciousness, or can original ideas emerge through processes fundamentally different from human thought? These questions reminded me of Arthur Koestler’s extraordinary book, The Act of Creation, published in 1964, whose ideas offer a surprisingly relevant perspective on the emergence of artificial scientific intelligence.

2. The Mathematics of Artificial Discovery

One of the clearest examples of genuine AI-generated mathematical discovery appeared in May 2026, when an internal OpenAI model produced a counterexample to a longstanding conjecture associated with Paul Erdős. The problem, originally formulated in 1946, is remarkably easy to describe: given a large collection of points on a flat surface, how should they be arranged to maximize the number of pairs separated by exactly the same distance? A regular grid provides an intuitive starting point, since many pairs of points arranged like intersections on graph paper share identical separations. For decades, mathematicians believed that lattice-like constructions were essentially optimal in a particular asymptotic sense.

The AI-generated result overturned that expectation by constructing families of point configurations with more equal-distance pairs than the conjectured bound would allow. What makes the discovery especially interesting is the method: the argument drew upon sophisticated ideas from algebraic number theory to resolve a question in elementary planar geometry. The result was subsequently examined by leading mathematicians, including Noga Alon and Timothy Gowers, whose paper, Remarks on the Disproof of the Unit Distance Conjecture, presented a condensed, human-verified reconstruction of the proof. Although the broader unit-distance problem remains open, the counterexample invalidated a longstanding expectation and revealed an unexpected mathematical relationship.

This discovery is particularly important because it illustrates something that cannot be reduced to computational speed. The machine did not simply calculate a larger number of examples or perform a familiar procedure more efficiently. It established a productive connection between mathematical frameworks that researchers had not previously combined in this way. As we shall see, this is remarkably close to the kind of intellectual transformation that Koestler identified as central to creativity.

Explore the mathematics behind Erdős’s famous unit-distance problem in my interactive Erdős Distance Lab: arrange and move points on a plane, experiment with different geometric patterns, and discover how their arrangement affects the number of pairs separated by exactly one unit (within the simulator’s numerical tolerance).

A major announcement came in September 2026, when OpenAI presented a proposed solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute. In this context, existence means that a solution can persist for all future time, while smoothness means that it remains mathematically regular, without developing singularities. The Navier–Stokes equations describe the motion of fluids such as air and water and provide the mathematical foundation for applications ranging from weather forecasting to aircraft design. Despite their enormous practical importance, a fundamental question remains: can a fluid flow that begins smoothly develop a singularity in finite time, losing the mathematical regularity that characterizes its evolution?

OpenAI announced that an AI system had produced a proof demonstrating that solutions to the Navier–Stokes equations can develop singularities under specific mathematical conditions. The argument was also formalized in Lean, allowing its logical steps to be verified computationally. However, the proof relies on a carefully specified external force, a crucial qualification because it remains an open question whether singularities can arise without this particular intervention. Although the official formulation of the Millennium Prize Problem permits constructions of this kind, the result does not, by itself, settle the broader question of singularity formation in three-dimensional fluid flows.

The Clay Mathematics Institute acknowledged the apparent breakthrough on September 11 while emphasizing that the evaluation of the result and questions of mathematical credit would proceed through its established processes. An October editorial in Communications Physics also emphasized that the construction does not undermine ordinary fluid-dynamics calculations or imply that aircraft simulations have suddenly become unreliable. The singularity arises under highly specialized mathematical conditions, while physical fluids are made of molecules and the continuum approximation has its own limitations. The result may represent an extraordinary mathematical achievement, but its interpretation still requires careful scientific judgment.

Explore the fascinating dynamics of fluid motion in my interactive Navier–Stokes Lab: create vortices, stir virtual fluids, adjust viscosity, and observe how complex flow patterns emerge from simple physical laws, while discovering the mathematical challenges behind one of the most famous unsolved problems in physics and mathematics.

The recent breakthroughs in AI-generated mathematics are not isolated achievements. They belong to a transformation that has been gathering momentum for several years. In 2023, Google DeepMind introduced FunSearch, which made progress on the cap-set problem, a longstanding challenge in combinatorics: how can we select as many points as possible from a high-dimensional grid without including three that lie on the same line? Rather than exhaustively testing every arrangement, FunSearch generated computer programs that constructed promising configurations, evaluated their performance, and progressively improved them. In 2025, AlphaEvolve extended this approach to the discovery of more efficient algorithms, including a method for multiplying certain 4 × 4 matrices using fewer arithmetic operations than a longstanding benchmark. These were not simply faster calculations, but improvements in the mathematical methods themselves.

Other developments demonstrated a growing ability to reason mathematically. In 2025, Gemini Deep Think achieved gold-medal-level performance at the International Mathematical Olympiad, solving five of six exceptionally difficult problems. By 2026, DeepMind’s Aletheia was going beyond mathematical competitions to participate in professional research, generating arguments, checking their validity, identifying weaknesses, and revising its own solutions. Yet an important distinction was emerging: solving a difficult problem, discovering a previously unknown result, and verifying an existing theorem are different mathematical achievements.

An impressive illustration of this distinction came in September 2026, when Anthropic reported that Claude had produced a complete computer-verified formalization of Fermat’s Last Theorem. Working through a largely autonomous network of agents, the system generated approximately 13 million lines of Lean code in just eleven days. This was an extraordinary technical achievement, but not a new mathematical discovery: Andrew Wiles, with contributions from Richard Taylor, had already established the theorem in the 1990s. The innovation was in transforming an exceptionally complex human mathematical argument into a form a computer could rigorously verify.

Independent testing provided another perspective. In October 2026, the First Proof project challenged advanced AI systems with ten research-level mathematical problems whose solutions were known to human mathematicians but had not yet been published. Thirty expert reviewers evaluated the submissions for correctness, clarity, and acknowledgment of previous work. ProofCouncil, a system coordinating several AI models, successfully addressed nine of the ten problems, while GPT-6 Astra, evaluated directly, solved seven. Every problem was solved by at least one system. However, even the strongest submissions frequently struggled to explain their reasoning clearly or properly acknowledge relevant mathematical literature. The machines were becoming remarkably proficient at constructing proofs, but communicating their intellectual significance remained a challenge.

The Problem of the Three Tourists and How to (Un)learn Physics with ChatGPT

A PERSONAL RETROSPECTIVE — MAY 2024

In light of the extraordinary recent advances in artificial intelligence in mathematics, it is worth recalling an experiment I conducted in May 2024, when ChatGPT was already generating enormous enthusiasm for its apparent intellectual abilities. I decided to challenge it with something far less spectacular than the great problems of mathematics: an elementary kinematics exercise involving three hurried tourists and a bicycle. After all, an artificial intelligence capable of discussing sophisticated scientific theories would surely have no difficulty applying the familiar relation v = d/t. Or so one might have thought.

The Challenge

Three tourists share a single bicycle and wish to travel along a straight avenue from their hotel to a tourist center in the shortest possible time. The bicycle can carry only two people, including the cyclist, and travels at 20 km/h. The third tourist must therefore begin the journey on foot.

The cyclist takes the second tourist to a point along the route, where the passenger gets off and continues walking at 4 km/h. The cyclist then returns to pick up the third tourist, who has been walking since the beginning, and carries that person toward the destination.

Given that the distance between the hotel and the tourist center is 8 km, determine:

a) What is the minimum time required for all three tourists to reach the tourist center? Remember that the clock stops only when the last tourist arrives.

b) How far from the tourist center should the second tourist be dropped off?

I invite readers to try solving the problem before continuing. No advanced mathematics is required: elementary kinematics and a little geometrical reasoning are all you need. A typical exercise for anyone who has completed high school.

ChatGPT’s Answer

In approximately ten seconds, ChatGPT produced a detailed, apparently logical solution, delivered with absolute confidence. It began by claiming that the second tourist should be dropped off after traveling two-thirds of the total distance, or 5.33 km. This first bicycle journey would take 16 minutes.

The model then described the cyclist returning to transport the third tourist, somehow treating the next stage as another 8 km journey completed in 24 minutes. Finally, it added a 2.67 km walk, supposedly requiring another 40 minutes.

The conclusion came without the slightest hesitation:

“Thus, the total time to reach the tourist center is 16 minutes + 24 minutes + 40 minutes, which is 80 minutes.”

For the second question, it claimed that the cyclist should carry the passenger for 3.33 km, a figure obtained by subtracting an inexplicable 2 km from the previously calculated 5.33 km. The calculation bore no consistent relationship to the movements described in the problem.

The answer was grammatically impeccable, numerically elaborate, and physically wrong. As my son promptly pointed out, ChatGPT had failed the exercise.

Well, ChatGPT, you would score zero on this question.

Confidence Is Not Understanding

What made the episode particularly amusing was not merely the mistake, but the confidence with which the model presented its conclusions. When I asked it to describe its own abilities in mathematics and physics, I received an extraordinarily enthusiastic self-assessment:

“ChatGPT is an advanced language model trained to understand and generate natural language in various fields of knowledge, including mathematics, physics, and chemistry. It is capable of reading, interpreting, and solving problems in these subjects with ease and speed, thanks to its vast knowledge base.”

The system went further, presenting itself as a source of quick, reliable scientific solutions and even as a tool capable of inspiring new discoveries. I had my doubts. After all, producing a convincing explanation is not the same as constructing a physically consistent argument. Linguistic fluency could easily conceal the absence of an adequate representation of the problem.

At the time, I wondered whether that model could genuinely solve the exercise through geometrical reasoning rather than simply reproducing an answer resembling explanations encountered during training. Perhaps sufficiently careful prompt engineering could guide it toward the correct solution. But that raised an uncomfortable question: how much of the reasoning would have to be supplied by someone who already knew the answer?

I then decided to add a touch of sarcasm, asking ChatGPT to praise its own scientific abilities in even more extravagant terms. It did not disappoint:

“ChatGPT is simply amazing, capable of solving all complex problems in mathematics, physics, and chemistry, as well as generating new creative solutions effortlessly.”

The parody continued, suggesting that the system could prove mathematical theorems, discover new physical laws, and dramatically accelerate scientific research. At least, in the end, it acknowledged that its supposed discoveries would still need to be validated by qualified researchers. Behind the irony lay a serious concern: the appearance of scientific rigor is no substitute for rigor itself, however articulate or persuasive an explanation may be.

My conclusion at the time was decidedly skeptical. The experiment gave me little reason to trust that version of ChatGPT to manipulate elementary physical concepts correctly in unfamiliar situations. Perhaps future generations of artificial intelligence would develop far more sophisticated capabilities. For the time being, I wrote, I was content to use it to edit and correct my texts.

Two Years Later: An Unexpected Reversal

Revisiting that experience in 2026 is almost as entertaining as conducting it was. Some of the abilities I had mentioned sarcastically—proving mathematical theorems, proposing scientific hypotheses, and contributing to original discoveries—are now being demonstrated by considerably more advanced AI systems. Naturally, we are not comparing identical models, and success in research-level mathematics does not guarantee that every elementary physics problem will be solved correctly. Nevertheless, the contrast is striking.

The episode, however, has acquired a significance that goes beyond comparing successive generations of AI models. In 2024, a convincing explanation concealed a physically incorrect argument. In 2026, AI systems can already produce mathematically correct proofs whose conceptual significance may require considerable effort from human researchers to understand. The distinction between appearing to understand, producing a correct answer, and deeply comprehending the meaning of a result has become even more intriguing.

There is an irony in this evolution. In 2024, the danger was accepting an incorrect answer because its explanation sounded convincing. In 2026, we must also consider the possibility of AI systems producing mathematically correct results whose deeper significance we do not yet fully understand. In both cases, critical thinking remains indispensable.

The three-tourist challenge therefore remains open to the reader. My original recommendation still stands: think like Euclid rather than blindly trusting a persuasive answer.

Fonte do exercício: Renato Brito, Mecânica Para Vestibulandos IME ITA, vol. 1 (2007).

The experience of the three tourists, when contrasted with recent mathematical advances, reveals an extraordinary transformation, but it also compels us to reconsider the very meaning of scientific discovery. As Terence Tao has observed, artificial intelligence may usher in an era in which mathematical proofs are produced on a previously unimaginable scale. Yet mathematical progress has never depended solely on the number of problems solved. Some of its greatest achievements have emerged from recognizing unexpected connections between seemingly unrelated ideas, revealing common principles where we once saw distinct phenomena. But what makes these connections genuinely creative? And could a machine accomplish something similar? These questions lead us directly to Arthur Koestler and his theory of bisociation.

3. Arthur Koestler and the Anatomy of Creativity

In The Act of Creation, Arthur Koestler attempted to identify a common mechanism underlying scientific discovery, artistic creativity, and humor. His central concept was bisociation, which he distinguished from ordinary associative thinking. Association operates within an established framework of concepts and relationships: we recognize familiar patterns, apply accepted rules, and follow connections shaped by experience. Bisociation occurs when two previously separate frames of reference, which Koestler called matrices of thought, are brought together in an unexpected relationship.

Consider a joke. Its opening establishes one interpretation of a situation, while the punchline suddenly reveals another, incompatible interpretation, producing laughter through the collision of two conceptual frameworks. In artistic creation, a comparable process can generate a surprising metaphor, an unusual combination of visual forms, or an unexpected interpretation of familiar experience. In science, the same structural principle may produce a discovery when concepts developed within one field reveal a previously unrecognized relationship with another. A problem that seemed insoluble within its original framework becomes accessible through a different intellectual perspective.

Koestler’s theory is attractive because it removes some of the mystery surrounding creativity without denying its extraordinary character. Creation does not necessarily involve producing knowledge from nothing; it may involve discovering a meaningful relationship between things that already exist. The celebrated Aha! or Eureka! moment is often the conscious experience accompanying this transformation. Yet the intellectual preparation may have required years of study, repeated failures, and processes that remain inaccessible to conscious awareness.

Of course, bisociation is not a complete neuroscientific explanation of creativity. Modern cognitive science reveals complicated interactions among memory, associative processing, cognitive control, emotion, and conscious evaluation. Nor is every unexpected combination creative: most possible associations are trivial, useless, or simply wrong. Koestler’s contribution was to identify an important structural feature of originality, not to provide a complete mechanism for generating and selecting successful ideas.

One of the most fascinating illustrations of Koestler’s theory comes from the history of chemistry. During the nineteenth century, scientists knew the molecular composition of benzene but had yet to understand how its atoms were arranged. In 1865, August Kekulé proposed a cyclic structure that would become fundamental to the development of modern organic chemistry. Twenty-five years later, in a speech delivered in Berlin on March 11, 1890, he recounted an unusual experience that he associated with this discovery.

According to his account, while working in Ghent, Belgium, Kekulé entered a state of semi-sleep in which he imagined atoms moving and joining together, forming chains that twisted like serpents. Suddenly, one of the serpents seized its own tail, forming a ring. The image evoked the ancient symbol of the ouroboros, the serpent devouring its own tail, traditionally associated with circularity and eternity. What makes this story fascinating is the transformation of an image seemingly unrelated to chemistry into a hypothesis about the molecular structure of benzene. An important historical qualification is necessary, however: Kekulé recounted the episode only 25 years later, and there is no conclusive evidence that the vision actually inspired his discovery.

Regardless of its historical accuracy, the story illustrates an essential feature of scientific creativity: an unexpected connection between seemingly unrelated ideas can reveal a solution that conventional reasoning has not yet uncovered. Inspiration, however, is not proof. Kekulé himself concluded his speech by reminding his audience that dreams must be examined by the waking intellect before their results are published.

The lesson applies equally to artificial intelligence: producing an original association does not necessarily mean producing valid knowledge; an idea must withstand rational scrutiny and scientific verification. But this raises an even more intriguing question. If a machine can establish unexpected connections between apparently distant concepts, performing something functionally similar to Koestler’s bisociation, can we attribute creativity and understanding to it, even if its underlying mechanisms are radically different from our own?

4. Computational Bisociation and the Question of Understanding

Modern artificial intelligence presents an intriguing parallel with Koestler’s theory. Large language models learn statistical and structural relationships from enormous collections of information, developing internal representations that allow them to connect concepts, recognize patterns, and generate combinations that were never explicitly programmed. Although their training depends on mathematical optimization, describing contemporary AI as merely manipulating statistical correlations provides an incomplete account of their capabilities. Advanced systems can construct multistep arguments, explore alternative solutions, recognize structural analogies, and test their proposals using mathematical software, search procedures, and external tools.

A human scientist may recognize an unexpected relationship between theoretical frameworks through intuition developed over years of research. An artificial system may discover a comparable relationship by exploring connections encoded in learned representations and evaluating candidate solutions. The processes need not be identical, but the resulting intellectual achievement may be similar. The Erdős example provides a particularly compelling illustration because the machine connected algebraic number theory with planar geometry in a way that produced an original and subsequently verified mathematical result.

There is also an enormous difference in scale. Human scientists possess remarkable powers of abstraction, but no individual can master the entire scientific literature. A sufficiently advanced artificial system can potentially draw upon information from thousands of specialized fields, combining knowledge that human researchers rarely encounter together. What appears to a person as an extraordinary conceptual leap may become more accessible to a system capable of exploring a vastly larger intellectual space. Yet greater access to information does not automatically produce creativity; the difficult part is recognizing the rare connections that are original, coherent, and scientifically valuable.

The analogy with Koestler therefore requires caution. His matrices were psychological constructs, while the learned representations of artificial neural networks are mathematical objects. Computational bisociation should be understood as a functional analogy, not as evidence that machines reproduce the cognitive or subjective mechanisms of human creativity. What the recent discoveries demonstrate is that artificial systems can sometimes produce the kind of unexpected conceptual relationships associated with creative achievement, even though the mechanisms by which they reach them remain fundamentally different from those of the human brain.

The distinction becomes more interesting when we consider understanding. In October 2026, John Pardon, one of that year’s Fields Medal recipients, described how advanced AI systems could interpret even his most abbreviated mathematical notes, reconstruct incomplete arguments, and identify subtle mistakes or missing assumptions. In an interview with Peggy Yin, he declared, “The AI understands. 100%.” Pardon explained that the system could recognize errors requiring knowledge of the broader mathematical context, not merely correct typographical mistakes, and that it had helped him establish nontrivial lemmas. His assessment of AI’s mathematical capabilities had changed dramatically within a single year.

Yet Pardon also made an important distinction: although AI could produce impressive proofs, he had not personally obtained from it a major conceptual breakthrough. His observations are particularly interesting because his own research involves bringing ideas from topology into algebraic geometry, a type of conceptual synthesis that resembles Koestler’s bisociation. Here we have a mathematician celebrated for creating unexpected connections between disciplines who now finds artificial systems capable of following his incomplete reasoning, detecting errors, and producing sophisticated mathematical arguments.

Does that mean the machine understands mathematics in the same way he does? I think it is useful to distinguish three related but different phenomena: creative achievement, functional understanding, and subjective consciousness. Creative achievement concerns the originality and value of a result; functional understanding involves the ability to use knowledge correctly, explain relationships, and transfer concepts to unfamiliar situations; subjective consciousness concerns the first-person experience of understanding. An artificial system may demonstrate extraordinary functional abilities without establishing whether it possesses subjective experience.

Philosophers such as John Searle have argued that manipulating symbols correctly does not necessarily produce genuine semantic understanding. His famous Chinese Room argument remains influential, although its implications are disputed. Conversely, human consciousness provides no guarantee that a scientific conclusion is correct, as the history of science contains countless examples of researchers who deeply understood theories that were subsequently disproved.

This brings us back to the experience of Eureka. A human scientist may suddenly become aware of a solution after years of unsuccessful effort, but the apparent spontaneity of the insight tells us little about the unconscious processes that preceded it. The brain may have been exploring relationships long before the answer entered conscious awareness. An artificial system may perform extensive computational searches without anything resembling human astonishment, yet its final result may still be original. Perhaps Eureka is the human experience of discovery, rather than a necessary condition for discovery itself.

5. The Risk of Scientific Oracles

The growing power of AI in mathematics creates a difficulty that extends beyond the question of consciousness. Imagine a system capable of producing thousands of mathematically correct results, many accompanied by formally verified proofs, while human researchers struggle to understand their deeper significance. The amount of available knowledge would increase dramatically, but scientific understanding might not expand at the same rate. Mathematics has always contained technically demanding arguments understood by relatively few specialists, yet its most influential discoveries often reveal organizing principles that make entire fields more intelligible.

A powerful theory frequently demonstrates that apparently unrelated phenomena arise from a common structure. It may reduce the conceptual complexity of our description of reality even when its mathematical formulation is highly sophisticated. A computational system, by contrast, might produce a correct result through an enormous sequence of transformations without identifying the central idea that makes the argument illuminating. The achievement would remain valid, but its contribution to a broader understanding of mathematics could be limited.

This raises the possibility of what I would call the oracular trap: an increasing dependence on computationally generated results that are difficult for human researchers to interpret, organize, or independently challenge. The danger is not simply that machines might discover truths beyond our immediate comprehension; that has always been possible through the efforts of exceptional human mathematicians. The deeper concern is that the production of knowledge could progressively outpace the development of conceptual explanations accessible to the scientific community.

The recent independent evaluations make this concern concrete. In First Proof, advanced systems solved difficult research problems at an impressive rate, while their explanations and citations remained substantially less reliable. The Navier–Stokes episode illustrates a different aspect of the same issue: an argument may satisfy a precisely formulated mathematical question while leaving significant physical questions unresolved. Neither example invalidates the mathematical achievement, but both demonstrate why scientific progress cannot be reduced to the accumulation of successful proofs.

Yet the oracular future is not inevitable. The same systems capable of producing complex arguments may eventually become extraordinarily effective at simplifying proofs, identifying common structures, and translating difficult reasoning into more intelligible conceptual frameworks. Indeed, Pardon’s experience suggests that this process is already beginning: AI can help researchers inspect, correct, and understand arguments that would otherwise require considerable effort. The most valuable scientific AI may therefore be one that does not merely generate new knowledge, but also helps organize it into explanations that human beings can understand.

6. Synthetic Science: Beyond Mathematics

Mathematics is particularly suitable for automated discovery because its results can, in principle, be established through formal proof. Experimental science is considerably more complicated. A mathematical theorem must satisfy logical constraints, while a physical theory, chemical mechanism, or biological hypothesis must also survive confrontation with empirical reality. Nature is under no obligation to agree with an elegant argument, however convincing its mathematical formulation may appear.

Nevertheless, artificial intelligence is increasingly participating in activities traditionally associated with human scientific imagination. In May 2026, research published in Nature described Co-Scientist, a multi-agent AI system developed by Google that generates, evaluates, debates, and refines scientific hypotheses. The system was tested in biomedical research, including drug repurposing for antimicrobial resistance, with preliminary experimental support reported for selected proposals. Other developments involve self-driving laboratories in which computational systems select experiments, robotic instruments execute them, and subsequent measurements guide further investigation.

A particularly interesting example appeared on October 21, 2026, when OpenAI, PerturbAI, and Scripps Research reported using thousands of AI agents to investigate experimental data from millions of mouse brain cells. Artificial intelligence analyzed genetic changes and identified a possible link between the DCTN1 gene, cholesterol regulation in the brain, and diseases that damage nerve cells. By combining findings from different studies, AI proposed a scientific hypothesis that still needs experimental validation.

This is another striking example of computationally generated connections between conceptual domains. The system did not merely summarize existing literature; it related experimental observations to external scientific knowledge and generated a testable hypothesis. Nevertheless, the proposed mechanism has not been established as causal, and laboratory experiments will be necessary to determine whether it is correct. The distinction is fundamental: in mathematics, a valid proof can settle a theorem, while in experimental science, a plausible hypothesis is only the beginning.

These technologies suggest the emergence of what I would call synthetic science: scientific research in which artificial systems increasingly participate in identifying problems, generating hypotheses, designing experiments, evaluating evidence, and constructing new knowledge. The term describes an emerging possibility rather than a fully established autonomous scientific methodology. One can imagine a continuous cycle in which an AI identifies an unexpected mathematical relationship, proposes a physical or biological model, designs an experiment, evaluates the results, and revises its interpretation. Scientific discovery would become an increasingly integrated interaction among artificial reasoning, computation, simulation, and physical experimentation.

The consequences could be profound, particularly if artificial systems eventually become capable of identifying research questions rather than merely answering those selected by humans. But the same developments are already extending beyond scientific explanation into technological invention, where the distinction between producing an original idea and claiming ownership of it creates an entirely new set of problems.

7. From Synthetic Science to Synthetic Invention

Artificial intelligence is beginning to transform technological invention, just as it has been transforming scientific discovery. AI systems already assist researchers and patent professionals in searching existing patents, analyzing prior art, and preparing technical documentation. These activities can substantially reduce the effort required to document an invention, but they do not necessarily involve inventing anything. Yet the role of artificial intelligence already extends beyond these supporting tasks. Advanced systems are beginning to participate directly in discovery and invention, identifying unexpected properties of known molecules, exploring new equipment geometries, and proposing engineering solutions. These developments raise questions about where human assistance ends and machine invention begins.

A particularly interesting example is halicin, a potential antibiotic identified by MIT researchers in 2020 with the help of artificial intelligence. Using a neural network trained to recognize antibacterial properties, the scientists screened thousands of chemical compounds and identified a molecule originally investigated for a different therapeutic purpose. Halicin showed activity against several bacterial species, including some resistant to conventional antibiotics, with promising results in laboratory experiments and mice. AI did not invent an entirely new molecule; instead, it revealed a surprising application for an existing compound. The case illustrates how artificial systems can uncover possibilities that might be difficult to identify through conventional approaches, although clinical use still requires further research.

Turbine engineering provides an example from an entirely different field. In a study published in 2024, researchers used generative artificial intelligence to develop new blade geometries for turbines designed to harness energy from ocean currents. The challenge was to find shapes capable of improving energy efficiency without compromising structural strength. Combining machine learning, fluid dynamics, and structural analysis, the system explored different configurations and identified promising designs. The results were obtained through computational modeling and optimization, rather than by demonstrating a commercial turbine in operation. Nevertheless, the example shows how AI can participate in the creative process of engineering, proposing geometric solutions that must subsequently be evaluated and validated by researchers.

The implications for intellectual property are particularly interesting. The discovery of new applications for existing molecules, as in the case of halicin, and the generation of innovative turbine geometries illustrate how artificial intelligence can contribute to different stages of the inventive process.

However, producing an original solution does not necessarily mean being legally recognized as its inventor. Under current legal frameworks, inventorship remains tied to human individuals, even when AI plays a significant role in scientific discovery or technological development. As these systems become more autonomous and begin proposing solutions that human researchers themselves had never imagined, an increasingly difficult question arises: who should receive recognition and legal rights for an invention conceived with the decisive participation of a machine?

The legal controversy is not entirely hypothetical. In 2021, South Africa granted a patent for a food container attributed to an AI system called DABUS, although the country’s procedure did not involve substantive examination of the invention. Attempts to designate DABUS as an inventor were rejected in other jurisdictions, including the United States and Europe. In November 2025, the United States Patent and Trademark Office reaffirmed that inventors must be natural persons while recognizing that AI systems can assist the inventive process. A February 2026 decision at the European Patent Office further clarified issues surrounding the designation of inventors without establishing that AI-assisted inventions are generally unpatentable.

Another distinction is essential: inventorship is not ownership. An inventor is the person legally credited with conceiving an invention, while patent rights may subsequently belong to a corporation, university, or another legal entity. As AI systems become capable of generating increasingly sophisticated technical solutions, both the attribution of inventive contributions and the concentration of patent ownership may become more consequential. Organizations with enormous computational resources could potentially develop extensive portfolios of AI-assisted inventions, accelerating innovation while also creating new barriers to technological competition.

SYNTHETIC PATENTS: A PERSONAL EXPERIMENT

Some years ago, while researching free radicals and photodynamic therapy, I developed an idea for an electric toothbrush incorporating optical fibers and light sources, intended to explore applications in oral hygiene, photodynamic treatment, and photobiomodulation. The concept emerged from combining technologies belonging to different fields: optics, photodynamic therapy, and an everyday household device. In Koestler’s terminology, it was an exercise in bisociation.

I prepared a patent proposal, but the idea attracted relatively little interest from my university’s patent office, unlike some of my earlier work involving nanotechnology. Years later, I revisited the invention and asked ChatGPT to reconstruct its patent documentation from a brief description of the original concept. Within seconds, the system produced a structured draft containing technical descriptions, proposed embodiments, and patent-style claims. The result was impressive, particularly considering how little information I had provided.

But had ChatGPT invented anything? Not in that experiment. The original concept was mine, and the machine had transformed a brief technical idea into a plausible patent document without establishing novelty, clinical efficacy, or patentability. By then, illuminated electric toothbrushes were already commercially available, although that did not establish that they embodied the same therapeutic proposal. The experience nevertheless illustrated how dramatically AI could reduce the distance between conceiving an idea and preparing its technical documentation.

The distinction becomes more interesting when we imagine systems that no longer wait for a human to supply the original concept. What happens when a machine proposes the unexpected connection, develops the technical solution, evaluates its feasibility, and prepares the corresponding patent application? At what point does artificial intelligence cease to be merely an assistant and become an inventor? And if that point is eventually reached, will our legal systems recognize it?

The connection with Koestler is again evident. A machine may establish an unexpected relationship between technologies previously considered unrelated, producing an invention that is both original and practically valuable. But conceiving the relationship, demonstrating its functionality, and assigning legal rights are different activities. Synthetic science may increasingly lead to synthetic invention, while the institutions governing intellectual property continue to assume that every legally recognized inventor is human.

8. Three Possible Futures for Science

The developments discussed here suggest several possible futures for scientific research, none of which should be treated as inevitable. In the most familiar scenario, artificial intelligence becomes an extraordinarily capable scientific partner. Human researchers continue formulating questions, developing theoretical perspectives, and interpreting results, while AI systems explore large spaces of hypotheses, identify unexpected connections, and accelerate investigation. This collaborative arrangement is already emerging in mathematics, pharmaceutical research, and experimental science.

A second possibility is more unsettling. AI systems may generate discoveries faster than human researchers can independently understand them, creating an increasingly asymmetric relationship between the production of knowledge and its interpretation. Scientists could become primarily responsible for verifying, organizing, and explaining results generated by artificial systems. The oracular trap would become a genuine danger, allowing a civilization to develop extraordinarily sophisticated technologies while understanding some of their foundations only imperfectly.

The third possibility is more radical: artificial systems might eventually formulate their own research questions, develop theories, design experiments, create inventions, and revise their conclusions with minimal human intervention. If their intellectual capabilities eventually surpass ours by a substantial margin, humans may cease to be the principal producers of new scientific knowledge. We could become collaborators, beneficiaries, or observers of an intellectual process extending beyond our direct comprehension. These scenarios are not mutually exclusive, and different scientific disciplines may evolve through different combinations of human and artificial capabilities.

There is an interesting institutional irony here. The disciplines concerned with knowledge, meaning, judgment, and human purpose might be considered increasingly dispensable precisely when their questions become most difficult to avoid. The corresponding academic reorganization would undoubtedly be explained with admirable clarity. More seriously, the future of science will involve decisions about which problems deserve investigation, who determines research priorities, and whether scientific inquiry continues to reflect human curiosity or increasingly follows objectives selected through computational optimization.

These questions also have an economic dimension. Advanced scientific AI depends on substantial computational infrastructure, specialized models, technical expertise, and, in some cases, expensive experimental facilities. If access to these resources remains concentrated among a small number of corporations and institutions, scientific independence may increasingly depend on financial and technological capabilities rather than intellectual merit alone. A university might possess the expertise needed to formulate an important question while lacking the infrastructure required to investigate it competitively.

The response of the mathematical community to OpenAI’s October release illustrates this emerging concern. The independent Advisory Group on Mathematics and Artificial Intelligence emphasized that publishing machine-generated results is only the beginning of incorporating them into mathematical knowledge and that researchers must retain the freedom to pursue questions independently. On October 15, the Simons Foundation announced an initiative involving $15 million in combined funding and resources from the foundation, OpenAI, and Anthropic to help mathematicians evaluate AI-generated results, gain access to advanced tools, and develop shared standards.

Such initiatives recognize that scientific discovery depends on institutions as well as individual intelligence. Corporate AI research is not necessarily incompatible with scientific openness; laboratories publish results, collaborate with universities, and release valuable tools. Moreover, AI could make advanced scientific capabilities accessible to researchers who previously lacked the resources to pursue ambitious investigations. The outcome will depend partly on institutional choices, scientific norms, access to infrastructure, and the degree to which results can be independently reproduced and critically examined.

The objective should therefore not be to defend human slowness against machine efficiency, nor to assume that the human contribution to scientific reasoning will remain permanently protected. It should be to preserve intellectual freedom and the ability to question assumptions, investigate anomalies, and pursue ideas whose significance is not immediately apparent. Science has never been merely a collection of correct answers; it is also an intellectual tradition built upon curiosity, criticism, explanation, and the attempt to understand reality. Those activities may increasingly be shared with artificial intelligence, but their importance will not disappear simply because machines become better at performing them.

9. Conclusion: The Act of Creation Reconsidered

Arthur Koestler proposed that creativity often emerges when previously separate matrices of thought intersect. His theory offered a way to understand the apparent mystery of creative insight without treating it as an inexplicable miracle. Today, artificial intelligence gives this idea unexpected relevance. The recent mathematical discoveries, independently evaluated proofs, biological hypotheses, and AI-designed molecules demonstrate that machines are beginning to participate in several distinct aspects of scientific creation.

These capabilities do not establish that artificial intelligence experiences creativity as humans do, nor that machine-generated results and human intellectual achievements emerge through identical mechanisms. They do, however, challenge the assumption that producing original knowledge necessarily requires human intuition. Perhaps creativity is not defined exclusively by the subjective experience accompanying discovery, but also by the meaningful novelty of the relationships established. If so, the distinction between human and machine creativity becomes more complicated than we once imagined.

This does not mean that consciousness, intention, and human experience are irrelevant. It means that creativity, functional understanding, and subjective consciousness may be distinct phenomena whose relationships remain incompletely understood. For me, that is the most fascinating implication of artificial scientific discovery. We are not merely building machines capable of calculating faster or solving more difficult problems; we may be developing systems capable of participating in the generation of new knowledge about the universe and translating that knowledge into inventions of their own.

This possibility brings to mind an extraordinary prediction made by mathematician Irving John Good in the 1960s: “The first ultraintelligent machine is the last invention that man need ever make.” Good envisioned a machine intellectually superior to humans that could design even more intelligent machines, triggering a genuine intelligence explosion. Sixty years later, the idea no longer seems quite so remote, although whether it will ever become reality remains uncertain. Perhaps we are approaching a moment when the ability to invent itself becomes a human invention.

Kekulé’s celebrated serpent remains an appropriate final image. The ouroboros represents a circle in which the end connects with the beginning, just as scientific knowledge develops through a continuing process in which existing ideas generate new connections, discoveries, and questions. Artificial intelligence may now become one of the most powerful participants in that cycle, changing not only the speed of discovery but also our understanding of the creative process itself.

The ultimate challenge is not to preserve human intellectual superiority at any cost, nor to surrender our understanding to increasingly capable computational systems. It is to develop a scientific civilization in which artificial intelligence expands both our knowledge and our capacity to understand it. Perhaps the most important discovery of the coming age will not be a new mathematical theorem, a physical law, or a revolutionary invention, but a deeper understanding of what it means to create, to know, and to understand.

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Sources and Further Reading

Creativity and the History of Science

• Arthur Koestler. The Act of Creation. Hutchinson, 1964.
• Alan J. Rocke. Image and Reality: Kekulé, Kopp, and the Scientific Imagination. University of Chicago Press, 2010.
• August Kekulé. Speech at the Benzolfest, Berlin, March 11, 1890.

Artificial Intelligence and Mathematics

• OpenAI. An OpenAI Model Has Disproved a Central Conjecture in Discrete Geometry. May 20, 2026.
• Noga Alon et al. Remarks on the Disproof of the Unit Distance Conjecture. May 2026.
• OpenAI. On the Navier–Stokes Millennium Prize Problem. September 8, 2026.
• Clay Mathematics Institute. Navier–Stokes Announcement. September 11, 2026.
• Communications Physics. The Navier–Stokes Equations Blow Up, and Planes Still Fly. October 14, 2026.
• OpenAI. Sharing AI Progress in Mathematics. October 2026; Mathematical Research Repository.
• Google DeepMind. AlphaEvolve, 2025; Gemini Deep Think and Aletheia, 2026.
• Anthropic. Formalizing Fermat’s Last Theorem. September 4, 2026.
• First Proof Project. Third Batch Results. October 2026.
• Peggy Yin. “The AI Understands. 100%”: Field[s] Notes with John Pardon. October 2026.
• Irving John Good. Speculations Concerning the First Ultraintelligent Machine. Advances in Computers, vol. 6, pp. 31–88, 1966.

Synthetic Science, Invention, and Patents

• Gottweis et al. Accelerating Scientific Discovery with Co-Scientist. Nature, 2026.
• OpenAI, PerturbAI, and Scripps Research. Using Thousands of AI Agents to Uncover New Leads in Biological Data. October 21, 2026.
• MIT News. Using Generative AI, Researchers Design Compounds That Can Kill Drug-Resistant Bacteria. August 2025.
• Insilico Medicine. First Patient Dosed in Rentosertib Phase III Trial. September 2026.
• United States Patent and Trademark Office. Revised Inventorship Guidance for AI-Assisted Inventions. November 2025.
• European Patent Office. Decision T 0528/25 — Designation of Inventor/DABUS. February 2026.
• Simons Foundation. Initiative to Help Mathematicians Navigate the AI Era. October 2026.
• Stokes et al. A Deep Learning Approach to Antibiotic Discovery. Cell, February 2020.
• Xia et al. A Novel Generative Approach to the Parametric Design and Multi-Objective Optimization of Horizontal Axis Tidal Turbines. Physics of Fluids, November 2024.

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Maurício Veloso Brant Pinheiro, PhD
Professor of Physics, Federal University of Minas Gerais (UFMG)
Founder, Author and Editor, AI-Talks.org
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Editorial transparency note: This article, as with all articles published on this site, was conceived, directed, written, and reviewed by Prof. Maurício Veloso Brant Pinheiro. Artificial intelligence was used as an assistant for editorial refinement, formatting, image generation, SEO metadata, and publication workflow.

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