Mathematicians warned against rising tech industry influence in a declaration describing the many challenges that AI poses to mathematics research. The timing of the declaration comes two weeks after OpenAI publicized one of its AI models as having disproved an 80-year-old mathematical conjecture in geometry.
The declaration was developed by a working group of 16 researchers over eight months following a conference held at Leiden University in the Netherlands in September 2025. Published on June 2, 2026, the resulting Leiden Declaration on Artificial Intelligence and Mathematics has been endorsed by the International Mathematical Union—the international non-governmental organization that hosts conferences and oversees the most prestigious prizes in mathematics such as the Fields Medal.
“Mathematicians should find it quite striking that tech companies are suddenly interested in their work,” said Kevin Buzzard, a mathematician at Imperial College London, in a statement. “The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space.”
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Physicists found that the music of Johann Sebastian Bach contains mathematical patterns that help convey information
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When most people think of visual art, they don’t usually think of math at the same time. One primary reason for this is that mainstream culture has framed art and math as two separate functions of the brain.
However, because the brain works as a whole when creating art and solving mathematical problems, a new study suggests that abstract art may follow hidden mathematical principles that influence how people perceive and respond to it.
For years, researchers have wondered why certain types of art move people more than others. Until now, however, there has been no direct explanation.
Using a sophisticated method from computational topology, researchers discovered that famous abstract artists appear to share a common structural pattern in their work. Researchers are calling this a mathematical “golden rule” that can distinguish real art from AI-generated “slop.”
Led by Jacek Rogala of the University of Warsaw and Shabnam Kadir of the University of Hertfordshire, the research team used a technique called persistent homology to analyze visual compositions. Persistent homology is a mathematical tool that breaks down how structures within an image change across multiple scales, revealing patterns that the human eye cannot see.
The team compared two sets of images: authentic abstract paintings created by celebrated artists such as Wassily Kandinsky, Mark Rothko, and Jackson Pollock, and “pseudo-art” produced by AI to mimic abstract styles.
The findings suggested the topological method could distinguish real art from AI-generated images. According to the researchers, the structural organization of authentic paintings changed in consistent, measurable ways compared to the computer-generated alternatives.
Senior author Jacek Rogala said in a statement, “What struck me most is that we could actually see the gallery environment doing something measurable. It wasn’t just a backdrop — it changed which images held attention and for how long. That’s a result you can put numbers on, and it still feels surprising.”
When examining the works of Wassily Kandinsky, Mark Rothko, and Jackson Pollock more closely, the researchers discovered that the artists’ paintings tended to converge on a similar rate of violation of a mathematical relationship called Alexander duality. This concept describes the balance between structures near the edges of an image and what is happening in the middle.
“An important part of our study was to explore the relationship between topologically derived image features, eye movement, and aesthetic experience,” the authors say in a co-statement. “Our research showed that our newly developed method not only clearly distinguished between two sets of images but also allowed us to map topological features onto gaze fixation heat maps.”
Researchers think many abstract artists may naturally arrange shapes and patterns in similar ways, even without knowing the mathematics behind them. This hidden structure could help explain why certain artworks feel more pleasing or emotionally engaging to viewers.
The researchers also took the study a step further by examining how people respond physically and mentally to abstract art. Participants studied both authentic and AI-generated images while researchers tracked their eye movements and monitored brain activity in laboratory and gallery settings. The results revealed noticeable behavioral differences. Real artworks produced more stable, integrated patterns of brain activity, while AI-generated art elicited more exploratory eye movements.
Overall, the study suggests that abstract art is not purely subjective or random. Instead, abstract art may follow hidden mathematical patterns that naturally connect with the way our brains interpret and understand images.
The study, “Art’s Hidden Topology: A Window into Human Perception,” was published in PLOS Computational Biology.
Chrissy Newton is a PR professional and the founder of VOCAB Communications. She currently appears on The Discovery Channel and Max and hosts the Rebelliously Curious podcast, which can be found on YouTube and on all audio podcast streaming platforms. Follow her on X: @ChrissyNewton, Instagram: @BeingChrissyNewton, and chrissynewton.com. To contact Chrissy with a story, please email chrissy @ thedebrief.org.
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