Mathematics is the language that allows data to speak.
At the crossroads of abstraction and perception, Belgian mathematician Ann Dooms has spent two decades teaching computers to read what human eyes cannot — finding in the numerical structure of images a common language that spans art authentication, historical preservation, and the fragile hopes of women facing cancer. Her work reminds us that data, however vast, remains mute until mathematics gives it voice. In an age of increasingly opaque artificial intelligence, her pursuit of transparent, structurally grounded models may prove as consequential as any single discovery she has made.
- Images that appear self-evident to the human eye conceal numerical structures that only mathematical decomposition can fully interrogate — a gap between seeing and knowing that Dooms has spent her career closing.
- The same wavelet techniques that authenticated Van Gogh and Gauguin canvases are now being turned toward microscopy images of egg cells, raising the stakes from art history to human fertility and the weight of a cancer diagnosis.
- Selecting viable ovocytes for cryopreservation is complicated by the fact that the most critical markers of cell quality are invisible to even trained medical specialists, creating an urgent need for mathematical augmentation of clinical judgment.
- As machine-learning models grow more powerful and less interpretable, Dooms positions mathematical image analysis as a corrective force — a way to build AI that is transparent, robust, and anchored in the actual structure of the problems it solves.
- The trajectory of her work points toward a future where mathematical intelligibility, not algorithmic complexity, becomes the defining standard for trustworthy artificial intelligence.
Ann Dooms is a professor at the Free University of Brussels who has spent more than two decades working at an unlikely intersection: the abstract precision of mathematics and the sensory world of images. Her core insight is that a digital image is not a picture — it is a numerical object with internal structure, and once you learn to read it that way, you can ask questions that no human eye can answer alone.
Her path into this work began in the early 2000s alongside mathematician Ingrid Daubechies, whose innovations in wavelets — mathematical transformations capable of compressing images while preserving their essential information — opened new analytical possibilities. Together they collaborated with the Van Gogh Museum in Amsterdam, using pattern recognition to authenticate paintings, study brushwork, and assess conservation status across works by Van Gogh, Gauguin, and Van Eyck. The project succeeded, and it revealed to Dooms how broadly these tools could travel.
The method works by decomposing the pixels of an image into mathematical building blocks, manipulating their numerical relationships, and translating the results into information a human can interpret. Its power lies in its universality: the same framework that reads a painting can read a biomedical scan or restore text in a damaged historical manuscript. The patterns differ, but the language is the same.
Her most recent application carries the highest human stakes. Working with the Center for Reproductive Medicine at the University Hospital of Brussels, Dooms is applying these pattern-recognition techniques to high-resolution microscopy images of ovocytes collected from women who wish to preserve their fertility before undergoing cancer treatment. The challenge is that the features most predictive of a cell's future viability are invisible to the human eye. Her team models those features mathematically, not to replace clinical judgment, but to give women a clearer, more honest picture of their chances.
Dooms also sees her work as a response to a broader crisis in artificial intelligence. As models grow more powerful, they grow more opaque — and opacity erodes trust. She argues that mathematical image analysis offers a path toward AI that is more transparent and more deeply connected to the structure of the problems it addresses. The future, she suggests, belongs not to greater complexity, but to greater intelligibility.
Ann Dooms sits at the intersection of two worlds that most people assume have nothing to do with each other: the precise, abstract realm of mathematics and the sensory, emotional experience of looking at a painting. She is a professor at the Free University of Brussels and one of Europe's leading specialists in digital mathematics—the mathematical framework that allows computers to recognize patterns hidden inside digital images. What she has learned, over more than two decades of work, is that images are not what they appear to be. They are numerical structures. And once you know how to read them as numbers, you can ask them questions that human eyes alone can never answer.
Dooms began this work in the early 2000s, collaborating with Ingrid Daubechies, a mathematician whose innovations in wavelets—a family of mathematical transformations that can compress images while preserving their essential information—opened new possibilities for analyzing visual data. Together, they worked with the Van Gogh Museum in Amsterdam on a project that seemed almost impossible: using mathematics to authenticate paintings, to date them, to study the brushwork and conservation status of canvases by Van Gogh, Gauguin, and Van Eyck. The work succeeded. It showed Dooms that pattern recognition in images could do far more than she had initially imagined.
The method itself is elegant in its logic. A digital image, to a computer, is not a picture at all. It is a numerical object with internal structure. Dooms and her team divide the pixels of an image into building blocks—mathematical units that can be decomposed, examined, manipulated, and then reconstructed. "We examine an image through its numerical structure, we manipulate those numbers mathematically, and then we translate the result into information that a human being can interpret," she explained during a public lecture in Madrid on May 12, marking the International Day of Women in Mathematics. The theoretical foundation for this work lies in functional analysis in Hilbert spaces, which provides both general frameworks for building blocks and more specialized ones tailored to specific types of images.
What makes this approach powerful is that it works across radically different domains. The same mathematical tools that authenticate a Van Gogh painting can also identify structures in biomedical images or restore text in damaged historical documents. The patterns are different, but the language is the same. Mathematics, Dooms insists, is not merely a tool for analysis. It is the language that allows data to speak. "Digital data is everywhere, but it does not speak for itself," she has said. "Mathematics is the language that allows us to extract its value."
One of her most recent projects illustrates how far this principle can reach. About a year ago, Dooms began working with the Center for Reproductive Medicine at the University Hospital of Brussels on a problem that sits at the intersection of mathematics, medicine, and human hope. Women facing cancer treatment often want to preserve their fertility before undergoing chemotherapy or radiation. The hospital collects high-resolution microscopy images of ovocytes—egg cells—that might be frozen for future use. But selecting which cells have the best chance of becoming viable pregnancies later is difficult. The human eye can see obvious damage, but there are properties of cell quality that no radiologist can detect by looking. This is where mathematics enters.
Dooms' team uses the same pattern-recognition techniques they developed for paintings to analyze the numerical structure of these cells. They model mathematically which features of an ovocyte's structure correlate with quality and viability. The goal is not to replace medical judgment but to augment it—to tell women, with some mathematical confidence, what their actual chances are of becoming mothers later with these frozen cells. "It is not an easy machine-learning problem because the data we have comes from cells that medical specialists already think are good," Dooms explained. "But there are certain properties that the human eye cannot detect." In moments of profound medical uncertainty, that kind of clarity—grounded in mathematics rather than hope alone—can be a comfort.
Beyond these specific applications, Dooms sees digital mathematics as essential to a larger challenge facing artificial intelligence and data science. As machine-learning models become more powerful, they also become more opaque. No one fully understands why they make the decisions they do. Dooms argues that mathematical image analysis offers a path toward models that are more robust, more transparent, more trustworthy, and more deeply connected to the actual structure of the problems they are trying to solve. The future of AI, she suggests, depends not on making algorithms more complex, but on making them more mathematically intelligible. In a world drowning in digital images and data, that kind of clarity may be the most valuable pattern of all.
Notable Quotes
Digital data is everywhere, but it does not speak for itself. Mathematics is the language that allows us to extract its value.— Ann Dooms
We examine an image through its numerical structure, we manipulate those numbers mathematically, and then we translate the result into information that a human being can interpret.— Ann Dooms
The Hearth Conversation Another angle on the story
Why does it matter that we understand images as numerical structures rather than just looking at them?
Because the human eye is limited. It can see surface features, obvious damage, gross differences. But a painting might have been altered in ways that are invisible to us—a layer of paint added centuries later, a restoration that changed the artist's original intent. Mathematics can detect those changes by reading the numerical fingerprint of the brushwork, the texture, the composition. It's like having a language that the image itself speaks, if you know how to listen.
And this same approach works for something completely different, like preserving fertility in cancer patients?
Exactly. The ovocyte—the egg cell—is also a numerical structure when you image it under a microscope. The cells that will produce viable pregnancies have certain mathematical properties. A doctor can look at a cell and say it looks healthy. But there are subtle features—the distribution of organelles, the texture of the cytoplasm—that correlate with quality but that human vision simply cannot resolve. Mathematics can.
So you're not replacing human judgment. You're extending it.
That's the right way to think about it. The doctor still decides. But now they have information they didn't have before. And for a woman facing cancer treatment, knowing the actual probability that a frozen egg will lead to a pregnancy someday—that's not just data. That's hope grounded in something real.
What's the connection between authenticating a Van Gogh and building better AI models?
Both require the same thing: understanding the structure of the problem deeply enough that you can describe it mathematically. Most AI models today are black boxes. You feed them data, they produce an answer, and nobody really knows why. But if you start from the mathematical structure of what you're trying to solve—the actual geometry of the problem—you can build models that are transparent, that you can trust, that you can explain.
Is there a risk that mathematical analysis could be wrong about something—that the numbers could mislead you?
Of course. Mathematics is a language, not truth itself. But it's a language that forces precision. If you say something mathematically, you have to be specific about what you mean. You can't hide behind vagueness. And that precision is what allows you to catch errors, to test your assumptions, to improve. The human eye can be fooled very easily. Mathematics is harder to fool.