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ASTANA – Kazakhstan welcomed more than 700 mathematicians, scientists and educators worldwide on July 21-25 for the first International Society for Analysis, its Applications and Computation (ISAAC) Congress ever held in Central Asia.
Photo credit: Nazarbayev University
On the sidelines of the mathematical gathering Nazarbayev University’s press office spoke with Carola-Bibiane Schönlieb, a professor at the University of Cambridge. Schönlieb specializes in the intersection of pure mathematics, machine learning, and practical applications such as medical imaging and cultural heritage restoration.
In an interview, she shared her views on Kazakhstan’s growing mathematical community, the evolving role of artificial intelligence in research, the balance between academic freedom and industry opportunities, and the beauty of translating abstract math into transformative technology.
Professor Schönlieb, you work on restoring damaged images. Could hosting ISAAC in Kazakhstan also be seen as a kind of restoration, filling a geographic gap in the global math map?
Yes, although I’d say it’s less about filling a regional gap and more about filling a gap in ISAAC’s own journey. It’s been incredibly enriching to connect with the mathematical community here in Kazakhstan. Just like in my research, mathematics is appearing in unexpected places and that’s a beautiful thing.
I’ve been extremely impressed by the level of mathematics at NU and by how mathematics is perceived in society. The standing of the discipline here could be a role model for the rest of the world. Mathematics appears genuinely popular in Kazakhstan, and there are some truly excellent mathematicians being educated, and educating the next generation.
For those far from math and AI, could you share an example where they helped restore something lost or invisible?
There are many examples. The connection to the real world in my work often comes through digital images, whether taken on a phone or used in specialized fields like medical imaging or cultural heritage. Once an image is digital, you can describe it mathematically as a matrix of intensity values. Once you have that, mathematics allows you to manipulate the image in powerful ways.
In our work, we use mathematical models to change and restore images based on expert knowledge. For example, museum conservators explain how physical restoration works, and we translate that into equations. These equations can then be applied automatically, following the principles we’ve learned from those experts.
More recently, AI, especially machine learning, has expanded this process. Instead of relying solely on expert input, we can now train algorithms to learn these equations from data. So rather than hand-crafting each model, AI helps discover the right mathematical tools directly from examples.
As machine learning spreads, do you think we’re close to creating artificial general intelligence, something that truly understands and learns like a human, not just today’s large language models?
That’s a big open question. One key issue with large language models is that they can generate outputs that seem new, but we don’t know whether that’s genuine novelty or just a remix of what they’ve seen before. Are they truly creating knowledge, or just interpolating from memory? We don’t yet have a solid answer.
Another challenge is whether these models are learning something meaningful. Our current mathematical understanding of deep learning is far behind the complexity of real-world systems like ChatGPT. So even if these models can “learn,” we don’t fully understand how, or whether what they learn is sensible.
That said, one powerful aspect of neural networks is their ability to combine existing ideas in novel ways. This can help in exploratory research by generating new hypotheses or directions that humans might not have considered. But when it comes to truly producing new knowledge, that still largely remains in human hands. At least for now.
What mathematical idea fascinates you most, especially one with exciting practical applications?
One idea that blows my mind is using stochastic differential equations to generate samples from complex distributions. This concept has recently been embraced by machine learning, particularly in diffusion models and flow matching. I find it beautiful how pure mathematical ideas are transformed into practical, powerful applications. It’s impressive to see deep theory applied in ways that have real-world impact.
Women are often underrepresented in mathematics and leadership roles. What message would you share with those who might feel out of place in the community?
Networking is crucial. In computer science, it’s the same: you naturally connect with people like you. Without that, it’s easy to feel isolated, which makes progress harder. Having a dedicated association, such as Women in STEM or mathematics network, can make a big difference. It empowers the students and faculty on all levels because otherwise it is a lonely journey.
Given your expertise in machine learning and the large funding available in industry, why did you choose academia, where resources are often more limited?
For me, it’s freedom. Freedom to pursue whatever research I want. Even big companies such as DeepMind or Google do original research and have amazing computational resources. In that sense, academia can’t compete. But what they don’t have is the openness I enjoy. I can discuss any idea or project without secrecy or shifting company priorities dictating a change in focus.
There’s also flexibility: I can travel, work anywhere and collaborate with anyone. That freedom is rare and precious. Of course, academic freedom isn’t guaranteed everywhere and can be affected by politics in some countries. But if corporate restrictions don’t bother you, then perhaps industry’s resources and funding are worth it.
The author is Akmaral Syzdykova, an expert of Nazarbayev University press office.
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