Daniel Persson is a good example of how physics and math go hand in hand. He realised early on that mathematics was crucial to solving many physical problems, including during his PhD in Brussels, where he worked on mathematical aspects of gravity.
Physics remains at the centre of Daniel's work, with concepts such as gravity, quantum mechanics and string theory at the forefront. The theory of gravity describes the universe on large scales, while quantum mechanics deals with our microscopic world. String theory unites these two fields.
- Usually, it works well to have one theory for the 'big' and one for the 'small'. But some questions, like the early universe and black holes, require combining both. The interplay between gravity and quantum mechanics is something that has fascinated me for years. And the more questions you ask about nature, the clearer it becomes that you either must learn or create new math, says Daniel.
Math as a basis for future technologies
After his PhD in Brussels, Daniel got a postdoctoral position at ETH in Zurich, where he worked for two years. He then came back to Chalmers to work at the Department of Fundamental Physics. His research went in the mathematical direction, focusing on the connection between black holes and number theory. In his quest to understand the quantum mechanical description of black holes, he studied so-called modular forms - a type of mathematical object central to number theory - which surprisingly turned out to have just the right structure to understand aspects of quantum gravity. Daniel applied for - and got - a position at the Department of Mathematical Sciences in 2017, where he is now working at the Division of Algebra and Geometry. And it was precisely his work on mathematical structures in physics that fuelled his interest in AI.
- If you're working with black holes or the Big Bang, it's quite a long way to experimentation. But when it comes to AI research, the step to testing data is much closer. Suddenly I'm closer to applications, which was unfamiliar to me at first but very exciting.
When the Wallenberg AI, Autonomous Systems and Software Program (WASP) started in 2015 - Sweden's largest single research programme ever - Daniel applied for a grant to hire a PhD student and investigate the mathematics behind AI. Within WASP, there is a special focus on basic research, which is then carried out in PhD projects. Daniel is supervisor for several PhD students within the WASP PhD School at the Department of Mathematical Sciences in Gothenburg. The PhD students take joint courses, go on trips and study visits to companies and thus get a natural connection with other academic environments in Sweden and industry. In the same spirit, Daniel has also taken the initiative to co-organise a workshop for other supervisors within the WASP programme.
Math makes AI effective
Today, AI development is driven by companies that are constantly launching new applications. According to Daniel, the basic research in mathematics is needed to answer the more fundamental questions about why AI works the way it does. This kind of basic understanding is also expected to make AI systems more efficient. Today, for example, an AI model needs to be trained with large amounts of data to understand and identify an object. For the AI network to recognise the same object, such as a coffee cup and from several different angles, thousands of images and data learning (so-called data augmentation) are required. We humans usually recognise a coffee cup no matter how it is rotated. Daniel believes that we can create the same type of understanding in AI by using mathematical formulas for symmetries.
- Data is expensive and takes up a lot of space. Using mathematical formulas for symmetries, we can make AI systems more efficient while reducing costs. This type of research has the potential to change the way AI is trained, especially in areas such as self-driving cars and medical imaging.
In physics and math, symmetry describes a kind of structure. By building that kind of structure into the way AI handles data, AI systems can become better at interpreting and understanding different objects. This is called geometric machine learning, which uses mathematical group theory to create AI models that handle symmetries in data more effectively.
- The exciting thing about mathematics is that one theory can be used in many different contexts. I saw an opportunity to use math to improve AI. In the future, I also want to study how AI can be used to develop math, Daniel finishes.
Text: Daniel Stahre
