Epidemiologists often use diagrams to understand how diseases spread. These diagrams show groups of people—some are sick, some are healthy—and arrows that represent the movement between these groups. This visual approach helps in creating equations to predict how an outbreak might unfold.
Recently, researchers like Osgood and Baez developed a tool called StockFlow. It allows experts to model various aspects of outbreaks, including how health inequalities can influence infection rates. According to Baez, “Category theory makes it easier to combine different models,” making this tool quite powerful.
While StockFlow hasn’t been widely adopted yet, Osgood is teaching it to his students. He wants to equip the next generation with the skills they need to tackle this crucial area in public health. Leinster, a colleague, emphasizes its potential value, saying, “This is genuinely something that could be used.”
In another initiative, Hadzihasanovic and Capucci are part of Safeguarded AI, a project funded by the U.K. government. They apply category theory to ensure that AI can operate safely in critical environments, like nuclear plants. Their approach is to build models that mimic real-world systems, so AI learns to navigate them effectively. Capucci points out, “Category theory offers a modular way to tackle complex issues.”
The trend toward more sophisticated modeling is driven by the growing complexity of our systems and the rising role of AI in daily life. Hadzihasanovic believes that this work will prove vital soon. “This is going to be, eventually, very important work,” he says.
Many mathematicians in this field share a passion for making a positive impact. They believe math can help tackle environmental challenges. Baez, who is related to the singer Joan Baez, was influenced by his uncle, a scientist and activist. “I want to help the world, not just enjoy myself,” he remarks.
Baez points out that we often misunderstand biological systems. We treat them like machines, focusing on outputs while ignoring waste and energy sources. “Our math is based on that attitude, and it’s failing us,” he explains. Living systems are intricate and interconnected, with no clear waste—what’s discarded by one organism often benefits another.
Baez thinks our current approach limits our understanding of nature. To improve this, we need new mathematical frameworks. “If we understand better, we might treat the world more kindly,” he suggests, criticizing the current mindset that leads to environmental degradation.
This perspective highlights the need for a more holistic view of ecosystems. By seeing living systems as part of a shared category, we can foster greater respect for nature. Many in this community hope their work will pave the way to a better future while deepening our understanding of the world around us.
The application of category theory in real-world issues offers a promising avenue for both math and environmental science. As researchers continue to explore this field, the quest to harmonize human activity with natural ecosystems remains critical. Time will tell if these mathematical tools genuinely help humanity and the planet. But for those dedicated to making a difference, the journey is worthwhile.
