Mathematics rarely makes front page news. However, ideas developed by mathematicians often underpin technologies and decision-making systems that affect everyday life. One such example is optimal transport theory, a field of mathematics that began with a deceptively simple question: what is the most efficient way to move something from one place to another? Today, the theory influences subjects as diverse as artificial intelligence, economics, climate science, logistics, medical imaging, and machine learning. It is also the field of research that has won Professor Robert McCann of the University of Toronto one of Canada’s most prestigious mathematical honours, THE CRM–Fields–PIMS 2026 Award.
The award, given jointly by the Center de recherches mathématiques (CRM), the Fields Institute and the Pacific Institute for Mathematical Sciences (PIMS), recognizes outstanding research achievements by mathematicians working in Canada. McCann was honored for his internationally influential contributions to optimal transportation theory, a field that has undergone tremendous growth over the past three decades.
McCann grew up in Windsor, Ontario. He studied engineering and physics at Queen’s University before majoring in mathematics and earning a PhD in mathematics from Princeton University in 1994. McCann is editor-in-chief of Canadian Journal of Mathematics and he was elected a Fellow of the American Mathematical Society in 2012. In 2025 he received the Norbert Wiener Award in Applied Mathematics.
The math of moving things efficiently
The origins of optimal transportation date back to the eighteenth century and the work of the French mathematician Gaspard Monge. Monge tried to determine the most efficient way to transport soil from one place to another, minimizing the overall cost of movement. While the initial problem was practical, it proved mathematically challenging.
Modern optimal transport theory extends this concept beyond physical materials. Researchers now use the discipline to study how distributions of resources, information, energy, probability or even data points can be most efficiently transformed.
At its heart, optimal transportation requires answers to questions such as:
- How should goods be distributed in a logistics network?
- How can resources be allocated while minimizing cost?
- How can one probability distribution be transformed into another?
- What is the most efficient way to compare complex data sets?
The math behind these questions has become increasingly important in a world driven by big data and artificial intelligence. McCann has long been regarded as one of the world’s leading figures in optimal transport. His research has helped create fundamental theoretical frameworks that are now used by mathematicians, economists, engineers, and computer scientists around the world. The Fields Institute described the award as recognizing McCann’s “outstanding contributions to optimal transportation theory.”
Among the reasons for the field’s growing importance is its ability to connect seemingly unrelated disciplines. Problems involving transportation networks, economics, image processing, and machine learning can often be expressed through similar mathematical structures. This interdisciplinarity has made optimal transport one of the most active areas of contemporary applied mathematics.
Why AI researchers care
Perhaps surprisingly, one of the fastest growing applications of optimal transportation lies within artificial intelligence. Machine learning systems often need to compare complex data sets. This could include comparing images, identifying similarities between patterns, analyzing medical scans or training generative AI systems. Optimal transport provides mathematical tools to measure the “distance” between data distributions in ways that conventional statistical methods cannot.
Many modern AI models rely on concepts resulting from optimal transport to improve performance and stability. Researchers increasingly use optimal transport metrics to evaluate how well machine learning systems reproduce data, classify information, or generate synthetic results. As Canada continues to position itself as a global leader in artificial intelligence, the mathematical foundations provided by researchers such as McCann become increasingly important.
Optimal transportation is also of increasing importance to management science and supply chain optimization. Organizations face constant challenges involving inventory distribution, transportation efficiency, warehouse placement, and network design. The same mathematical principles used to analyze probability distributions can often be adapted to examine the movement of physical goods through complex supply chains.
Recent Canadian interest in resilient supply chains illustrates this connection. Researchers examining how organizations can respond to disruptions increasingly rely on sophisticated optimization and modeling techniques. The mathematics developed within optimal transport theory provides a rigorous framework for understanding many of these problems. As supply chains become more complex and globalized, mathematical approaches are becoming essential tools for decision makers.
The impact of optimal transportation extends beyond AI and logistics. Researchers use the theory to model climate systems and atmospheric dynamics, develop advanced medical imaging techniques, and analyze economic inequalities and market behavior. This breadth illustrates an important characteristic of modern mathematics. Fundamental theoretical advances often create ripple effects across multiple scientific disciplines, sometimes decades after the original discoveries were made. McCann’s work illustrates this phenomenon. Research initially pursued for its mathematical elegance has become increasingly relevant to some of the most important technological and scientific challenges of the twenty-first century.
Canada’s Mathematical Ecosystem
The award also highlights the strength of Canada’s mathematical research community. Institutions such as Fields Institute in Toronto have built an international reputation for advancing the mathematical sciences and fostering collaboration between academia, industry and government. The Institute’s current research programs include areas ranging from artificial intelligence and quantum computing to information security and data science.
Canadian mathematics has often operated quietly in the background, producing fundamental discoveries that later influence technological innovation. Recognition of McCann’s achievements serves as a reminder that mathematical research remains a critical driver of economic competitiveness and scientific progress.
Optimal transportation theory may seem abstract, but its applications are becoming more and more tangible. From helping train AI systems to improving transportation networks and supporting scientific discoveries, the field illustrates how deep mathematical thinking can generate practical benefits across many sectors.
