Old Math Questions, New Applications
Chemists, physicists, engineers and other scientists explore new areas of discovery, such as nanotechnology or advanced materials. Mathematicians, on the other hand, are unusual in that they continue to look at long-standing problems, including some that are centuries old. While some of the questions they probe have been pondered for generations, the solutions to these problems, and the number theory related to these problems, have important applications in contemporary technology.
Without number theory, for example, electronic commerce would not be a reality, since information technology relies on the secure and efficient transmission of data, and this transmission relies on the theory of numbers. Mathematicians use techniques from geometry to construct “transmission error-correcting codes”—codes to ensure data arrives as it was sent. Mathematical ideas like characters, exponential sums, recurrence sequences and notions of uniform distribution, meanwhile, are used in designing advanced cryptographic (or code) systems to ensure the security of transmitted data.
Dr. Cameron Stewart, Canada Research Chair in Number Theory, is one of Canada's leading number theorists. His work in areas such as combinatorial number theory, Diophantine approximation and Diophantine equations—all of which are central topics in number theory—is recognized around the world. He is particularly well-known for his work on the so-called “abc conjecture,” one of the best-known Diophantine inequalities.
As Chair, Stewart will try to resolve several open problems in the theory of numbers. By incorporating students, his work will also train the next generation of mathematicians to develop creative approaches to these outstanding mathematical problems.