In a superficial sense, mathematics is a human construction. 1+1=2 only insofar as we give meaning to numbers and symbols, in a similar way that we give meanings to nouns and verbs in language.
But on a deeper level, mathematics exists in the world around us as part of the fundamental building blocks of existence itself. We can see mathematics expressed in the natural world and in the many ways it is incorporated in living and nonliving things.
This comes as no surprise to researchers working in the Faculty of Mathematics here at the University of Waterloo. Our Department of Applied Mathematics is full of brilliant students and professors using math to understand things like climate change and pandemics. And our Department of Pure Mathematics has researchers who use math to understand the primal rules governing everything in the universe.
Join us as we explore the top four expressions of mathematics in the natural world.
- Fractals. For many students in junior high and high school, fractal geometry is among the first introductions to the way that math exists in nature. We look with awe at the branching of a tree or the leaves on a fern and see intricately repeating patterns. Fractals are a huge area of mathematical research, and if you are interested in learning about fractals at a university level, check out professor emeritus in applied mathematics William Gilbert.
- Fluid dynamics. The way that liquid functions is governed by a specific set of mathematical laws. Think about the formation, crest and fall of waves on the ocean, or the way a river or stream meanders through a landscape. There’s a formula for that. Learn more about fluid dynamics with our applied math professor Marek Stastna, and if you’re on campus check out his fluids lab.
- Epidemiology. Since early-2020, everyone has had a crash course in epidemiology and learned all about the spread and reproduction of viruses. Mathematicians have been at the forefront of data science and modeling throughout the pandemic. Some of our researchers have even used mathematical modeling to investigate how COVID-19 works on a cellular level. Check out research from applied mathematician Anita Layton to learn more. As Layton puts it, “mathematics is our microscope.”
- Cosmology. When we talk about cosmology, we are talking about the existence and the ordering of, well, everything. It’s the theory of how the universe works. Researchers in pure mathematics have taken up these big questions and given some startling answers. Take, for example, mathematical research on string theory, showing there are six or seven extra dimensions that we can barely comprehend bundles up in everything perceptible in the natural world. Professor of pure mathematics Spiro Karigiannis is one of our resident string theory experts that you should check out if you’d like to learn more.
By the Numbers is a weekly series that reflects on the lighter side of student life, research and innovation in the Faculty of Mathematics at the University of Waterloo. Stay tuned to this space for the next installment.