"One of the lovely features of mathematics is when someone manages to show that it's impossible to know the answer to a particular question. Not that the answer is 'I don't know,' but the answer is 'there is no way anyone can know.' The first time I came across that, I was hooked."
Assistant professor of mathematics
As an assistant professor of mathematics, Adam Piggott finds an unusual source of joy in his discipline.
"One of the lovely features of mathematics is when someone manages to show that it's impossible to know the answer to a particular question," he said. "Not that the answer is 'I don't know,' but the answer is 'there is no way anyone can know.' The first time I came across that, I was hooked."
Piggott's specialty is Group Theory, which he explains is the study of the symmetries of objects.
"A symmetry of an object is a transformation you can perform to that object so that an observer can't tell that you did anything," he said. For example, a square looks the same before and after it is turned 90 degrees. "That's a symmetry of the square. Every object in the universe, whether it is a physical or an abstract object, has an associated set of symmetries - this is all the different ways you can look at this object so that it appears the same."
Studying those sets of symmetries is useful "because one way to find a link between two apparently unrelated things is to discover that their groups of symmetries are the same."
This brand of mathematics is a far cry from most people's memories of balancing equations in algebra or even wrestling with derivatives in calculus. While acknowledging that many people’s early experience of mathematics is focused on calculation, Piggott defines the true nature of mathematics as "establishing the truth of a statement, writing a proof, discovering what is true and why," he said. "That's what I mean by the true nature of math."
Whether students pursue a career in mathematics, make use of math's practical lessons as engineers, or follow another path, learning how to work through a proof requires precise logic and problem-solving skills that will serve them well as professionals and as citizens.
"The number one thing is it can help make them critical consumers of information," Piggott said. "Writing a proof requires you to expose your reasoning in as much detail as possible so that a reader can make up his or her own mind about whether or not this is true."
Posted Sept. 22, 2008