Over the years, University of Idaho math graduate student Jesse Oldroyd has developed a severe mistrust of threes. He likes fives much better, and feels that sevens are weird.
Oldroyd, a native to Anchorage, Alaska, has been at UI for four years in the mathematics graduate program. While attending the University of Alaska, Oldroyd originally planned to study Spanish — because he was not a fan of math in high school, but liked languages.
As an undergraduate, Oldroyd discovered his love of math in an algebra course. The class was focusing on solving equations, and he came across the formula x2 + 1 = 0. Until that point, Oldroyd had never been able to solve that equation.
His professor then introduced the imaginary number i. Rather than the idea that numbers could be imaginary, Oldroyd latched onto the idea that mathematicians could introduce something entirely new to solve a problem. He felt that imaginary numbers proved math’s potential to break the rules.
He switched his major to engineering for a little while, but it was just the math he found fun.
“I decided if I’m going to be doing something, I might as well be doing something I like,” Oldroyd said.
He then switched his major to mathematics.
He had discovered what many overlook — there is more to math than numbers.
“A lot of people describe math as poetry,” Oldroyd said.
Math attracted Oldroyd with its intuitiveness and ties to human history. Concepts dating back to Aristotle, Pythagoras and Euclid, even though they may be modified from their original form, are essential to modern mathematical studies.
Oldroyd said he could be an adrenaline junkie, because of math. The problem-solving aspect of math is like a difficult puzzle — inspiring hours of frustration before the light bulb goes off. Something clicks, Oldroyd said, and the click spurs a rush of excitement.
“Interest is what got me into math.” Oldroyd said. “But it is the problem-solving-light-bulb aspect that keeps me here at all hours of the day.”
The graduate student teaches Original Differential Equations and researches linear algebra — specifically equiangular tight frames. His research focuses on how signals are sent and received by systems — the kind of algebra used in signal reconstruction.
To transfer a signal, Oldroyd said, it has to be decomposed, transferred and then reconstructed using a mathematical object. Oldroyd spends his time figuring out when these tight frames exist, and, if they do not, if can they be approximated.
According to Oldroyd, the FBI uses a related concept to store fingerprint files and reduce the size of the data.
While equiangular tight frames are Oldroyd’s work, his fascination lies in another mathematical concept. Euler’s Identity, , has captured the graduate student’s attention ever since he saw it.
“The first time I saw that, my mind was blown,” Oldroyd said.
All of the numbers in the equation are incredibly different. There is no reason to believe they are related in any way, but Euler’s Identity puts them together into one formula. Each number represents a distinct idea: Euler’s number e represents the natural logarithm, i is imaginary, pi is an irrational number, 1 is the multiplicative identity and 0 is the additive identity.
“That is what really got me thinking about being a mathematician,” Oldroyd said.
Euler’s Identity is often extended to solve equations with imaginary numbers in an exponent.
Leonhard Euler, the equation’s creator, is Oldroyd’s favorite mathematician. According to Oldroyd, much of modern mathematics is based off of Euler’s work.
Oldroyd joked that theorems, numbers and many other concepts had to stop being named after Euler or math would be full of “Euler’s whatever.”
Euler’s Identity is often cited as an example of “mathematical beauty,” the idea that math can bring about aesthetic pleasure — much like the joy Oldroyd gets from working with numbers.
Written by Claire Whitley