Most people use math to do everyday things, like balancing their budgets, designing gym workouts, or building bridges. But for many mathematicians, the beauty of mathematics outweighs its practical use. For those who work in pure mathematics, it is seen as an art form. The fields of number theory, knot theory, and set theory each contain unexplored worlds of possibilities. For Professor Emeritus Jerry Johnson, the beauty of mathematics is its main attraction.
“Almost every math a person does has some potential to be used at some point, even though you may have no idea what it will be,” Johnson said. “People like me do math just for the pure joy of it.”
“If you can imagine yourself as an explorer walking to the South Pole for the first time, being excited about what you will find there, you are.”
Srinivasa Ramanujan, a famous mathematician from India, was a number theorist whose work, although he would never know, would be important to the mathematics of how black holes form. But Ramanujan wasn’t doing the math to learn about black holes. He did mathematics to do mathematics, like many mathematicians in the College of Science, including Johnson.
“A lot of the math we do is not applied math, it’s for its own sake,” Johnson said. “It’s almost like philosophy. It’s not necessarily applicable to anything, it’s just beautiful and creative and neat and you love doing it.”
Mathematician GH Hardy, who brought Ramanujan to Trinity College in Cambridge from India, was “absolutely opposed to any application of mathematics”, Johnson said. Hardy was also a number theorist. “He thought mathematics was just pure beauty and creativity, and it would terrify him to think that it had any application.” Ironically, Internet encryption relies on theorems from number theory. Without these theorems, online shopping would not be possible. “We always joked that if Hardy were alive today, he would just be troubled by the idea of using his beautiful number theory for online transactions,” Johnson said.
“The main motivator is just exploring these forms of beauty in the abstract,” said mathematics professor Stanislav Jabuka.
Associate Professor of Pure Mathematics Ed Keppelmann agrees.
“Mathematical problem solving became a cornerstone of my life,” Keppelmann said. “We try to show that there is much more to math than routine worksheets.” Keppelmann is part of the Nevada Math Project, which aims to improve the math and science education of children in Nevada.
Keppelmann hopes to inspire a sense of awe in his math students, whether they’re in elementary school or college. Mathematics is hidden in art. The reason why the National Geographic and Twitter logos are attractive is because they follow the rules of the Golden Ratio. The poem is written in iambic pentameter, which gives a nice cadence to the poem. Mathematics is hidden in nature’s fractals like river deltas or veins in a leaf.
As technology improves and brings quantum computing closer to reality, Keppelmann notes that computers have become increasingly integral to pure theorem-proving mathematics.
“We assume that something works a certain way. We have computers that do the calculations,” Keppelmann said. But he points out that there are some things computers can’t do, like form an idea that leads to a hypothesis. “Computers don’t think like that.” It takes a mind to formulate an idea out of thin air, to find mathematics in nature or the laws of physics or a pattern.
Mathematics also appears in philosophy. A notable example that Keppelmann gave was Gödel’s famous theorem, which states that in any system where a set of truths is identified, there will always be some truths that exist but cannot be proven.
Johnson said that once you find an answer to a math problem, it usually leads to even more questions. “It’s like science that way.”
Mathematics is unique among the sciences in that its theorems are provable. In other scientific disciplines, a hypothesis cannot be proven, but it can be strongly supported. Mathematics has rules that must be followed. And those proven theorems that mathematicians come up with that can take centuries to solve have been there all along.
“The math was there, waiting for someone to need it,” Keppelmann said. Waiting for a mind to pluck the idea out of thin air.
“If you can imagine yourself as an explorer walking to the South Pole for the first time, being excited about what you will find there, you are,” said Jabuka. “Some of these spaces, no one has studied before. You can look at them and say, ‘Oh, look at this wonderful property that I discovered that we didn’t know this space could have.’ It still happens.”
Johnson differs from Hardy in that he acknowledges the practicality of numbers.
“There are applications,” Johnson said. “There are several faculty members in the department who are applied mathematicians. Their interest is in mathematics that is applicable to some real world thing. I can see both sides of it.”
One of those applied mathematicians is Associate Professor of Mathematics Paul Hurtado, who uses statistics and other processes to analyze patterns of ecology. He said the beauty of applied mathematics becomes apparent when he’s developing models, and sometimes the beautiful parts are in what he’s missing.
“Sometimes it’s very enlightening not because you discover this wonderful, beautiful new thing, but you discover this knowledge gap that no one else has recognized as important, and it gives you something to fill,” Hurtado said. He also mentions that art benefits primarily from creativity, but that creativity is not limited to art.
“In the same way that once you know how to sculpt or paint, once you’ve got the basics of math under your belt, then you can do creative things with it,” Hurtado said.
Mathematics is often found in art, but many mathematicians think that mathematics itself is art, that formulas are elegant and graphs are beautiful.
“You get to work with these problems and they become fascinating,” Johnson said. “You want to solve problems for their own sake, so you can share them with your colleagues.”