Mathematics as art | University of Nevada, Reno
Most people use math to do everyday things, like balancing their budget, designing gym workouts, or building bridges. But for many mathematicians, the beauty of mathematics outweighs its practical uses. For those who work in pure mathematics, this is considered an art form. The fields of number theory, knot theory, and group theory each contain unexplored worlds of possibility. For Emeritus Professor Jerry Johnson, the beauty of math is its main attraction.
“Almost all the math a person does has potential for use at some point, although you may have no idea what it’s going to be,” Johnson said. “People like me do math just for fun.”
“If you can imagine yourself as an explorer walking to the South Pole for the first time, excited about what you’re going to find there, that’s it.”
Srinivasa Ramanujan, a famous Indian mathematician, was a number theorist whose work, although he never knew it, would be relevant to the mathematics of black hole formation. But Ramanujan wasn’t doing the math to learn more about black holes. He did math to do math, like many mathematicians in the College of Science, including Johnson.
“A lot of the math we do isn’t applied math, it’s for its own good,” 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, Cambridge from India, was “absolutely opposed to any application of mathematics”, Johnson said. Hardy was also a number theorist. “He thought mathematics was all pure beauty and creativity and it would appall him to think there were applications.” Ironically, Internet encryption relies on number theory theorems. Without these theorems, online shopping would not be possible. “We’ve always joked that if Hardy were alive today, he’d cringe at the thought of his fine number theory being used for internet transactions,” Johnson said.
“The main motivation is just to explore these forms of beauty in the abstract,” said math professor Stanislav Jabuka.
Associate Professor of Pure Mathematics Ed Keppelmann agrees.
“Mathematical problem solving has become the mainstay of my life,” Keppelmann said. “We’re trying to show that there’s more to math than routine worksheets.” Keppelmann is part of the Nevada Mathematics Project, which aims to improve math and science education for children in Nevada.
Keppelmann hopes to inspire a certain sense of admiration in his math students, whether they are in elementary school or college. Mathematics hides in art. The reason National Geographic and Twitter logos are attractive is that they follow the rules of the golden ratio. The poetry is written in iambic pentameter, which gives a beautiful cadence to the poem. Mathematics hides in the fractals of nature like the deltas of rivers or the veins of a leaf.
As technology improves and brings quantum computing closer to reality, Keppelmann notes that computers are increasingly becoming an integral part of pure mathematics for proving theorems.
“We assume something works a certain way. We have computers doing the calculations,” Keppelmann said. But he points out that there are some things computers can’t do, like forming 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 the math 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 truths that exist but cannot be proven.
Johnson said 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 can be proven. In other scientific disciplines, a hypothesis cannot be proven but can be strongly supported. Mathematics has rules that must be followed. And these proven theorems that mathematicians come up with, which 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 pop the idea out of nowhere.
“If you can imagine yourself as an explorer walking to the South Pole for the first time, excited about what you’re going to find there, that’s it,” Jabuka said. “Some of these spaces, nobody’s looked at them 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 happens again.
Johnson differs from Hardy in recognizing the practicality of numbers.
“There are apps,” Johnson said. “Several faculty members in the department are applied mathematicians. They are interested in mathematics that applies to something in the real world. I can see both sides of it.
One such applied mathematician is associate professor of mathematics Paul Hurtado, who uses statistics and other processes to analyze patterns of ecology. He said the beauty of applied math becomes evident when he develops models, and sometimes the beautiful parts are in what he lacks.
“Sometimes it’s very enlightening not because you discover this wonderful, beautiful new thing, but you discover this void of knowledge that no one else has recognized as important, and it gives you something to fill” , Hurtado said. He also mentions that art benefits greatly from creativity, but creativity is not limited to art.
“The same way that once you know how to sculpt or paint, once you know the basics of math, you can do creative things with it,” Hurtado said.
Mathematics is often found in art, but many mathematicians believe that the math itself is art, the formulas are elegant, and the graphs are beautiful.
“You find these issues to work on and they become fascinating,” Johnson said. “You want to solve problems for themselves and so you can share it with your colleagues.”