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7 Creativity Tips From a Top Mathematician

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As an undergraduate, I studied calculus and physics; when I became an artist, I remained fascinated with the question of what artists and mathematicians can learn from one another. That's why I wanted to talk with mathematician Steven Strogatz, the New York Times columnist and author of the new book, The Joy of X. It's a juicy read, whether you're working through one of its gripping case studies with a pencil or leisurely perusing a chapter during a long, hot bath. In our conversation, we talked about ways that math and art are alike, and how adopting the right mindset can lead to breakthroughs in creativity. Strogatz, who has experimented with making drawings and is coincidentally married to an artist, says the professions definitely share affinities: "We're all trying to express ourselves. We're also struck by the wonder in the world around us." Here are Strogatz's top insights about the creative nature of mathematics, which are relevant to any creative person.

1. The pleasure lies in participation. Says Strogatz, "You can get a certain amount of pleasure as a mathematical spectator, reading and watching some of the most beautiful arguments that have been created in the history of humanity. But that's too passive." He's a believer in the value of everyone -- even non-professionals -- grappling with math problems. Says Strogatz, "It's not meant to be easy." Similarly for artists, the process matters: when you visit a museum, sketch from paintings to actively work through their components and download visual concepts for later use. And artists who paint primarily from photographs can also make preparatory drawings and paintings from life. It's more work, but your results will look both richer and more effortless.
2. Choose your path with savvy. If you're going to devote time to something, you want it to be meaningful. "Look for something with a big payoff," says Strogatz. "Make this process part of your style of working." Whether you're solving a math problem, starting a new painting, or looking for an entirely new direction as an artist, take things that interest you and play with them in a loose way. Sooner or later you'll find a unique and intriguing path that holds the potential for a major breakthrough.
3. Love your problems. Everyone faces difficulties in their work. But instead of running away from them, says Strogatz, you should embrace them. "It's more than understanding the problems or conventions; it's making them your own," he says. "When you love a problem, its contours, obstacles and resistances are all just part of its character." When I paint cross-sections of ships and buildings, it's a challenge for me to create cohesive narratives and themes from the dozens of vignettes in the rooms. But the difficulties in your work can fan your desire.
4. Go nonverbal. Intuition is real, but you can't always muscle your way toward it. Says Strogatz, "Mathematicians can get a big sketchpad and go without words and equations like my former teacher Art Winfree." For artists, this could mean doodling without preconceived ideas. Strogatz says, "we are told to be rigorous, with no mistakes or unstated assumptions. But geniuses don't work that way. Their thinking is loose and amorphous."
5. Play strategically, and play often. The mythic "accidents" that lead to breakthroughs don't just randomly happen. You have to already be playing around with the idea to identify a good result when it materializes. A famous "aha" moment came to Alexander Fleming, discoverer of penicillin, while he was cleaning up spilled petri dishes. But it wasn't really an accident: he was already setting aside hours a week to play with the bacteria, thus gaining a better understanding of it. He was even painting with the stuff. Playing is an essential part of gaining a thorough understanding of your problem.
6. Flow, interrupted. Mathematicians and artists lead similar lives, because math is a kind of art. We get distracted by our conundrums and forget to bathe. We play with our food, looking for answers. And most of us spend our working days alone. The best part is when we lose our sense of time and the right side of the brain feels cranked up and creativity seems effortless. Says Strogatz, "You're trying all kinds of things, and nothing works. Then you find a passageway forward and there is definitely a feeling of flow, until you get to the next place where you're stuck. I wish I could say there's a lot of feeling of flow in math but I find it's mostly flow interrupted by frustration." There can be a lot of obstacles, and much of the time you won't know what to do so it could make you want to quit. Says Strogatz, "When you're enamored with a question and you really want to know the answer, there's something in you that makes you not give up."
7. Keep your fighting spirit. In solving a difficult challenge -- whether mathematical or artistic -- it's easy to get frustrated. Sometimes, grappling with the mystery and essence of the problem may even feel like a violent impulse. "When you create something new," says Strogatz, "you're breaking tradition -- which is an act of defiance."

In my conversation with Strogatz, his favorite theme was about loving your chosen problems. For artists and mathematicians, it can feel like the real problem is with our abilities, but we should remember the difficulty lies in the amazing feats we attempt. Says Strogatz, "We're curious, sure, but we can glimpse something beautiful and want to know more."

Watch Strogatz's inspiring TED Talk where he shows how flocks of creatures (like birds, fireflies and fish) manage to synchronize and act as a unit -- when no one's giving orders.