For as long as I can remember, I have been drawn to, consumed by, even obsessed with, ideas. I’m a meta-idea person, meaning I like to spend a lot of time thinking about the idea of ideas. I’m often accused of being “in my head.” Specifically, I’m fascinated by the design and structure of ideas.

Now, there’s been a lot written about ideas—how they stick, how they spread. But even bad ideas can stick and spread. Our struggling economy is in part due to bad ideas that stuck and spread quickly. I’m more interested in what makes a great idea.

For roughly the last six years or so, I’ve been on quest to track down a special breed of ideas: elegant solutions. The term “elegant solution” isn’t as mainstream as it should be. Scientists, engineers, mathematicians have long embraced the elegant solution, devoting their careers to explaining and expressing vastly complex concepts in the simplest possible terms, theories, and equations.

But to the everyman, an elegant solution is difficult to define. The dictionary doesn’t define it. It defines elegance, though, this way: “marked by concision, incisiveness and ingenuity; cleverly apt and simple, as an elegant solution to a problem.” That doesn’t really define elegance as much as it describes it. And it doesn’t really help us craft an elegant solution in useful, practical way.

And that was exactly my challenge six years ago, as I found myself utterly stuck. I was working closely as an advisor to a large and very successful company, and I was struggling in my effort to tell them what to do. What made it difficult was that an internal, informal mantra centered on the word elegant. It went: “When it comes to solutions, simple is better. Elegant is better still.”

I knew more what it wasn’t, by virtue of seeing and hearing certain ideas rejected. What elegance isn’t: confusing, wasteful, excessive, unnatural, hazardous, hard-to-use, and ugly. Those are the "seven dirty words" any one of which will qualify something as inelegant.

In the midst of my struggle, I read an December 2003 end-of-year essay by Jim Collins in USAToday, the last paragraph of which grabbed me, shook me, and completely changed how I viewed the world. It was one of those moments of epiphany, of clarity. It read:

“A great piece of art is composed not just of what is in the final piece, but equally what is not. It is the discipline to discard what does not fit—to cut out what might have already cost days or even years of effort—that distinguishes the truly exceptional artist and marks the ideal piece of work, be it a symphony, a novel, a painting, a company, or most important of all, a life.”

I suddenly realized that I had been looking at the problem in the wrong way. As is natural and intuitive, I had been looking at what to do, rather than what to not do. My new perspective not only allowed me to do my job and solve the problem of giving good advice, it did two other very important things.

First, it allowed me to define an elegant solution for myself in an accessible way: An elegant solution is one that achieves the maximum effect through the minimum means. And it allowed me to describe elegance more succinctly than the dictionary does. Elegance is the unique pairing of two often contradictory qualities: extreme simplicity and surprising impact.

Second, it sparked the journey I’m still on, and hope to be on for quite a while, that of chasing elegant solutions all over the world in any domain. We all reach for elegance at some level, and yet it so often exceeds our grasp. Just why that’s so is what I wanted to explore. And as if in response to the seven things elegance isn’t, there are seven lessons I’ve learned, which I’ll list as design lessons.

• Design Lesson #1: What isn’t there can often trump what is.
  As Lao Tzu once said, "Shape clay into a vessel, it is the space within that makes it useful." The use of white space in design is critical.
• Design Lesson #2: The simplest rules create the most effective order.
  Example: Sudoku. It has only one simple rule, but is a worldwide craze to put nine numbers in order.
• Design Lesson #3: Limiting information creates intrigue.
  Example: the smile of the Mona Lisa is seductive because the lines are indistinct.
• Design Lesson #4: Restraint and removal allows the receiver to collaborate.
  David Chase designed the last episode of The Sopranos without a traditional ending. Viewers created their own.
• Design Lesson #5: View limited resources as the source of innovation.
  Mohammed Bah Abba changed the world in northern Nigeria, a land without electricity, by creating a produce cooler from two clay pots separated by wet river sand, in effect becoming a refrigerator powered by evaporation.
• Design Lesson #6: Doing something isn’t always better than doing nothing.
  National Geographic adventure journalist Boyd Matson taught me an important lesson: stand still when the hippos charge. That’s a fairly elegant solution!
• Design Lesson #7: Break is an important part of any breakthrough.
  Neuroscientists have proven that your brain needs calm before its storm, not stress and pressure. That’s why your best ideas come in the shower, driving, or sleeping.

Keep these seven principles in mind as you begin crafting, shaping and sculpting your next great idea!

Matthew E. May is an innovation consultant and the author of In Pursuit of Elegance: Why the Best Ideas Have Something Missing. He blogs here. You can follow him on Twitter here.