For most people, failure is limited to its definition: the nonperformance of something due, required, or expected. But plenty of successful entrepreneurs, including the late Steve Jobs and Sir James Dyson, believed that true innovation could only begin outside the realm of what's expected. Another believer in that theory is Wharton School professor Paul Schoemaker, whose latest book, Brilliant Mistakes, challenges the negative stigma often attached to mistakes and failure.

"The benefits of a mistake can be greater than the costs. Failure is simply a departure from expectations," he says. "Basically, it's the world telling you that you didn't see things in best way to begin with."

In January, the Wharton School held a contest, co-sponsored by Inc., asking readers to submit examples of their most brilliant mistakes. Take a look at the three winners, all of whom have examined their personal failure and have discovered deeper success.

The Deliberate Mistake: Matthew Lynch

In the late 90s, Lynch was working for a contractor that investigated Medicare fraud.

"At that time, we invested fraud via complaints, which took a lot of energy and rarely led to actual cases of fraud," he says. "Soon, the industry switched to a data-based system, which allowed us to mine a wealth of information on everything from billing histories to claim submissions from any time period."

Unfortunately for Lynch, his superiors felt there was only one approach to mining this data. Lynch was told to only look at activity that was higher than average--large, red-flag payments, for example.

"They thought it was a mistake to investigate activity lower than average. They thought it would be a waste of time," he adds.

So, Lynch decided to make a mistake. Despite discouragement from his bosses, he checked the lower spectrum of activity...and discovered a gold mine of fraud.

"These people had been clever enough to stay under the radar. And almost every red flag we found in that spectrum turned out to be actual fraud," he says. "If I hadn't checked, they would have gotten away with it."

Lynch, who is now a manager at a compliance process operations firm in Westbury, Long Island, eventually convinced his team and the higher ups that this was a valid and efficient way to find fraud. It became a best practice.

The Failed Experiment: Dr. Stephen Salzman

Salzman made an error at the beginning of his medical career that has stuck with him to this day.

During his fellowship training at Ohio's Western Reserve University in the mid-1960s, Salzman became very interested in cardiology. Soon, he had a hypothesis: Because athletes are known to have lower heart rates than the average person, those hearts must be less sensitive to the effects of adrenaline.

For months, a young Salzman tested his hypothesis on mice; one group of mice excersised and the other goup did not. The results?

"I realized at that moment I was not as smart as I thought I was. That failure informed the rest of my career."
—Dr. Stephen Salzman

When Salzman examined the mice, he was shocked to see he was not only wrong, but that the exact opposite of his hypothesis was true. The excercising mice were more sensitive to adrenaline.

"I realized at that moment I was not as smart as I thought I was," he says. "That failure informed the rest of my career."

Today, as a teacher at Olive View UCLA Medical Center in California, he passes on this lesson to his students.

"I always try to emphasize how important it is to know what you don't know," he adds.

The Unprepared Epihany: Laura Caldwell (a.k.a. Annie Banannie)

In 2004, Caldwell was a Colorado-based performer who spent summers putting on live shows for local libraries. 

"It was a comedy storytelling show that encouraged reading during the summer. I had these balloon props and a prepared story to perform in front of 200 or so kids," she says. 

But at one performance that summer, Caldwell made a huge mistake. 

"I showed up to a show with a bunch of balloons and no plan," she recalls. "Funny thing is I don't even remember why I didn't prepare. But I was in trouble."

So, she decided to wing it. She quickly made a bunch of random "twisty" shapes with her balloons and encouraged the kids to come up with a story line with her. She then created the balloon characters along the way. 

"It was like a lightbulb went off," she says. "I knew from the kids positive reaction that making my show more about creative storytelling was how I could improve my show."

After moving to southern California to marry her long-time beau (also a balloon artist!) in 2006, Caldwell has continued to grow her business from that fateful performance. 

"I now work with local schools here to incorporate State Educational Standards for Language Arts into a similar show that I do for school assemblies," she says. "I'm also just about to launch a new company that will provide an online community for children who want to write stories."