Genius. Some view it as an inborn gift, perhaps combined with a stroke of luck that strikes at just the right time. Many others see it as something completely outside our control and not likely to happen to any one person.

Others imagine that perhaps it can be manufactured—learned, even―by unlocking the secrets of those who have come before. A belief that fuels an entire self-help industry.

Researchers, like the rest of us, have long sought to explain the origins of talent and innovation. And while there is still no guaranteed method for pulling Earth-shattering, fail-proof ideas from the ether, science has begun to shed light on some possible means of, at least, maximizing productivity and opening the door to creative insight.

But most of the gimmicks you’ve heard about, they say, probably don’t work. The path to maximum mental functioning is likely both simpler—and much more difficult—than most of the silver bullets found on today’s market.

There are three basic mental states that lead to success in business, according to Holly Strokes, a Salt Lake City-based hypnotherapist known as The Brain Trainer. The creative mindset is necessary for envisioning new ideas, realism is essential for implementing ideas in feasible ways, and the internal critic is useful for identifying and solving problems.

All three are necessary to launch a business venture. But while society often gets caught up in the worship of the creative process, Ms. Strokes says that in her experience, it’s not the brainstorming phase that troubles most entrepreneurs.

“Your mind is full of all these million dollar ideas,” Ms. Strokes says. “The problems is, we have all these ideas, but then how many of those ideas do we follow through on?”

Ms. Strokes believes most would-be entrepreneurs “shoot themselves in the foot” with habits that engage the critic mindset too early and leave too little time to allow the realist to put a creative vision into practice. The solution, she says, is to examine—and rebuild—your mental habits.

“A lot of those brain habits have to do with messages we picked up through years of schooling, or even through our experiences,” Ms. Strokes says. “Maybe we tried something and it didn’t work out, and now our brain says, well, nothing will work out.”

People who tend to get stuck in these dubious, self-critical mindsets tend not to be innovators, she says, because they don’t ask themselves the right questions. Instead of asking themselves questions that point toward success—questions such as, how might I solve this problem?—they ask themselves what might go wrong.

Whichever question you ask yourself, she says, your brain is going to find an answer. People who achieve success typically cultivate a positive attitude that focuses more on opportunity than on risk. Perhaps the key to genius, she says, is first believing that you could be one.

“Most of the blocks to our ability to create come from our own mind—what we’ve been taught about who we are, and what’s possible for us,” Ms. Strokes says. “Our mind tends to generalize some of these ideas: if I failed on a test, that means I’m going to always fail. However, we can promote positive beliefs: oh, I’ve had this success and this success. The more you look at how you’ve been successful, the more it opens up the possibility of success.”

Sound too good to be true? While it may not be possible to directly will success into being, the notion of using positivity to train one’s brain for better performance does have some scientific merit.

Participants in a three-month-long meditation retreat improved their attention span and other mental abilities, says Anthony Zanesco, a post-doctoral associate in the University of Miami’s psychology department. Somehow, getting away from it all and meditating for eight to ten hours per day improved the human brain’s ability to stay focused—and the benefits remained intact four years later when Mr. Zanesco and his team followed up with the study’s participants.

Mr. Zanesco is now experimenting with teaching members of the military to meditate, and finding similar results. Learning to be aware of one’s thoughts—a meditative practice called mindfulness—improves the soldiers’ mental performance.

The military program, unlike the meditation retreat, allows very little time for mental training, and so Mr. Zanesco’s current work involves comparatively simple exercises. His team may have the soldiers sit or lay quietly with their eyes closed and ask them to pay attention to their breath as it flows in and out. Whenever their mind wanders or they begin to think about a task or stressor, they’re instructed to direct their attention back to their breathing.

Why does this type of mindful meditation improve brain function? Scientists aren’t sure. But Mr. Zanesco believes it may be tied to a theory known as brain plasticity.

Scientists once believed that certain traits, like intelligence and personality, were essentially fixed by the time a person reached adulthood, Mr. Zanesco explains. But they now know that’s not true, the brain is constantly rewiring itself to adapt to an individual’s environment and thought habits.

Today’s modern society of electronic notifications and instant gratification has programmed our minds for impatience and made focusing more difficult. Meditation, on the other hand, trains the brain to focus through daily practice, potentially reducing mental wandering in the future.

In a military setting, this increased ability to focus helps soldiers stay on task in perhaps the most stressful, distracting setting of all—war. But how do you apply this to business?

Imagine an entrepreneur who is preparing to pitch his idea to investors, Mr. Zanesco says. The amount of time he spends preparing his pitch deck will have a direct impact on his success. But even if he locks himself in a room to focus on his task, there’s the potential his own mind will distract him with thoughts of, say, what might go wrong during the pitch.

Mindfulness, Mr. Zanesco says, may help teach the brain how to set those kinds of thoughts and worries aside so that “you’re pointing your attention in the direction of your goals.”

But it’s different from simple positivity or visualization methods. Mindfulness is more related to, “your goals right there in the moment. What you’re doing right now, let’s keep the focus on right now. Big, nebulous, lofty goals tend to be detrimental psychologically and hard to stay focused on and to achieve.”

This isn’t to suggest that mindful meditation is a cure-all, grand secret to success and productivity. The reality, Mr. Zanesco says, is that the mental improvements identified by his research are relatively small. They affect different people to different degrees, and they all require diligent, continued practice.

The participants in the retreat study did successfully re-train their brains but, Mr. Zanesco points out, they actively practiced meditating for eight to ten hours a day and continued to practice for an average of one hour per day in order to achieve the benefits his team measured. The military experiment involves shorter periods of practice, which have resulted mostly in small productivity gains.

Mr. Zanesco compared the differences between two groups of athletes. The retreat group was already adept at meditating. Like an Olympic athlete, they understand how to achieve peak fitness at just the right time. But further gains in mental fitness could be, for this group, difficult to achieve—and just maintaining their current level of fitness takes hours of dedicated training. The military group, on the other hand, are the mindfulness equivalents of couch potatoes.

“If you’re a couch potato and you start running, you’re going to see some improvements,” Mr. Zanesco says. Meaningful mental change is “probably possible, but like anything that leads to meaningful change, it probably takes a lot of effort.”

It’s also unclear what, precisely, is causing the brain to change, says Clifford Saron, another research scientist at the UC Davis Center for Mind and Brain. The retreat was a three-month, multifaceted experience. Did participants benefit from the meditation itself, or did other factors, such as spending time with like-minded people, or leaving the cell phone and email at home also contribute?

In the case of the retreat study, Mr. Saron points out, the individuals who showed the most improvement were those who, when they began the retreat, tended to be high-strung and pessimistic. The question, then: did the retreat improve mental function, or heal the damage associated with chronic stress and distraction?

When people talk of wanting to “hack,” their brains, Mr. Saron says, they tend to forget they’ve already been “hacked” by the environment and by their interactions in ways they’re not aware of.

Mr. Saron believes that the community element—the fact that these practitioners engaged in a retreat together—also had a positive impact on brain function. It’s not just about taking care of yourself, he says. Humans need a sense of community that comes from caring for others, and being surrounded by people with a concern for their own well-being.

When these needs are met, Mr. Saron suggests—that’s when people are able to unlock their brain’s true potential. “Life is not so complicated,” he says. “What you just need healthy relationships, enough sleep, exercise and good nutrition, and some feeling of purpose.”