Trying to stay healthy into old age is a better goal than attempting to live as long as possible. Of course, no matter how hard we try, most of us will still fall ill at some point in our lives, whether because of genes or just bad luck. And people with chronic diseases “can have extremely meaningful lives even as maybe their physical capacity declines,” said Dr. Deborah Kado, a professor of medicine at Stanford University and a director of the Stanford Center on Longevity.

Perhaps even more vital than the number of years a person lives, in sickness or in health, is their attitude and the way they spend the time they do have. “How you decide to live, whatever your time horizon, is extremely important,” Dr. Kado said. “None of us have that much control, and so it’s really how do we address the challenges as they come at us.”

It turns out there’s science behind the old saw “the older you get, the wiser you are.”

Laura Carstensen, founding director of Stanford University’s Center on Longevity, says research has made surprising discoveries about the way older people view their lives. With fewer “what-ifs,” they appear to gain more clarity on their place in the world.

The number of Americans living to at least 100 is expected to quadruple over the next 30 years, to about 422,000 by the mid-2050s, according to the Pew Research Center.

Carstensen, who is 71 and a professor of public policy and psychology, says changes will be needed to make the most of those added years. She talked with The Wall Street Journal’s Future of Everything podcast about how we could rethink life’s traditional milestones.

“The first step before you take inventory of your body is to decide that you care about living a long, healthy life,” says Deborah M. Kado, a professor of medicine at the Stanford University School of Medicine and co-director of the Stanford Longevity Center. “But it’s worth taking this inventory only if you’re going to do something about it. Your attitude is important. You have to be saying to yourself, ‘I’m going to look aging in the eye because I want the truth about what’s going on with my body.’”