PHILADELPHIA — Jerry Jackson, a retired accountant, described the accumulation of losses that accompany old age in concrete, mathematical terms.

When he and his wife moved to Rydal Park, a Jenkintown, Pa., retirement community, they joined an informal breakfast group of about 10. “They were a great bunch of people,” said Jackson, who is now 90.

Seven years later, “I’m still in the same chair as when everybody was here, but there are only two of us left, and we eat at different times.” Among the empty chairs is the one his wife of almost 70 years occupied. She died in May.

Coping with the deaths of friends and family members and the inescapable knowledge that time is limited for remaining peers is among the great emotional challenges of aging. “It sucks, period,” said Dorree Lynn, a 77-year-old psychologist in Charleston, S.C., who recently lost two close colleagues. “It starts in your 60s and gets worse.” Not everyone can overcome it, but those who are resilient enough to navigate this dance with mortality well can find wisdom and everyday joy made sweeter by the depletion of time.

Thelma Reese, 85, Bella Vista neighborhood of Philadelphia

History: A retired professor of English and education, she coauthored The New Senior Woman and The New Senior Man and is working on another book about seniors.

Wisdom: She’s a believer in “doing things that take you out of yourself enough to widen your horizon a little” to improve mental health and prevent focus on the physical problems of old age.

It’s tough to lose old friends, either from death or growing apart. “You feel like you’re losing part of your history when they go.” New friends can listen to your stories, but you haven’t “lived and breathed it together.”

She is “extremely” conscious of her mortality and has been reading about psychologist Erik Erikson’s stages of development. His last stage (65 and up) is the age of integrity or despair. That resonates with Reese. Once you have a “sense of an ending,” she said, “it can either make you despair or make you think: ‘I’ve got to do something. I’ve got to get it done somehow.’ “

Interviewing other seniors who are leading active lives helps her open up. “I’m interested in these people because they’re doing things I’m not. I admire them. I find it encouraging that they’re in the world.”

There’s no doubt that many elders let their social world contract. “They sort of shrink into a box,” said Thelma Reese, an 85-year-old Philadelphian who has written books about aging. Scientific evidence that isolation and loneliness are harmful, both physically and emotionally, is mounting. “Being by yourself with the shades drawn and not interacting with other people can be deadly,” said Stephen Scheinthal, a geriatric psychiatrist who is chair of psychiatry at the Rowan University School of Osteopathic Medicine.

And yet research also shows that, as a group, older people in decent health score higher on measures of happiness than young and middle-aged adults. (Scores sometimes dip a bit as infirmities increase.) This is true even though deaths are not the only losses the aged face. Many have also lost their independence and professional prestige. Friends and family members have moved away or cut ties.

What allows some people to thrive emotionally at a time when losses are piling up like leaves under a maple tree in October? How do they find the courage to care when they have so much experience with heartbreak?

Virginia Sale, 90, Rydal Park retirement community

History: Sale was a Presbyterian minister like her husband. He died in 2015 of Alzheimer’s disease. They had lived and worked together for almost 60 years. She has outlived most of her longtime friends.

Wisdom: During her husband’s nine-year illness, she learned to find positives, even in their suffering. “What I discovered was that, in this daily struggle for both of us, we learned how much we loved each other,” she said.

After years of counseling others, Sale was surprised by how traumatic her husband’s death felt. She realized she had lost a part of herself that had belonged to the marriage. “When that bond is broken, there is part of you that’s missing, not just the loss of the person, the loss of the identity,” she said.

At 90, she asked herself, “‘Well, Virginia, you’re old. What are the possibilities?’”

“A lot of life is a matter of stops and starts,” she has learned, “and every time we grow.”

She decided she would stop feeling sorry for herself. “Somewhere along the way you say, ‘I am worth living for myself. . I claim myself.’”

After her husband’s death, she learned to make decisions for herself, without compromise. She redecorated. She plays bridge and works in the library. She takes walks. An introvert, a few friends are enough for her. She relishes the time she has to read. “I just love to learn,” she said.

Is she happy? “I’m at peace,” she said, “and that is the kind of happiness you can count on.”

“I live for the day,” said Marian Poole, 88, a Rydal Park resident whose husband died eight months ago. “I’m anxious to get up in the morning. I want to see what happens.”

Even for people who are outgoing, this takes work. Seniors who are thriving despite loss say they make a point of trying new things and meeting new people. They accept the possibility of failure, rejection, and pain. They cherish memories. They do not fear grief.

“A hunch that I have is that pain and joy are really located right next to each other in our heart,” said Rabbi Dayle Friedman, a chaplain and spiritual director whose Philadelphia-based practice is focused on serving people beyond midlife. “To be open to one, you have to be open to the other.”

Friedman’s sister died four years ago at age 61. Think of life, she said, as a half marathon. You start off with lots of other runners, but, if you take a long time to get to the finish line, the field thins out. “That really hurts. It can be lonely, and it can start to feel like you know more people on the other side than this side.”

Pat Killen, 76, Roxborough

History: A former dietary clerk at Roxborough Memorial Hospital, she was widowed at 52 and “thought my life was over.” She later dated an older man, but since his death has avoided romance. Depressed in retirement, she joined an exercise class at the Center at Journey’s Way, her local senior center, and started taking trips. She has taken voice lessons, joined a church choir, and volunteered in a church bereavement program where she helped families plan funerals. She helps older seniors in her neighborhood who have trouble getting out. She started a walking group. She has met most of her good friends since 2010 and says the friendships are deeper than her earlier ones. “I am having the time of my life.”

Wisdom: Killen goes out of her way to try new things. “Older people have to fight it a little bit rather than settle in.” She thinks virtual reality is “the coolest thing.”

Helping people at the end of life, she said, gives her strength. “I have accepted the fact that each of us, our days are numbered and just whatever time that I have with these people, I would make the most out of it and enjoy,” she said.