At age 40, we don't care what they think of us.
At age 60, we discover they haven't been thinking of us at all."
On the Psychology Today site I found a series of fifteen outstanding and inspirational quotes about aging by Susan Krauss Whitbourne, Ph.D. It's well worth the time to read not only the quotes she chose, but the explanation she added to each one.
With the quote above from Ann Landers she wrote:
The guru of advice columns (along with her twin sister, Abigail Von Buren), Ann Landers reminds us that as people get older, they move away from the egocentric concerns of youth to the more realistic perceptions of midlife and older adults, who realize that they are not the center of the universe. As a result, older adults are free to do what they want, not constrained by what they construe to be the opinions of others (who themselves are thinking only about themselves).