This past week, former President Jimmy Carter announced that his skin cancer has metastasized to his brain and other parts of his body. The 39th president is undergoing immunotherapy, which is considered the vanguard of treatment for the disease.

Now, the nation — and much of the world — is watching, waiting, and praying for his recovery. Carter said he was "surprisingly at ease" when he received his diagnosis. Perhaps part of that serenity comes from the knowledge of the good works he has done in his life, including his many accomplishments during the years of what's commonly characterized as "old age."

Of the many reasons that the world is a better place thanks to Carter, his productivity in later life has inspired me the most. Carter has shown by example that old age can provide the most defining decades of one's lifespan.

The 91-year-old former president and his 88-year-old wife Rosalynn Carter's list of achievements includes contributions to the field of aging, dating to both Carter's term in office and afterward. While president, Carter signed into law the creation of the National Institute on Aging, a vital part of the National Institutes of Health that has added greatly to our understanding of, and improvements in, human aging. His wife of 69 years, Rosalynn, has been among the first and most articulate advocates of family caregivers and their needs.

Meanwhile, during his "old age," Carter's rigorous schedule of international diplomacy, charitable work (including, but not limited to, his dedication to Habitat for Humanity), religious education outreach, public speaking, and book authorship has seemingly become more demanding with each passing year.

His example is especially meaningful in the context of the current-demographic longevity revolution, which has added 30-plus years to the average American life since 1900, a trend that stands to continue. As we live longer, more of us reach old age, and birth rates slacken, a question in health, social, and aging policy circles has developed: How old is "too" old? When, the thinking goes, is aggressive treatment of disease, especially terminal conditions, appropriate? How much should "we" (presumably meaning individuals, families and society) invest in those advanced in years and with advanced disease?

Dr. Ezekiel Emanuel articulated this school of thought in a recent article in The Atlantic titled "Why I Hope to Die at 75." Physician-turned-philosopher Emanuel writes:

By the time I reach 75, I will have lived a complete life. I will have loved and been loved. My children will be grown and in the midst of their own rich lives. I will have seen my grandchildren born and beginning their lives. I will have pursued my life’s projects and made whatever contributions, important or not, I am going to make. And hopefully, I will not have too many mental and physical limitations. Dying at 75 will not be a tragedy.

In fairness, Emanuel is nowhere near making a Logan's Run-esque argument for euthanasia at a set age. However, he is suggesting that 75 may be the time when most of us are officially over the hill: the moment when our years of making a contribution and experiencing love are behind us, while years experienced through only depleted physical and cognitive capacities stretch out before us.

Carter stands as a sterling example of how wrong this approach can be. Yes, as a former United States president — the most select and smallest of clubs — he in no way represents any kind of norm. But that's precisely the point: thanks to his high visibility, Carter has redefined aging, and now certain types of cancer in old age, in the public mind. At 91, he is busy by anyone’s standards. He finished this summer's tour in support of his most recent book, A Full Life: Reflections at Ninety, despite an earlier cancer diagnosis. And even after his most recent diagnosis, he taught Sunday school for 45 minutes this week — something he does 40 Sundays a year. Despite age and cancer, he has significant future goals. If his physicians approve, Carter hopes to travel to Nepal in November to build houses for Habitat for Humanity.

It is true that Carter is an epidemiological anomaly in terms of his contributions to society as well as the demographic norms of his cohort. Few of us will write a book, especially not in our ninth decade, but Carter just finished his 29th, at age 91. Few will build homes for the poor in countries two continents away, or battle such public health scourges as the guinea worm, let alone do so in their 70s, 80s, and 90s. But thanks to Carter, we all now know that such later-life contributions are possible.

At the same time, neither science nor public policy has developed the means to know at what age all grandfathers are capable of telling their last joke to a grandchild, or when all grandmothers will have rolled their last meatball. Moreover, we do not have the tools to determine what we individually consider and experience as quality of life. Science and policy may be informed by data and facts. However, unlike scientists and policy wonks, the public learns from — and bases their expectations on — stories. Carter is a character in an important story, rich with lasting and emotional imagery. He is someone that everyone feels they know: Carter and his wife Rosalynn have worked for decades to make their lives more personal than distant to all of us. His life in advanced age is creating a new narrative about how we might live and confront disease, even in our 90s. Suddenly, living far longer than our parents is expected, not out of the ordinary. Battling advanced cancer in our ninth decade is not only possible, but also (possibly) appropriate. And, with all deference to Emmanuel, maybe, just maybe, 75 years old may be at least 16 years too early to declare life complete.

As Carter said while teaching Sunday school this week, "I'd like for the last guinea worm to die before I do."

MIT AgeLab’s Luke Yoquinto contributed to this article.