Julian Zelizer, a CNN political analyst, is a professor of history and public affairs at Princeton University, and author of the forthcoming book, "Burning Down the House: Newt Gingrich, the Fall of a Speaker, and the Rise of the New Republican Party." The views expressed in this commentary belong to the author. View more opinion at CNN.

(CNN) Former President Jimmy Carter took a shot at presidential candidates Joe Biden and Bernie Sanders when he said on Tuesday that he couldn't have handled the presidency at the age of 80. Speaking at the Carter Center, the former President said he hopes "there's an age limit" to the job.

"If I were just 80 years old, if I was 15 years younger, I don't believe I could undertake the duties I experienced when I was President," Carter said.

Though Democratic candidates in the 2020 primary have sometimes tiptoed around discussing age, it becomes a legitimate question when Biden, 76, seems to struggle for his words, or makes outdated references like suggesting that black parents should turn on their record players to help improve their children's education. "Is Joe Biden 'Too Old?'" ran an Atlantic headline this July. The question has come up with President Donald Trump as well; the President's frequent verbal salads are often linked to concerns about his mental fitness.

Should old age matter in a president? After all, there is reason to be skeptical of the critics, especially if we think that 80 is the new 60. We have had presidents who were considered old at the time but nonetheless found success in the job. Ronald Reagan, who was 69 when he took office, was in his seventies when he negotiated a historic agreement with the Soviet Union and a series of bipartisan agreements, including on immigration and tax reform.

Despite concerns at the time about his memory, Reagan, who would later be diagnosed with Alzheimers, ended his second term with strong approval ratings. Dwight Eisenhower, 62 when he was inaugurated, kept the nation out of nuclear war and departed as one of the most successful figures to hold the position, even mounting an ambitious campaign, though unsuccessful, to cut domestic and military spending. George H.W. Bush, who was 64 when he took office, helped oversee a peaceful end of the Cold War while pushing a historic deficit-reduction package through Congress.

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