Based on this pattern, one might assume that once you pass this early career stage, your chances of making a breakthrough drops precipitously. Einstein, who developed his theory of special relativity at the tender age of 26, put it bluntly: “A person who has not made his great contribution to science before the age of thirty will never do so.”

Yet as we show in a paper recently published in Science, our ability to have a creative breakthrough does not diminish with age. It is our productivity and will to keep trying that decline, not our creative potential. For those who stick with it, success can come at any point in their career, and if they keep trying, it can return over and over again.

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Our understanding of creativity comes mainly from studies of recognized geniuses. Studies conducted in the 1980s by psychologist Dean Keith Simonton, who inspected the careers of 2,026 notable scientists and inventors from antiquity to the 20th century, found that most of them made their mark on history around the age of 39, bolstering the contention that youth equals creativity. Benjamin Jones, an economist who analyzed 525 Nobel Prizes between 1900 and 2008, saw a slight increase in the age of winners across the years, rooted mainly in the increased schooling as time passed.

We took a different tack. The long-standing focus on genius prompted Professor Roberta Sinatra and me to ask: When do bursts of creativity happen in not just extraordinary but also ordinary scientific careers? We thought this would give us better insight into the effect age has on creativity at large, as opposed to just creativity in extreme and unusual careers.

We inspected the careers of tens of thousands of scientists in disciplines ranging from physics to math, biology to computer science. Our results confirmed the decades of research on creativity: Most scientists published their defining work within two decades of the start of their scientific career. In other words, geniuses and everyday scientists alike cease to be creative by the third decade of their career.

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When we asked why, however, we stumbled across something unexpected. First, we found that productivity — the number of papers published by an individual — has the same early peak as creativity. We scientists are not only the most creative in the first two decades of our careers; we are more productive as well. This made Roberta and me suspicious about the roots of our creative success: Is it because we are young, or is it because we simply buy more raffle tickets during those early decades?

We next arranged every paper the scientists had published in chronological order, asking if the highest impact paper was among the earliest of each person’s career, somewhere in the middle, or perhaps among the last. In other words, we took age and productivity out of the equation, viewing each paper as another attempt at a breakthrough.

And there lay something unexpected. The highest impact papers were rarely the scientists’ earliest ones. Instead, the biggest hits were completely random: They were just as likely to be a first work as a last one, or anywhere in between.

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Our surprising conclusion: Fresh-faced thinkers disproportionately break through not because youth and creativity are intertwined but because they produce more work early in their career. Indeed, 30 years into a scientific career there is a sixfold drop in productivity compared with productivity at any time within the first 20 years. Hence scientists’ early success has little to do with the vibrant ideas they bring to the stodgy establishment. Rather, undeterred by disinterest or failure, young people try again and again.

These results are good news for those of us with graying hair. Sure, success can come early, as it did for Frank G. Wilczek, who received the 2004 Nobel in physics for the very first paper he co-authored as a graduate student. But it can also come later, as it did for this year’s Nobel winner in physiology or medicine, Yoshinori Ohsumi, who was 48 when he made his breakthrough. In fact, it can even come very late, as it did for John B. Fenn, a chemist whose Nobel-winning discovery came after Yale shut down his lab when he turned 70, the mandatory retirement age then.

Equally important, our data show that if you were fortunate enough to have had that coveted early-career breakthrough, there may be more to come. Einstein, despite his age-of-30 admonition, was 59 when he published his finding on quantum entanglement, his most cited work today. And our finding is likely not limited to scientists. Steve Jobs, for example, may have founded Apple at 21, but the company’s most commercially successful innovations — the iMac, the iPhone — came only in his 40s and early 50s.