"For in those days I was in the prime of my age for invention & minded Mathematicks and Philosophy more than at any time since."

An interesting pattern recurs across the careers of great scientists: an annus mirabilis (miracle year) in which they make multiple, seemingly independent breakthroughs in the span of a single year or two.

Einstein had his annus mirabilis in 1905. While he was still a patent clerk, he wrote four papers that revolutionized our understanding of the photoelectric effect, Brownian motion, and special relativity.

Newton’s annus mirabilis came to him between 1665 and 1666, when Cambridge responded to the Bubonic plague by sending its students home to quarantine. During that time, Newton, aged 22, developed the theory of gravity along with the language of calculus required to express it. He recalled of that year:

I began to think of gravity extending to the orb of the Moon & computed the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth … & found them answer pretty nearly. All this was in the two plague years of 1665–1666. For in those days I was in the prime of my age for invention & minded Mathematicks and Philosophy more than at any time since.

Many other great scientists - Copernicus, Darwin, von Neumann, and Gauss - also seem to have had an annus mirabilis.

Miracle years happen outside of pure science too. In his memoir, Linus Torvalds talks about how he spent the summer before turning 21 reading an operating systems textbook cover to cover, how later that year he built a terminal emulation program just for fun, and how he spent all his time working on this program until pretty soon it morphed into a full operating system called Linux. That was his annus mirabilis.

Even writers have miracle years. Just recently, the popular fantasy author Brandon Sanderson announced that in the year or two since the pandemic began, he has secretly written five extra novels in addition to the ones his fans knew he was writing. The kickstarter to access these secret novels has already reached $40 million.

So across a range of creative professions, but especially in science, high achievers tend to experience a year of extraordinary, career-defining productivity. How can we this explain remarkable pattern?

Explanations

Selection bias

If great discoveries are randomly distributed across the career of a scientist, then, with some non-negligible probability, they will fall within a year of each other. Which means that out of hundreds of great scientists, a few are bound to have a miracle year.

But Einstein, Newton, and Darwin are not just a random selection across the sample of important scientists - they are the Mount Rushmore of science. A pattern across the careers of these giants cannot be dismissed by saying, “Oh, it had to happen to somebody.” Even if they were the only scientists who have ever had an annus mirabilis, the phenomenon would still be among the most important in the history of science.^[1] 

In any case, it turns out that the miracle year goes far beyond this trinity of science. Yair and Goldstein (2020) show the existence of miracle years in the careers of Israeli ‘star scientists’, highly-cited physicists, and economists in an elite American departments. Their sample sizes are admittedly small, but so are the number of great scientists, and their results are consistent. They conclude:

On average, we find the annus mirabilis to be triple to four times higher than each scientist’s typical annual productivity (3.76 for Israeli Prize Awardees, 2.91 for highly-cited physicists, 3.16 for economists).

So the pattern of miracle years is probably real and not just a result of selection bias. How else can we explain it?

Right problem at right time

If you’re working on the right problem at the right time, you’re going to come up with a lot of important solutions really quickly. This is especially true if these solutions line up behind each other like in a tech tree. You need calculus in order to express gravity, so it’s no wonder that Newton was the first to discover both. Here they argue that Einstein’s papers on Brownian motion and special relativity follow naturally from the theoretical arguments in his first paper on light quanta.

In Kuhnian terms, you could say that the great scientists found a new paradigm and then spent a year gobbling up all of the important, low hanging discoveries before their competitors could catch up.

Youth and freedom

Perhaps there’s a brief window in a person’s life where he has the intelligence, curiosity, and freedom of youth but also the skills and knowledge of age. These conditions only coincide at some point in a person’s twenties. It wouldn’t be surprising if the combination of fluid intelligence (which declines steeply after your 20s) and crystalized intelligence (which accumulates slowly up till your 50s and 60s) is highest during this time. Stephan and Levine (1993) find that most Nobel laureates do their prize winning work in their late 20s or early 30s.

During his miracle year, Einstein was a patent clerk, Newton was a college student dismissed for quarantine, and Darwin was a trust fund kid who had just finished a long voyage aboard the HMS Beagle and still didn’t know what to do with his life. They had no obligations to research some old professor’s hobby horse using his particular technique or paradigm. They were Twentysomethings with a lot of time on their hands and nothing better to do.

Success brings obligations

Von Neumann showed remarkable productivity in his late twenties. Between 1927 and 1929, he published nearly one major paper a month. But after growing worried about the trend of politics in Germany, he left for Princeton’s Institute for Advanced Studies. Feynman said of this place:

I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever … Still no ideas come. Nothing happens because there’s not enough real activity and challenge: You’re not in contact with the experimental guys. You don’t have to think how to answer questions from the students. Nothing!

And then he got married and had a kid. Then World War II loomed over the corner, and the government had him doing research on ballistics and later on nuclear implosion devices - important applied work in a war, no doubt, but not the source of the kind of foundational ideas which make an Einstein or Newton.^[2] 

By this point, he was an aged senior by the standards of mathematical research and, worse still, he had gained influence (and thus time consuming commitments) on defense policy.

I can’t disagree with any one of these uses of von Neumann’s time individually. I can’t say that he should not have had a family, that he should not have helped us win World War 2, or that he should not have helped advise government research and strategy regarding the Cold War. But I find it tragic that, collectively, these obligations sapped away decades out of the short life of the greatest known genius in history and prevented him from working on the basic theoretical research at which he was clearly gifted.

Ken Thompson built the basic chassis of UNIX in a week when his wife went on vacation and he had a lot of time on his hands.^[3] Applied Divinity Studies responds to this anecdote:

How terrifying would it be if that was true? Is it possible that Thompson was burdened by responsibilities his entire life, and then in a brief moment of freedom did some of the most important work anyone has ever done?

Paul Graham notes that after Newton completed his work on optics, he spent the rest of his scientific career embroiled in feuds over who deserved credit for his discoveries.

After publishing his theory of colors in 1672 he found himself distracted by disputes for years, finally concluding that the only solution was to stop publishing:

“I see I have made myself a slave to Philosophy, but if I get free of Mr Linus’s business I will resolutely bid adew to it eternally, excepting what I do for my private satisfaction or leave to come out after me. For I see a man must either resolve to put out nothing new or become a slave to defend it.”

Sometimes these obligations come not from disputes, family, or career, but from attachment to one’s ideas. After developing general relativity, Einstein spent the rest of his life trying various dead-end solutions to the contradiction between his theory of relativity and the seeming non-locality and indeterminism of quantum mechanics.

There are so many distractions that come from being successful. The university wants you to become department head and serve on a committee or two. Some government panel wants you to advise them on a growing security threat. Now you’re getting handsome offers from startups looking for advisers, publishers looking for new pop-sci books, and online course platforms looking for celebrity teachers. A new paper comes out claiming to demolish a prominent result of yours from a decade ago, and you must respond. And then there’s aging itself, which brings family, dullness, and complacency.

It is worth noting that a few scientists like Feynman who made a point of avoiding scientifically irrelevant commitments were consistently able to produce important results decade after decade. In response to a draft of this post, Stephen Malina pointed out that John Bardeen, Fred Sanger, and Marie Curie also remained productive throughout their lives. I don’t know enough about them to figure out what they had in common, but my guess is that they avoided getting conscripted into these kinds of extracurricular duties.

Coda

I still don’t think I fully understand why these miracle years keep showing up in the lives of great scientists, except that it has something to do with them being young, concentrating intensely on the right problems, and remaining open to fresh perspectives.

Given how many of the great scientific discoveries have come about during miracle years, we should do everything we can to help smart Twentysomethings have an annus mirabilis. We should free them from rote menial work, prevent them from being overexposed to the current paradigm, and give them the freedom to explore far-fetched ideas without arbitrary deadlines or time-draining obligations.

It’s depressing that I have just described the opposite of a modern PhD program.^[4]

1. ^{^}

   Although Stephen Malina offered an interesting alternative hypothesis. He suggests that perhaps we have flipped the causality around here, and these scientists are so famous because they had a memorable annus mirabilis. I don’t think this is true - Einstein became widely known of after he developed general relativity, which was much after his 1905 annus mirabilis. And Newton and Darwin didn’t even release their discoveries until long after their early-20s science spree.

2. ^{^}

   For more, I highly recommend Ananyo Bhattacharya’s new book about von Neumann, The Man from the Future.

3. ^{^}

   See my review of Brian Kernighan’s UNIX: A History and a Memoir.

4. ^{^}

   Slime Mold Time Mold’s solution to this problem is the charter house.