The power of ridiculous persistence

Twin prime day

One challenge of certain problems in pure mathematics is that their discussions quickly stray beyond what most people can even comprehend, let alone add to. The starting premise may be elegant and easily described, while the next steps involve a jumble of symbols and intertwined theories that geniuses spend their careers trying to unpack. Some of them frustrate the best minds in the field for generations.

The twin prime conjecture is one such problem, and it was consuming the waking hours of an unassuming and unheralded mathematician by the name of Yitang Zhang.1

Zhang was a lecturer in mathematics at a university in New Hampshire, having landed there via a circuitous route after his upbringing in China. This included a few stops bumping around outside of academia, working in accounting and even helping with a colleague’s Subway sandwich shop while he struggled to find a relevant posting. Outside of his formal teaching responsibilities, he was privately grappling with a way to tackle the twin prime problem.

Prime numbers are those divisible by only themselves and 1, and there are an infinite number of them, a fact proven by the ancient Greeks. The twin prime conjecture extends this result to assert there are also an infinite number of prime pairs that are only 2 apart. No matter how deep you go into the universe of unimaginably large numbers, you’ll always find primes that differ from each other by exactly 2 (or some other predefined number, like 23 or 10,000). At least that’s the theory, as no one had come close to proving it and some doubted if it was possible.

For the lay person wondering what exactly the practical applications of such a finding would be, the answer is nothing at all, at least for now—the pursuit is simply part of humanity’s endless thirst for knowledge.2 For Zhang, the problem was a worthy goal in itself, one that he attacked with monk-like asceticism, spending 10 hours a day thinking about it, seven days a week, for four years.

In keeping with Zhang’s understated, methodical style, his eureka moment came without fanfare.

During a brief break from his teaching job, he was in a friend’s backyard in the mountains of Colorado thinking over twin primes.3 As if in a dream, the scaffold of a solution emerged from the cumulative reflections of thousands of hours, crystallizing in his mind without all the details but clearly enough that Zhang knew he had an answer. His major insight involved combining two previous techniques that mathematicians never saw how to integrate.

In keeping with academic convention, he worked out his findings in a tightly reasoned paper and quietly sent it off to one of the most prominent mathematics journals. The rest proceeded at lightning speed, at least by the standards of refereed publications read by a narrow specialist audience. While he hadn’t proven the twin primes conjecture down to the final distance of 2, he had done so for a gap of 70,000,000—and if that sounds considerably less impressive, just remember the upper bound was previously infinity.4

For Zhang this set off a flurry of activity, with near-instant acceptance of his article, a speaking tour to prominent universities to discuss his results, heavy media interest in a topic that rarely breaks into the public consciousness,5 plus a belated upgrade of his non-tenure track teaching position to a full professorship by an administration suddenly realizing what they were dealing with. The next year he was awarded a MacArthur genius grant, which along with national recognition carried a stipend worth $625,000.

Keep at it

In his classic management book Good to Great author Jim Collins developed the concept of the flywheel, an object which is hard to start moving and spins very slowly at first. With sustained effort it eventually starts to reinforce its action as its own momentum makes it easier to spin faster. By the end it accelerates exponentially, even though the input applied was level throughout.

Many problems similarly yield only to the continuous application of focused energy. The hasty strategic jumps of an unfocused leadership team kill momentum before it moves far enough down a path to have deep impact. Listicles and tweets provide truncated surface facts without the structural insights needed to tie them into a coherent framework. On a micro level, the flow-killing, staccato interruptions of technology and jumbled schedules combine to prevent progress on subjects that don’t yield to quick interventions.

What’s worse, surface indicators of movement can obscure the fact that real progress isn’t being made—we confuse activity with achievement. By the standards of his peers Zhang was a nonentity in the discipline. His list of published articles was minimal and reputation in the field so slight that much of the buzz around his seminal paper stemmed from the fact it came from an unknown.

In mathematics, as with many other fields, the easy problems have been solved. To meaningfully advance the state of the art now requires directed, intentional, committed effort. Zhang’s experience with the twin primes conjecture is instructive, even for those without a working knowledge of abstruse number theory. Whatever your discipline, consider two things:

• Align deep work with how you’re wired. Even among mathematicians Zhang appeared to be a rare beast. During his wilderness years Zhang chose to work alone, eschewing the typical collaboration that characterized others working on similar topics. His own department head didn’t know what he was spending his free time on. He was also blessed with an astonishing memory, such that the contents of specific conversations or random telephone numbers were filed away for instant access, as if his brain possessed its own Google search function.6 This came in handy when the answer called for synthesizing diverse strands of thought into a new approach. You may not possess the numerical genius of Yitang Zhang, but you can still contribute to developing a solution that matters in your domain.
• Accept that the goal is worthy, even if your dive returns empty. Many unknown mathematicians have labored with the discipline of Zhang for years on end, without any breakthroughs to show for it. Sometimes the result is simply discovering that certain paths are unfruitful. Since his fame Zhang himself has turned his attention to other, similarly complex theorems of mathematics, which he continues to work on quietly. He may not have another dazzling finding, but that is no preoccupation of his. Zhang cares little for fame, even less for money—the math is enough.

Significant impact requires corresponding commitment. What important problem are you working on, and how are you building momentum to solve it?

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References

The New Yorker had a long article on Zhang’s life story after his fame exploded.

Quanta reported the news after Zhang’s proof was first published. It also went deep on the technical aspects of the twin primes conjecture and subsequent advancements.

In his interview with Nautilus Zhang describes his relentless focus on the solving this problem.

Jim Collins describes his flywheel concept on his website.