In 1963, a 10-year-old boy at Cambridge, England, stopped by a local public library while coming back from school and chanced upon a mathematical problem that greatly fascinated him. The problem statement looked quite simple. Even an elementary grade student knows about the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Based on this fact, it is possible to find infinite number of triplets (a, b, c) of integers such that a2+b2=c2. The problem that fascinated the boy was just an extension of this theorem to higher powers (such as squares, cubes etc.). He learned that someone named Pierre De Fermat in 1637 conjectured that no such triplets of integers (a, b, c) exist such that an+bn=cn for any value of n (an integer) greater than 2. He also found out that until then no one had been able to either prove or disprove this conjecture, famously known as Fermat’s Last Theorem.
The boy in later life chose mathematics as his field of study, completed his doctoral thesis from Clare College, Cambridge, and became a professor at Princeton University. His area of expertise was the arithmetic of elliptic curves. However, he remained passionate about his childhood dream—the dream of solving Fermat’s Last Theorem. So he secretly started working on this problem in 1986 without disclosing it to any of his co-workers. He confided about this mission to only one person—his new wife.
He worked tirelessly for seven long years and came up with a solution. However, a critical flaw was detected in the initial proof during the peer review process. But he didn’t lose hope and started working on the issue along with one of his students, Richard Taylor. Eventually in another year’s time, in September 1994, Sir Andrew Wiles succeeded in solving Fermat’s Last Theorem.
Building and Honing Expertise
This case study can establish the key factors required to build and hone expertise—especially in the fields of scientific research. To do this analysis, it is best to start with a quote from Sir Andrew Wiles himself. During an interview for a BBC documentary, author, journalist, and TV producer Simon Singh asked him what he felt about this process of solving such a hard problem to which he gave an analogy of the problem with the exploration of a dark mansion (Simon). Wiles said:
“You enter the first room of the mansion, and it’s completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of, and couldn’t exist without, the many months of stumbling around in the dark that precede them.” (Simon)
This exploration of the dark room is very similar to Coyle’s description of the activities of any individual involved in a “deep practice.” He refers to it as a “sweet spot” (Coyle, 19) where one works at the edge of his or her abilities, makes mistakes, and learns from them. In Wiles’ case, it was like “bumping into the furniture” (Simon) in a dark room. Like learning from repeated mistakes, one also would find the right way to the switch that can turn on the light and remove the darkness around. Then the explorer (in this case, the problem solver) would move to the next dark room and start all over again until eventually the entire mansion becomes illuminated (and the problem gets solved).
Two Key Elements: Grit and Self-Control
What else can we learn about expertise from this case? I think two more important elements that come out are “grit” and “self-control.”
Angela Lee Duckworth, a foremost expert on grit, defines grit as the “tendency to sustain interest in and effort toward very long-term goals” (Duckworth). Similarly, “self-control is the voluntary regulation of behavioral, emotional, and attentional impulses in the presence of momentarily gratifying temptations or diversion” (Duckworth). Sir Wiles clearly demonstrated extraordinary grit and self-control in the process of working toward the solution to a supremely difficult problem. In fact, there was no certainty that he would succeed in solving the conjecture in his lifetime. Almost all famous mathematicians in the last 350 years (including the likes of Carl Gauss and David Hilbert) had failed to crack it!
It is also interesting to note the original motivation behind such an attempt. Simon Singh, in his blog, noted, “Money, awards, and honor were not the driving force behind Wiles’ achievement.” In Wiles’ own words:
“This was my childhood passion. There’s nothing to replace that. I had this rare privilege of being able to pursue in my adult life what had been my childhood dream. I know it’s a rare privilege, but if you can tackle something in adult life that means that much to you, then it’s more rewarding than anything imaginable. Having solved this problem, there’s certainly a sense of loss, but at the same time there is this tremendous sense of freedom. I was so obsessed by this problem that for eight years I was thinking about it all the time—when I woke up in the morning to when I went to sleep at night. That’s a long time to think about one thing. That particular odyssey is over. My mind is at rest.” (Simon)
Success Factors
Based on this case study, we can say that to achieve extraordinary success, it is important to have the following traits:
- A burning passion toward the subject of interest—it should be so intense that one can derive happiness out of the work alone without any expectation in terms of money, awards, or fame.
- “Grit” and “self-control” to have a devoted focus over a long period of time on the task.
- “Deep practice” to relentlessly try on the edge of one’s abilities and be ready to face and overcome the challenges ahead.
Once a person becomes an expert in a field, he or she must be ready to extend the frontiers beyond what is state of the art at that moment. So an expert continues to venture into the unknowns and be comfortable with (in fact, also derive satisfaction from) the experience of working in the unknown. This, I think, is one of the most defining elements of expertise.
There are so many more things one can learn from this case study that it is difficult to exhaustively list all such learnings. However, the most important learning that gets reinforced time and again is the fact that the reward of any work is the work itself. Once someone has this mindset, everything else may easily fall in place. This was mentioned centuries ago in a Hindu scripture, called the Bhagavad Gita that says we must relentlessly perform our duties without any desire for results (“Bhagavad Gita,” Wikipedia).
This case study also raises several questions, including:
- Is passion toward work an intrinsic ability or can it be developed?
- Does passion toward work lead an individual to aspire to achieve difficult long-term goal(s)?
- Does “deep practice” accelerate the path toward success in scientific research?
One question I keep raising to myself very often is: “How can I manage my multiple long-term goals?”
The real-life story of Sir Andrew Wiles tells us how factors such as “burning passion,” “grit,” “self-control,” and “deep practice” play vital roles in the development of scientific expertise of the highest order. It also raises several questions that are worth exploring for further research. We are still just scraping the surface of our understanding of how talent and expertise can be built—hopefully someday, we will reach a state where we will be able to not only understand but also control the factors that can decisively enhance our ability to become experts in fields ranging from sports to music to literature to scientific research.
REFERENCES
Wiles, Andrew, Wikipedia. http://en.wikipedia.org/wiki/Andrew_Wiles Last modified June, 14, 2014.
Bhagavad Gita, Wikipedia. http://en.wikipedia.org/wiki/Bhagavad_Gita Last modified June 15, 2014.
Coyle, Daniel, “The Talent Code (London: Arrow Books, 2010; New York: Bantam Dell, 2009).
Duckworth, Angela Lee, Home Page, The Duckworth Lab. https://sites.sas.upenn.edu/duckworth. 2014.
Fermat’s Last Theorem, Wikipedia. http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem Last modified June 14, 2014.
Singh, Simon, “Who is Andrew Wiles?” http://simonsingh.net/books/fermats-last-theorem/who-is-andrew-wiles.
Pranab Chakraborty is a senior manager in the corporate Human Resources development team of Wipro Technologies. He has been associated with the it industry for the last 19 years during which time he gained extensive expertise in client engagement, program management, and delivery management roles. He is passionate about contextualization of learning using practical experience. He can be reached at pranab.chakraborty@wipro.com
