Growing up, I always imagined that the kids with the greatest sheer intelligence were the ones most likely to achieve notable things in their lives, albeit in the narrowly scoped space of technical achievement. After all, this belief is continually reinforced through one’s experience in school: the “smartest” kids are, almost by definition, the quickest to break through a problem correctly. This experience continues nearly unerringly through college.

The surprising thing is that this very consistent linear trend fails to extend beyond traditional schooling: in industry or in a PhD program (which has the unfortunate misnomer of still being labeled a “school”), this extrapolation fails. People who go on to achieve maximally are often distinguished not by their raw intelligence but other factors. The questions then are: why and what are these other factors?

To continue with this discussion, I will put down my working definition of intelligence: the sample complexity of an agent to “acquire” a skill, where acquisition is deemed based on some accuracy measure on unseen tests of that skill. Intuitively, by this definition, I mean intelligence is the number of times examples of a particular activity must be shown or tried before it is learned.

Interestingly, there are a number of correlates of intelligence that we intuitively proxy for this underlying ability. One such correlate is mathematical aptitude: for some reason, even more so than other subjects, mathematical aptitude appeared highly predictive of intelligence. While seemingly arbitrary, this proxy is actually surprisingly not baseless: mathematical ability is synonymous with abstract reasoning, and abstractions are precisely how one can become more “sample efficient” through the transfer of learnings from one domain to another. This, somewhat unintuitively, is an important reason to learn math in school: while the exercise of factoring quadratic expressions is completely meaningless in a broader sense, it serves to develop the meta-skill of reasoning and pattern recognition that underlies intelligence more broadly.

Returning to the topic at hand, intelligence, therefore, amounts to learning speed. When concretely phrased, this ability would seemingly correlate strongly with achievement. The correlation is largely undeniable: those who achieve great feats, whether Newton, Marie Curie, Steve Jobs, Feynman, Bill Gates, or Grace Hopper, are often very intelligent. Yet, there were almost certainly people of equal or greater intelligence around them who achieved less: the question, as before, is why?

The explanation reduces to where achievement is born from. In certain domains, achievement is no more than the successful following of a prescriptive path: graduating from a prestigious medical school and running a clinic or becoming a Supreme Court judge. These are not the achievements I am focused on here; instead, I am talking about fields where achievements are, at least in part, characterized by novelty. In certain domains, novelty is critical to achievement; this is canonically true in scientific research, art, or startups, for instance.

To again provide a working definition, let us take achievement to be defined as the influence of a particular invention or discovery over the time horizon of all future times. For instance, the discovery of general relativity was a significant discovery not only for its sheer non-obviousness, but also its ramifications on the fields of physics, in the study of cosmological objects both theoretically and experimentally, and engineering alike. Achievement in domains of novelty, therefore, is more elusive: its definition is almost always only prescribable in retrospect, for, if a prescription could be given, there would be a clamour of people seeking glory, fame, or money pursuing such a path. For instance, if there were a recipe of “how to found a successful company,” more prescriptive than the vague, often vacuous advice given that is advertised as such, then every last person would be able to follow such a path to success. Obviously, however, such exact prescriptions are not possible.

As a result, the direction of inquiry becomes highly non-obvious. This is completely dissimilar to how school is framed growing up. In school, there is a clearly stated goal, and the task, in its best form, is simply to learn the material towards that goal as efficiently as possible. To make lasting achievements, in contrast, the directions to pursue are completely unknown.

This, then, is where the mismatch between intelligence and achievement arises from. If we view people as tunnel-boring machines in a dirt world of infinite expanse, the goal is to strike upon deposits of diamonds. Intelligence, then, is the horsepower of such a machine. If directed in a particular orientation, more intelligent people will go faster and, thus, discover the diamonds than others heading the same direction, but the more critical factor is in setting this initial heading.

The natural question, then, is how one can set this heading. This, however, is precisely the case of prescription discussed earlier: there is no way to answer this question in general. However, one general property is that the greatest achievements require “burrowing” a substantial distance before reaching the point of achievement. This means that a persistence in pursuit of a direction is often much more predictive of success than sheer intelligence.

This persistence is often born of a combination of intrinsic curiosity and self-confidence and is the far more common theme underlying success. Some examples: Jennifer Doudna and Emmanuelle Charpentier discovered CRISPR not from any prescriptive sense that it would arise from the study of bacteriophages but just from an intrinsic curiosity of how bacterial immunity works; many years of study were spent away from the limelight just in pursuit of this knowledge for its own sake. Similarly, much of the history of deep learning was shrouded not only in ignorance but outright hostility from the rest of the space of computer science; Geoffrey Hinton and Yoshua Bengio spent countless years to pursue this direction not for clear foresight that this would yield the remarkable achievements we see nowadays but largely of a curiosity of how this approach works and could be improved. The founding of Pixar was much the same: despite having the dream of making an animated movie in the mid-1980s, Ed Catmull and team had to work through nearly a decade of development of technical development before actualizing this vision in 1995. Critically, this decade of development was not viewed by the team as something to be “put up with” to reach the goal, but rather as an inherently satisfying piece that, even had the goal not have panned out in 1995, would have been an inherently worthwhile experience.

The conclusion, therefore, is that, while intelligence accelerates progress, it is often the setting and pursuit of a direction that are far more critical for success: achievement is the ability to direct intelligence consistently in a particular direction, which amounts to being psychologically bought into pursuing said direction over long stretches of time. To summarize, then, cultivate a curiosity and pursue it.