In today's world, we often praise experts with deep, specialized knowledge, but what about those who excel across multiple fields? These "polymathic" individuals, who bring a wealth of experience and intellectual range, are the ultimate connectors—bridging ideas between disciplines and sparking new, innovative solutions. Jeff Hulett makes a compelling case for why these versatile thinkers are more valuable than ever. As we dive into how “smart” is defined, the unique talents of polymaths, and why we need them alongside specialists, this article offers an eye-opening perspective on the power of having range in a hyper-focused world. Curious to learn more? Let’s explore!
Table of Contents:
What Makes Someone Smart? - A fresh take on how to define "smart" in both personal and market-driven ways.
Skiing Down the Smart Slope - A look at the curve of mastery—what it means to move from generalist to expert, and where polymaths fit in.
Why Range Matters - Discover why individuals with broad expertise are crucial for connecting ideas and driving innovation.
Conclusion - The case for embracing generalists in a world that often pushes for narrow specialization.
Notes - Supporting references and deeper insights into the topics discussed.
About the author: Jeff Hulett leads Personal Finance Reimagined, a decision-making and financial education platform. He teaches personal finance at James Madison University and provides personal finance seminars. Check out his book -- Making Choices, Making Money: Your Guide to Making Confident Financial Decisions.
Jeff is a career banker, data scientist, behavioral economist, and choice architect. Jeff has held banking and consulting leadership roles at Wells Fargo, Citibank, KPMG, and IBM.
1. What makes someone smart?
Imagine if we all had a personalized app on our phones that could pinpoint exactly why we’re smart. Every report would be different, because here’s the thing—smartness isn’t one-size-fits-all. It’s as unique as you are. Some of us have sharp memories, others process information quickly, while some are exceptional at connecting seemingly unrelated ideas or understanding emotions. You might build deep, meaningful relationships or excel at something entirely different. All of these abilities are a form of intelligence.
In this article, we take a two-fold approach to defining "smart": one from the inside-out and one from the outside-in. [ii] On the inside, being smart means reaching a higher-than-average level of mastery in a subject that you’re passionate about. But there’s more to it—on the outside, it’s about how valuable your mastery is in reducing chaos and disorder (or entropy) for others. After all, when you use your intelligence to help people or solve problems, you’re not just smart—you’re valuable.
In the notes, we reference the fascinating link between the physics concept of entropy and our work. Entropy, a measure of universal disorder, is also known as the second law of thermodynamics. Ultimately, the work we accomplish using our “smarts” is closely tied to the economic value we create for others. [i]
Let’s make this even simpler: the work we do with our “smarts” creates economic value for others. Whether you’re a tech wizard building apps that streamline our lives, or an artist creating beauty that soothes our souls, you’re actively reducing entropy.
Both perspectives matter. On the one hand, your personal sense of accomplishment drives you to mastery, but on the other, it’s the way the world sees and values that mastery that defines its impact. In this way, smartness isn’t just about being good at something; it’s about how the world needs and appreciates your expertise.
We may not always consider certain disciplines as having “smart” providers. For example, athletes are not always considered smart. Following this “reducing entropy equivalence to smart” logic, the consumption of sports entertainment may not be considered necessary for reducing entropy. (Even though, professional sports athletes achieve well above-average mastery specific to sports entertainment.)
So, this is a way to define “smart.” But what about different levels of smart? Would most people consider Nobel-winning scientists smarter than those not receiving the Nobel? If you are considered smart by the mastery definition but have not received a Nobel, are you less smart? Then, what about polymaths? These are people who achieve deep mastery in multiple disciplines. Is a polymath without a Nobel less smart than a single-subject Nobel winner? It does seem our society rewards “narrower and deeper” over “broader and shallower.” [iii]
So, whether your brilliance shines in mathematics, biology, or something more creative, it’s clear: your unique intelligence plays a vital role. Ready to explore just how deep this idea goes?
2. Skiing down the smart slope
In this section, we present a framework illustrating the comparison between depth and breadth of mastery. Picture mastery depth fitting within a normal distribution, where the number of individuals achieving this level of expertise in any given discipline follows the shape of the curve.
The global population
passed 7.8 billion in 2020
People who attain deep mastery fall within the 4th standard deviation (SD) on the right tail of the curve, while those reaching "Nobel-level" mastery are positioned in the 5th SD. The average person, located at the center of the curve, possesses general-level knowledge. As you move to the right, the curve's tail quickly flattens compared to the steeper middle section. To make the estimated number of individuals in these tail sections clearer, a log scale callout box has been included for better visibility. [iv]
What does this mean? Essentially, everyone fits somewhere along this "smart" curve within at least one area of expertise. Their chosen discipline—whether it’s biology, literature, mathematics, economics, or construction—becomes their way of learning how to think. Over time, the skills they develop in that discipline are applied in the job market. As individuals gain more experience or education, they move further to the right on the smart curve.
Let’s start with the global population, which surpassed 7.8 billion in 2020. Most people, approximately 3.9 billion, have general knowledge—think of this as the midpoint of our curve. These individuals represent a baseline of understanding, often gained through primary education and lived experiences. This group has learned enough in one or more areas to be functional but hasn’t delved deeply into any particular discipline. As you move farther to the right on the curve, you encounter individuals who have achieved a deeper level of mastery. These people, who reside within the 4th standard deviation (SD), have developed a high degree of expertise in their chosen field. This is where the specialists live, roughly 500,000 globally. They’ve invested time and effort, whether through formal education, professional experience, or self-teaching, to reach a level of mastery beyond the average person. They may hold advanced degrees, publish research, teach, or practice their discipline professionally.
It’s important to clarify that we do not know the absolute level of intelligence on this curve. Intelligence and mastery are dynamic concepts—people’s ability to develop their "inside-out" mastery (personal expertise) and the "outside-in" societal need for that mastery (market need for expertise) change over time. Our framework is relative, not absolute, meaning we rank individuals based on a functional curve that follows a normal distribution. What we can determine is the general shape of this curve and the approximate number of people located at different points along it, rank ordered by their "smarts" at any given period.
In today’s world, the number of available disciplines for specialization continues to grow, and more people are gaining the ability to specialize. Some may have advanced degrees, while others may be employed in roles that allow them to hone their expertise. There are also those who are autodidacts, self-taught in their field. This article does not take a stance on the specific paths people take to reach the upper levels of the "smarts" curve. We acknowledge that there are many ways to learn, and the effectiveness of each method depends on the individual learner.
Those who achieve Nobel-level mastery are exceedingly rare, positioned in the 5th standard deviation of the curve. Globally, only about 5,000 individuals reach this level. These are people who typically hold PhDs or equivalent education and operate at the cutting edge of knowledge in their field. Due to their advanced expertise, their focus is often quite narrow, diving deep into their specialized discipline. While not all will receive a Nobel Prize, they belong to an exceptionally rare group. Most of their time is likely spent on research rather than teaching, as they are primarily dedicated to pushing the boundaries of their field.
3. Why range matters
What about polymaths? These are individuals who achieve Nobel-level mastery across multiple disciplines. Famous polymaths include Benjamin Franklin, Leonardo da Vinci, and John von Neumann. Polymaths are even rarer than single-discipline experts. While the world certainly needs specialists, it also relies on those who can connect the dots between different fields. Most of the time, solving complex problems and improving lives requires combining knowledge from various areas rather than relying on expertise in just one. In fact, many groundbreaking innovations stem from this blend of disciplines.
That said, a Nobel-level polymath might be more than necessary for bridging the gap between specialties. Often, someone who has developed a deep understanding across several fields—without reaching the extreme level of Nobel mastery—is more than capable of making these valuable connections and fostering new capabilities.
The Case For Range
What are your superpowers?!
Please Note: These are five example disciplines, your range is likely different.
This is where the true value of "polymathic" individuals shines. [vi] These people achieve high levels of mastery across multiple disciplines, using their broad knowledge to connect ideas and identify opportunities that others may not see. While they can tap into deeper expertise when needed, their real strength lies in their ability to blend insights from different fields to create well-rounded solutions. Polymathic individuals are especially valuable because their unique combination of skills is rare. They are like chameleons, able to quickly adapt and apply their knowledge to a variety of challenges.
Physicist and mathematician Freeman Dyson captured this balance perfectly. He believed the world needs both specialists and those with a broad range. In his words, we require both "focused frogs" and "visionary birds" to thrive. [vii]
"Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. We need birds and frogs working together to explore it."
- Freeman Dyson, Birds and Frogs: Selected Papers of Freeman Dyson, 1990–2014
Why is a polymathic individual so rare? The explanation lies in straightforward probability. Let’s start by assuming someone achieves mastery in a discipline at a level 2 standard deviations above the mean. Statistically, this means they’ve surpassed 95% of the general population in that field. While impressive, this still represents a sizable group—around 350 million people globally.
However, instead of continuing to push further in this single area, polymathic individuals often pursue mastery in additional disciplines. Their curiosity and wide-ranging interests lead them to explore other fields. Now, let’s consider the same person reaching 2 standard deviations of mastery in four more disciplines. The probability of achieving this level across five disciplines is calculated by multiplying the probabilities: 0.05^5, which equals approximately 0.0000003125. Based on the current global population, this results in only about 2,400 people worldwide achieving this rare level of mastery across multiple fields—fewer even than those who achieve Nobel-level expertise in a single discipline.
This highlights just how uncommon it is to find individuals with a unique combination of mastery in multiple disciplines. The challenge for polymaths is that pursuing mastery in diverse fields carries inherent risk. It takes time to build expertise in each area, and there’s no guarantee that the world will value the specific mix of disciplines they choose. That said, there are strategies to increase the likelihood of pursuing careers with high global demand, including the positive effects of job changes and the value of continuing education, as outlined in the notes section. These strategies can enhance the chances of achieving mastery in disciplines that offer strong career and financial benefits. [viii]
4. Conclusion
Journalist and author David Epstein champions the importance of having a wide-ranging skill set, one that bridges gaps between disciplines in a society increasingly focused on specialization. Mr. Epstein said,
“The challenge we all face is how to maintain the benefits of breadth, diverse experience, interdisciplinary thinking, and delayed concentration in a world that increasingly incentivizes, even demands, hyperspecialization”
― David Epstein, Range: How Generalists Triumph in a Specialized World
This article aligns with Epstein’s perspective but takes it a step further by presenting a framework that argues those with "discipline smarts" across multiple fields are just as rare and valuable as Nobel-winning specialists. In fact, as specialization becomes more dominant, individuals with broad skills are vital for navigating today’s complex world. It is often entrepreneurs and inventors with this range of knowledge who develop novel and innovative solutions.
However, we must also acknowledge that not everyone has equal access to education and opportunities. In our model (as noted earlier), the normal distribution of mastery is an "upper bound" of those who could potentially reach expertise. A better world is one in which we unlock the full potential of humanity, including the untapped brilliance waiting to be harnessed from minds across the globe.
5. Notes
[i] Hulett, An example of the Stoic's Arbitrage - how our work enables kindness to others, The Curiosity Vine, 2021
Hulett, Fight Entropy: The practical physics of time, The Curiosity Vine, 2021 These articles provide background for how reducing entropy is the purpose of our work.
If the term "entropy" feels unclear, you can easily substitute it with "value" without losing much of the intended meaning. For example, in the context of app engineering, instead of saying "decreasing their entropy," you could say "increasing their value," and the concept remains essentially the same.
[ii] We dig deeper into the inside-out and outside-in "smart" dynamic in the following article. We provide the neurobiological basis for inside-out mastery building via curiosity. Included is how the "elasticity" microeconomics demand interaction impacts the outside-in perception of the value of a set of skills.
Hulett, Curiosity is the most powerful thing you own, The Curiosity Vine, 2022
[iii] Malone, Laubacher, and Johns, The Big Idea: The Age of Hyperspecialization, Harvard Business Review, 2011
[iv] The shape of this curve, and its position, is a stylized deduction that I'd love to test! Here's my reasoning: the assumption is based on "relative intelligence" through mastery in a single discipline. Imagine if every person on Earth had a “mastery score,” and the entire global population could be ranked accordingly. The median level of mastery, based on a world population of 7.8 billion, would be located at the 3.9 billionth person on this rank-ordered list.
The assumption of normalcy for this curve needs some clarification. Normal distributions depend on random errors following a normal pattern, meaning individual observations must be independent. In controlled environments, like physics experiments, this independence holds. A classic example is the Galton Board, created by Sir Francis Galton in 1889, where each blue ball that hits a peg has an equal chance of going left or right, independent of any previous ball.
However, in real life, people and cultures are rarely independent. Imagine each peg on the Galton Board representing a "yes/no" input to a person's ability to learn and master a subject. These inputs can include factors such as a) coming from a two-parent household, b) having parents who have already achieved mastery, c) having access to education enabled by social capital, d) having the financial resources to access education, or e) being part of a culture that encourages learning. These inputs are interdependent, which means that learners often benefit from momentum or inertia created by their circumstances. In this sense, we can view the normal distribution as an ideal upper limit, with real-world barriers—such as lack of access to educational opportunities—resulting in fewer people reaching the higher end of the curve. In a perfect world, everyone would have independent access to these learning resources.
While the normal distribution doesn't fully reflect reality, the general ranking of mastery levels remains valid. Fortunately, with the rise of technology and platforms like Khan Academy, access to education is improving. As more opportunities to reduce entropy emerge, society will likely become more motivated to create independent learning environments. Over time, the normal curve may become a more accurate representation of mastery levels globally.
Reaching 2 SD mastery across multiple disciplines takes time, which, in turn, helps overcome the challenge of interdependence. Time acts as a buffer, allowing mastery opportunities to arise faster than a person can gain expertise in each field. This helps limit the impact of inertia, as it's difficult to replicate the unique combination of skills across individuals within a short period. This aligns perfectly with Seneca's saying: “Luck is where preparation and opportunity meet.” In this case, preparation must always come first in order to create luck.
[v] For example, Ben Franklin's inventions were very useful in the day. Examples include:
Franklin stove
Bifocals
Armonica
Rocking chair
Flexible catheter
Franklin's polymathic subject knowledge was necessary. His subject-matter mastery included: Physics, metallurgy, anatomy, medicine, music, chemistry, mathematics, and others.
[vi] To clarify the distinction between a "Polymath" and "Polymathic people": A "Polymath" is someone who attains deep mastery across multiple subjects, pushing far out on the flat ends of multiple discipline curves. John von Neumann is an exemplary polymath, having achieved Nobel-level expertise in fields like mathematics, physics, economics, and computing.
On the other hand, "Polymathic people" are those with a wide range of interests across various disciplines, but they generally don't reach the same profound level of mastery in each field. As mentioned in this article, they fall within the top 5% in multiple areas but not at the extreme ends of expertise. These individuals are often seen as intensely curious and passionate about exploring a broad array of subjects.
Ken Jennings, the all-time winningest Jeopardy player and famous “polymathic person” said:
"I would say the general rule is if I learn something once and I find it interesting, I think it's more likely to stick. But again, I think that's near universal. You know, somebody who thinks they have an unremarkable memory or a kid who can't learn their times tables, they still know every word of every song on their favorite album and they know every player on the roster of their favorite team. The memory is working just fine when engaged. Like the people you see on Jeopardy tonight. I don't have photographic memories. That's not a real thing. They're just interested in like ten times the things you are. And so more facts stick..."
Levitt, Ken Jennings: “Don’t Neglect the Thing That Makes You Weird” People I (Mostly) Admire, 2021 (bold and italic emphasis added)
[vii] Dyson, Birds and Frogs: Selected Papers of Freeman Dyson, 1990–2014, 2015
As for me, I consider myself a diving bird. That is, I generally like to fly high like a bird, connecting the dots between concepts and helping provide solutions to diverse problems. I do periodically dive into topics. I'm not averse to "being like a frog" and diving into the details. This is often for deeper understanding and as an enabler to be a better bird.
[viii] Hulett, They kept asking about what I wanted to do with my life, but what if I don't know? The Curiosity Vine, 2021
This article provides a framework for increasing the chances of pursuing high-value careers (disciplines).
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