I spend every Wednesday volunteering at a community tech hub some kilometres away from my house. The vision of this hub is to bring together out-of-school children from underserved family backgrounds and equip them with the necessary skills to become innovators and thought leaders.

My job there is simple: I come in once a week to teach these kids (ages 14–19) the soft skills necessary to thrive in the 21st century, skills like leadership, creativity, and public speaking. There is a special name for this class; it's called the “Case Study Class,” a name coined from the idea that the class is supposed to mimic real-life situations and train these kids on how to act proactively.

Aside from the mental space I occupy while working at the intersection of medicine and Artificial Intelligence, the community hub is my favourite place to be every week, making Wednesdays the best day of the week for me.

Last week, I walked into the hub for another Case Study Class, and the topic this time was “Critical Thinking: Why People Only Have Thoughts but Don't Think.” While walking them through the importance of this skill in problem-solving, one of the students, Eze, a 14-year-old boy, asked a question:

“Mr Kenny, what is a problem? I can feel it when I have a problem, but I have never been able to find the right combination of words to describe it.”

This simple question opened a Pandora's box of ideas, which made for one of the most memorable teaching experiences of my entire life.

I thought through the question and replied:

“You are said to have a problem when you exist in a state that is undesirable to you.”

The follow-up question from Eze was:

“Then what is a solution?”

My answer was:

“A solution is an action or series of actions taken to move from an undesirable state to a desirable one. However, for this solution to be classified as the best, the action or series of actions must, subjectively, be the most optimal one.”

After almost 30 minutes of simplifying my thought process for the kids, one of the new students in the class, Amarachi, raised her hand and said:

“Mr Kenny, I have three sets of questions.” “One: Does every problem have a solution?”

My reply:

“Yes.”

She proceeded to ask:

“So this means that if I have 50 different problems, then there should be at least 50 different solutions to these problems?”

Rather than respond to the second question, I asked her to continue with her third question, and she said:

“If question two is yes, then Must Infinite Problems Have Infinite Solutions? If it's no, then how is that possible?”

Just like every other essay you have read from me, or will read from me, my job here as a writer is to make you intellectually uncomfortable, to force you into clarity. The kind of discomfort that forces you to wrestle with complex ideas until the obvious begins to reveal itself.

So, I write with the intention of doing exactly that: changing how you think about things, or better still, changing how you ask questions.

Before you continue reading, if you were in my shoes, what would your answer be?

Think about this carefully, because every word in this essay is converging toward answering her questions.

In primary school, we were taught that the area of a rectangle is length × breadth. To test whether we truly understood, we would be given classwork.

In the classwork, the first question could be:

What is the area of a rectangle with a breadth of 2 cm and a length of 10 cm?

The second question might read:

A piece of wood in the shape of a rectangle is 1.5 m wide and 5 m long. What is the area of this piece of wood?

Since the details changed, it is reasonable to infer that these are two different problems. However, any student with a basic understanding can easily answer both questions correctly by multiplying the numbers together.

This sets a precedent for a hypothesis:

“n different problems do not necessarily require at least n different actions, or sets of actions, to solve them.”

There are two ways to frame this hypothesis.

First, n different problems may have more than n different solutions available to them. Second, n different problems may have fewer than n different solutions available to them.

However, by the law of simplicity, less is often better. It is, therefore, a more worthwhile pursuit to develop solutions that can be easily generalised across a multitude of problems.

While writing this, I realised that mathematics had been revealing the best approach to us all along, hidden in plain sight: a tool capable of solving entire classes of problems through a single structured operation.

That tool is called a “formula.”

Britannica defines a formula as a plan or method for doing, making, or achieving something.

Hence, when you are faced with n different problems, you need only one formula; adjusting the variables is what transforms an undesirable state into a desirable one.

To provide further evidence for this hypothesis, it is generally accepted that problem-solving ability is developed through exposure to problems. The most effective solution providers, therefore, are those who have been trained through repeated encounters with a wide variety of challenges.

In theory, this would imply that the greatest problem-solver is one who has been exposed to an infinite number of problems. However, human mortality makes such exposure impossible. It follows, then, that the highest form of problem-solving cannot depend on experience alone, but must instead rely on a transferable framework, “a formula” that can be applied across categories of problems to uncover solutions.

So, the final answer to Amarachi is that infinite problems do not require infinite solutions. Instead, what is required is a formula that can be applied ingeniously across different categories of problems to produce solutions. In other words, an infinite number of problems can be addressed with only a finite set of solutions.

To stretch your thinking further, I intend to propose a specific number for that finiteness. My proposed number is one. I mean that you need only one formula, one solution, one methodology, for every problem you encounter.

In the early 300s BCE, some intelligent philosophers had a problem. They were looking for a way to turn ordinary stone into pure gold. They called this process “Alchemy.” During the course of numerous experiments, studies, and investigations, they came to the discovery that, to convert stone into pure gold, they needed to heat the stone to an intense degree and then add a special kind of stone, the almighty stone, to aid the conversion process. This stone they named “The Philosopher's Stone.” They never got to see the stone, and so they never succeeded in converting ordinary stone into pure gold.

Unlike the intelligent philosophers of the 300s BCE, I feel quite presumptuous in saying that, for solving any problem, I have a Philosopher's Stone. Hence, I propose that you need only one formula to solve any problem you encounter. That formula is a very ancient thinking process called “First-Principles Thinking.”

First-Principles Thinking is a method of reasoning in which you break down a problem into its most fundamental truths or axioms and then build your understanding or solution from the ground up rather than relying on conventions, assumptions, or biases.

The First-Principles Thinking methodology can be broken down into three steps:

-> Identify assumptions:What does everyone assume is true? -> Break the problem into fundamental truths: What facts do I know are objectively true? In other words, what are the axioms concerning this subject matter? -> Rebuild from the ground up: Construct a new conclusion exclusively from the fundamental truths.

The thing is, most people think by analogy as opposed to First-Principles Thinking. They say, “Others do it this way, so I should do it this way.”

The most popular version of this is:

“That's how they do it.”

When you employ First-Principles Thinking, you begin to think radically, which propels you to ask questions about what is fundamentally true. The interesting thing is that reality does not bend itself to our assumptions; it operates according to underlying truths. Therefore, when you construct a solution using only those truths as your building blocks, the solution stands a much greater chance of being the best one available.

If a thinking process as beautiful and accurate as this exists, why don't more people use it?

The answer, as I have come to understand it, is that it requires a tremendous amount of time, effort, and intellectual honesty. First-Principles Thinking forces you to keep asking questions, keep researching, and keep digging until you arrive at what is fundamentally true. In the process, it demands substantial intellectual work, the willingness to dispose of your ego, and the courage to look foolish while asking questions whose answers seem obvious to everyone else.

Another reason is that the vast majority of people do not enjoy thinking deeply. They see intellectual inquiry as optional, something they may choose to pursue or ignore, often under the illusion that their lives will be just as meaningful, successful, or fulfilling either way.

Little wonder the world is the way it is today. It is largely shaped by people who view deep thinking as an unnecessary exercise rather than one of the most powerful tools available for understanding and improving reality.

Perhaps the greatest advantage of First-Principles Thinking is that it does not teach you how to solve a problem; it teaches you how to solve problems.

At the beginning of this essay, my intention was simple: to write with enough clarity, soul, and sincerity to challenge how you think about problem-solving.

If, by the end of these words, I have managed to do that, please don't hesitate to tell me.

It would mean the world to me. God is helping us.