Do All Problems Have Solutions?

When I am on a trail like this one, I find the space to think of things like this question.

For the past few weeks the same question keeps rolling around in my head like a marble below deck on a ship at sea. The world and our lives seem to be inundated with insurmountable problems. From war torn countries, to famine, to mass shootings, to a lack of education funding; the list seems to never end.

You see I look at all of these problems and wonder, how do we solve them?

Problems have to have solutions. That’s the nature of a problem. Right?

Do all problems have solutions?

It just keeps rolling back and forth in my mind like that marble at sea.

When I present my second graders with a new math problem, we talk about strategies to find the solution to the problem at hand. If there’s a disagreement in my classroom, we talk it out to get to the bottom of it and agree on a solution. If I lose my car keys, I look for them until I find them.

So why can’t we seem to solve any of these big problems we as a society face?  

Am I lying to my second graders? Am I lying to myself?

Do some problems not have solutions?

Merriam-Webster defines problem as, “a question raised for inquiry, consideration, or solution”, “a proposition in mathematics or physics stating something to be done” or “an intricate unsettled question.” Based on those definitions, problems should have solutions.

When you define a problem like Merriam-Webster did there, it sounds like something we can solve. So what are we missing?

As I have sat with the question of “do all problems have solutions” I keep going back to the movie The Imitation Game. This film in part tells the story of mathematician Alan Turing who worked during World War II as a code breaker. It is a very interesting look at persistence in the face of what seems impossible.

Turing laid the groundwork for what we know today as computers and computer science. As someone who teaches second graders the basics, and I mean basics, of computer coding it seems impossible to have created the entire system you are reading this on now. But Turing did, or at the very least spurred that invention along.

Through his work with code breaking and computing machines, Turing showed us that if you state your problem in the proper way and have enough time, all problems have solutions.

So how do we solve the problems we face?

Problems are inevitable. They are the force that keeps us challenged and creative. I cannot fathom a day without facing a problem.

The more I think about it, the more I feel problems must be soluble.

From how to manage our time, what to wear, the most efficient route at rush hour, ect problems are everywhere. We will always face problems. Some may seem impossible, like breaking an unbreakable code or stopping genocide. For some problems, the solution may be as simple as “wake up ten minutes earlier to not be late in the morning”, which I will still argue seems somewhat improbable. But problems have to have solutions.

“It’s not that I’m so smart, it’s just that I stay with problems longer.” – Albert Einstein

Here is what I propose to the world at large. Whether we find ourselves facing the enormity of a problem such as systemic oppression or the seemingly smaller of who took my pencil in the second grade, we need to stop. We need to stop and work to understand our problem. We need to look into our bag of strategies for solving problems and see if any of those will help. We need to sharpen our creativity and open our minds to look for the solution no one else will see. We need to ask for help. We need to believe whatever it is we face has a solution. Then, we work towards that solution.

As I reflect on big and small problems I myself have faced over time, I realize that many times the solution looked far different than what I thought I was trying to solve. But the solution at hand did solve the problem. When solving problems, don’t limit yourself to the solution you want. Look instead for the solution that solves the problem.

I do not expect any of the colossal problems the world faces to be solved overnight, or even this week. But as we all work to find solutions for the individual and collective problems we face remember this quote from the Imitation Game.

“Sometimes it’s the very people who no one imagines anything of who do the things no one can imagine.”

Be the one who imagines a solution to what seems impossible.


One thought on “Do All Problems Have Solutions?

  1. Merriam-Webster defines problem as, “a question raised for inquiry, consideration, or solution”
    I wonder… if we define the inquiry from all angles then linger at consideration, if we might see a glimpse of the solution. The key I believe is found at lingering- it requires patience and silence. It also takes much longer than we hope or anticipate, which applies to lost keys. The time sent searching for the keys ticks by fast it seems as we rush to find them. I retrace my steps and that is when I can clearly see- in hindsight. Great read and very insightful!


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