Have a Difficult Problem to Solve? Use Your Breath.

For many, solving a difficult math problem can make a person feel incredibly tense. I have been practicing for the GMAT Quantitative section recently and the practice has taught me a good lesson. I found myself at the beginning of problems, thinking about things that had nothing to do with the problem at all: “Wait, you don’t know the answer to this immediately? You have a Ph. D in mathematical sciences, what’s wrong with you?” My ego and fear of failing were getting in the way.

I was also able to relate (again) to students learning math and the experience that must often have. In the back of my mind, I surely already knew this, but it was good to feel this again; it was good to get a glimpse of the anxiety of not knowing something that I was supposed to know.  

Everyday at work I run into students who are just flat out afraid of math. I spend a large percentage of my class time trying to make it less scary. Perhaps the worst part, for them, is when I put a problem up on the board and I ask them to solve it.  Some don’t even try.  Even after I have finished doing some examples where I clearly say “Here is how you start…” and provide an explanation, some students still can’t find it in them to begin the problem. 

We know why this happens, although I think we make the reason more complicated than what it is. Mathematics is a different language and to understand what is really going on in a math lecture, one has to be focused and concentrating at a high level. Ego and fear can’t be part of the equation (no pun intended).

Yeah, so John and Mary are at a coffee house. John walks for 3 hours before Mary starts following him. Mary is walking 5 miles per hour and John is walking 2 miles per hour. How long before Mary catches him?

First step?


Isn’t it so obvious? You are about to embark on a seriously difficult mental exercise. Shouldn’t you ready your brain with what it needs before you start?   

That’s my big lesson and one that I will make sure to pass on to my students from now on. Breathe at the beginning of a problem. Breathe at the roadblocks of a problem. Continue breathing throughout the problem.

I learned that breathing is a force field. It helps keep out the fear, subsides the anxiety, diminishes the doubt, while inwardly it increases my focus, sharpens my concentration, and builds my confidence.

Without it, it wouldn’t be as easy to find out (spoiler alert) that it took Mary two hours to catch John.

But as you might imagine, this goes beyond some made-up math problem. What about the big decisions in your life? What about the ones that require some serious decision making on your part? What about the real math problems in your life?

  1. Should we really spend this much on this house?

  2. Is my money in the right account for it to grow?

  3. How do I balance my kid’s tuition needs with my retirement needs?

First step?


While the ego may tell you that you will look great in that house, or that you will be able to make more money so that account doesn’t matter, or that your smart kid will get a full scholarship, breathing opens up the door to the truth. It allows you to think clearly and logically about what is really happening.

I will tell you that my lungs have now been opened. My teaching methods (and life) have changed forever. My first step used to be “Label the unknowns.” Now, it’s “Breathe.” After all, how can you find “x” if you are too busy thinking about what would happen if you can’t find it?

Want help using your breath to solve difficult problems? Check out Spire, a small wearable device that tracks your breathing, activity and state of mind.  It has guided breathing exercises designed for focus and calm.


About the Author:

Aris Winger was born and raised in the nation’s capital.   A proud graduate of Howard University, he moved to Pittsburgh, PA, where he obtained his Masters and Ph. D in Mathematical Science at Carnegie Mellon University in 2000 and 2005 respectively.  After spending some time in Virginia at his first job at Emory and Henry College, he moved to Georgia in 2010 to live with his wife.  He currently and proudly teaches mathematics at Georgia Gwinnett College.  His current areas of interest are Social Justice Mathematics and the area of effective teaching methods in mathematics. 

Photo Credits: Matt Chan – Math & Physics


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Spire is dedicated to helping you live a happier, healthier lifestyle with an easy-to-use device for mindful breathing techniques. Learn more about the benefits of breath-tracking at Spire.io.


Anxiety, Body & Mind



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