The hardest problems I’ve solved

July 27, 2015 by Joshua
in Creativity, Education, Nature, Stories

How did it begin?

After the first two years of classes in graduate school I had to take Qualifying Exams to continue to research.

Columbia’s Qualifying Exams are three days of about six hours a day. You get eight problems and have to solve six of your choice. They can cover any physics subject covered in classes to that point. If you remember high school or college physics being difficult, graduate problems are harder. Since they can ask questions on any subject you can’t focus on one area. You have to study everything.

What was the process?

First you read all the questions. Some you can see how to solve right away. Some you can’t understand the question.

I solved the ones I knew I could first. Next I pushed myself on the next harder ones. Eventually, I would have about four hours to solve two problems.

I felt helpless. The situation felt futile. But it didn’t make sense to leave. When I looked around the room no one else seemed to have given up. What else could I do but try what I could. I had no resources or tools but a pen and paper.

I would write a relevant equation to get at least some credit. Then, once I saw the equation written out, I’d realize I could do something. I’d write an assumption, write a different relevant equation, use a simplification, or whatever I thought would advance my solution.

After a couple hours, I found myself making headway. I’ve never felt so academically challenged, but I realized I was rising to the challenge. I’d write a bit more, transform the equation a bit more, re-read the problem for more insight, and so on.

When the clock ran out each day I had answered nearly all the problems. The school grades numerically but only tells the students if they passed or failed so I don’t know my precise score, but my advisor told me my score was up there with the theory students, which means it was high.

How did you overcome obstacles?

I realized I had no alternative that made my life better than to stick with it. And I realized I could do something, that I wasn’t powerful.

I knew the problems had solutions. I had some relevant knowledge. I applied it step by step, doing what I could where I was even if I didn’t know where I would go next. I’d figure that out when I was there.

What was the result?

Beyond solving the problems and passing the tests, I felt able in a way I never had before. I felt myself closer to being a peer of great physicists.

I found greater expectation of success for solving more physics problems, which motivated me to try. I felt confidence like I had never felt before on a challenging and demanding area of my life.

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2 responses on “The hardest problems I’ve solved

  1. What an intense yet enlightening experience! Thank you Josh for sharing. It is important for others to hear about these types of challenges because it helps us to understand that we – humankind – are not born with knowing all the answers. Rather, we all have these struggles and fears and feelings of futility. Yet, when we put aside the anxieties and fears, we learn from ourselves that we have it in us to achieve. We may not always succeed the first time (I didn’t get into medical school the first time I applied – which was a blessing for me because it helped me choose the path I am now on for which I am very happy), but we should not give up and know that like your fellow exam takers, we’re not alone.

  2. Pingback: The five times I got mugged growing up | Joshua Spodek

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