» A look at previous inaugurations,

Mathematicians know what it’s like to be nagged by a problem. Like an itch that is just out of reach, we can be preoccupied by finding a way to scratch the surface of a solution.

I had this feeling on the night of Jan. 6. As I viewed the scenes from Washington and saw debates raging on social media, I wanted to be able to say something that would fix it, or at least calm things down. Surely I could make a rigorous, logical argument that would convince people to open their minds to new

perspectives.

I couldn’t find a solution. The itch persisted. I decided to ease my discomfort by telling myself that the problem itself, like some in mathematics, is unsolvable. If I know that no solution exists, I don’t feel so badly about not finding one.

The approach provided temporary relief, but, of course, we cannot abandon our efforts to address the troubles and division that we now face.

In 2015, I traveled with a group of university students to Corrymeela, a peace and reconciliation center in Northern Ireland. We learned a great deal about The Troubles, an intensely hateful 30-year period of violent conflict between Catholics and Protestants. During this time, children were taught that people on the other side were clueless at best and evil at worst. Each group genuinely believed that truth was on their side and that the other side lived in a fictional reality.

Sound familiar? I’ve visited Northern Ireland several times since then, and each time I see a little more of America in what we learn. To be clear, our conflicts are not the same in terms of context, complexity or timing, but noticing the similarities has been eye-opening.

Things have improved in Northern Ireland since the Good Friday Agreement in 1998, but tensions remain. The walls dividing Protestant and Catholic neighborhoods still stand, almost all schools are segregated, and there are unwritten rules about which side of the street is safe for walking. Groups have regular celebrations of heritage that frequently turn hateful and violent. Again, sound familiar?

Since before The Troubles, the Corrymeela center has helped to bring about reconciliation among the most bitter of enemies. Their guiding idea is “together is better,” and their efforts and strategies to break barriers inspire me each time I see them up close.

As a math professor, I teach students that the first step in solving a problem is to recognize and understand it. This is also necessary in conflict resolution. Opposing parties must recognize that something needs to be done — that no one wins when the conflict continues indefinitely. Each side must be willing to do the difficult work of reconciliation.

Another mathematical problem-solving strategy is to start small. Corrymeela brings people together in small groups. Adults who lost family members in the violence of The Troubles meet with those who caused their pain. Protestant and Catholic schoolchildren interact with one another (for the first time!) on the playground. People “on the other side” are humanized. We can do something similar here. Maybe I can’t make a perfect social media post that will fix all of our problems, but I can spend some time in genuine conversation with somebody who sees things differently.

Mathematicians solve problems using ideas and facts that are based on a common set of axioms. I think I’ll try something similar with my conversation partner. Even though we disagree on a number of important things, can we find some things on which we can both agree? These things may be very basic, but it always helps to start from a place of agreement.

Finally, it is important in problem solving of any kind to stay focused on the things that are helpful. At Corrymeela, they emphasize the need to avoid “whataboutism” — the tendency to respond to something that is uncomfortable to you by pointing out something that is uncomfortable to someone else. “I may have hurt you before, but what about that time you really hurt me?” “Yes, these riots at the Capitol were bad, but what about all of those riots last summer?” If we can avoid this in our conversations with others, we can make better progress.

Have the right attitude, start small, find commonalities and stay focused on the goal. If we keep these strategies in mind, maybe we can discover that the problem is solvable after all.

CAROLYN KASTER/ASSOCIATED PRESS After the horrific attack on the U.S. Capitol on Jan. 6, and the subsequent raging debate on social media, we cannot abandon our efforts to address the troubles and divisions that we now face.

John Harris