I have a confession. I have been wondering whether I should admit this to such a large crowd, but here we go. My confession is that I love mathematics! I know that for some of you, the word math brings a flood of bad memories. So before people get up to leave, let me share with you a different way to see math.
Unfortunately, many people have the mistaken idea that math is just a set of rules and calculations. That is not mathematics.
My family and I love the NCAA March Madness basketball tournament. Sitting around with friends and watching an underdog team beat a highly favored team with a last-second desperation shot is exciting. Compare such a thrilling basketball game to being alone in a gym shooting hundreds and hundreds of free throws. If all I ever did were to shoot free throws over and over all by myself and never play or watch a real game of basketball, I wouldn’t like basketball. The same is true with math. Doing endless math drills is like shooting free throws over and over. It is not mathematics.
To me, math can be like a game of strategy, such as The Settlers of Catan. Once you know the rules of the game, you can explore where the game can take you. In some ways math is like genealogy. You have several family lines to work on, and you may get stuck. But then a new piece of information opens up a previously blocked family line. You get excited and new results are uncovered. The same happens with mathematics.
You could be working at the Disney Research Group using math to create realistic-looking hair in the movie Moana, you could be designing a new method for Netflix to determine what movies a subscriber would like, or you could even be working on an abstract math problem that uncovers new results, such as finding a fast algorithm to determine whether or not a number is prime. That is how I see math and why I love it. To me, mathematics is beautiful.
Now, the world has many beautiful things. Watching a rising full moon peek over the Wasatch Mountains on a dark winter night, sitting outside on a New Hampshire fall evening while savoring poetry by Robert Frost, listening to the Vienna Philharmonic perform Beethoven’s Symphony no. 9 in D Minor in the 150-year-old neoclassical Wiener Musikverein concert hall—all of these things are beautiful to me.
Likewise, mathematics is beautiful. Some of you may think I am crazy. Remember, when I think of math, I am not talking about the endless drills that you probably did in high school.
When people ask me what research I do, I say that I study the math of soap bubbles. These bubbles are actually soap films that are formed by dipping wires or frames into a bucket of soapy water. To me, these soap films are fascinating—the shapes they take, the way they reflect light, their fragile nature. They relate to mathematical shapes known as minimal surfaces. There is a harmony between the shapes soap films take in nature and the mathematics behind minimal surfaces. I study the mathematics related to this and find it beautiful. I encourage you to explore how mathematics is different than a set of rules and calculations.
Seeing with a Different Perspective
In much the same way that I hope you will begin to see mathematics in a different and positive way, I want my students to see me, as their professor, in a different and positive way. Some students are afraid of their professors, especially their math professors. On the first day of the semester, I tell my class that students often ask how they should address me. Should they call me Professor Dorff or Dr. Dorff or Brother Dorff? When I tell them that I want them to call me Coach Dorff, they look a bit puzzled. I tell them that I want them to see me as their math coach—someone who is there to guide them and help them succeed, just like a sports coach would do. I want them to see me not as someone who is trying to fail them but as someone who is trying to help them succeed. I want them to see me differently.
In addition to seeing mathematics and my role as a professor differently, I think of Christmas differently. If you talk with my students, they will tell you that Coach Dorff loves Christmas. I look forward to Christmas, and I mention it occasionally when I teach my classes in the fall—okay, perhaps more than occasionally. Some people say you shouldn’t talk about Christmas or listen to Christmas music until after Thanksgiving. That may be true, but that perspective looks at Christmas only as a specific date—December 25. I like to think of Christmas not as a date but as a way of thinking, or as a “state of mind.”1 To me, Christmas is about remembering Jesus Christ, His birth, and His gift of eternal life. To me, Christmas is about remembering how we should treat the people we interact with, whether they be our family, our friends, or strangers; whether they have the same beliefs or different beliefs than we do; and whether they look like us or look different than us.
I experienced this Christmas state of mind a few years ago at Jackson State University in Mississippi. The university was opening a new center for undergraduate research, and I was invited to give some talks to the faculty and students. Jackson State University is an HBCU (historically black colleges and universities), and more than 90 percent of the students are African American.
During my visit, the university was inaugurating a new president, and I attended the ceremony along with the Jackson State faculty and staff. During the ceremony, I was introduced and asked to stand. As I did so, I could see almost the entire audience. It was apparent that I was one of very few Caucasians in the group. I have to admit I felt a bit out of place.
Are there times when you have felt out of place, when you are not sure you belong? Or are there times when you do not feel out of place but there are others in the audience who might feel that they do not belong? What can we do in such situations?
After the inauguration ceremony at Jackson State, and throughout my visit there, I felt at ease because of how the faculty and students went out of their way to meet me, talk to me, and be friendly to me. That experience reminds me to think about how I treat people who may feel out of place, who may be lonely, or who may be different than me.
Seeing Opportunities for Kindness
The importance of how we treat people is a recurring theme in the gospel of Jesus Christ. President Russell M. Nelson remarked:
Today we have a little more time to bless others—time to be kinder, more compassionate, quicker to thank and slower to scold, more generous in sharing, more gracious in caring.2
This is embodied in the story of the good Samaritan, who went out of his way to help a stranger who had fallen “among thieves, which stripped him of his raiment, and wounded him, and departed, leaving him half dead.” Other people who saw this stranger “passed by on the other side” and did not help him.3 Despite the historical antagonism between the Samaritans and the Jews, the good Samaritan treated this Jewish stranger with kindness.
In Matthew 25:35–36 we read:
For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
Who are the people around us who hunger or who thirst or who are strangers? At first we may think of people who hunger for food. There are also people who “hunger and thirst after righteousness.”4 Are there other ways people hunger? How about those who hunger for someone to listen to them? Who hunger for friendship? Who hunger for encouragement? Who hunger for respect? Who hunger for compassion?
Treating people with kindness is easier in theory than in practice. During Christmas break, my family and I saw the movie Wonder. That movie made such an impact on me that I read the book afterward.
Wonder is the story of a ten-year-old boy, August (Auggie) Pullman, who is anxious because he is entering fifth grade in a new school. There are two things that make Auggie different from the other school children. First, until now, he has been homeschooled by his mother. Second, Auggie has a medical condition that makes his face look different—so much so that some people stare at him and some kids run away screaming when they see him. The story is about how, at first, most of his classmates treat him as though he has a contagious disease. They avoid him, they think he is a freak, and some bully him. But as his classmates slowly get over their initial prejudice, they begin to see that he is a funny, smart, and fairly normal fifth-grade boy.
At the end-of-year graduation ceremony, the Henry Ward Beecher medal is given. Mr. Tushman, the director of the school, says:
Courage. Kindness. Friendship. Character. These are the qualities that define us as human beings, and propel us, on occasion, to greatness. And that is what the Henry Ward Beecher medal is about: recognizing greatness.5
The medal goes to Auggie. During the ceremony, Mr. Tushman quotes J. M. Barrie: “Shall we make a new rule of life . . . always to try to be a little kinder than is necessary?”6
What does it mean to “be a little kinder than is necessary”? Many of us are good at being kind to others, especially in circumstances in which we feel good. But it is harder to be kind when you haven’t slept well for several nights, when you’re feeling sick, when you’re stressed because of financial problems, or when you have procrastinated doing something important, such as writing that six-page paper for your class or finishing a presentation (perhaps even a devotional talk). Also, it is harder to be kind to others—not to mention kinder than is necessary—when they act, look, or think differently than you do. However, one of Christ’s teachings from the Sermon on the Mount invites us to do just that:
Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy.
But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you.7
Seeing People Differently
I think this last scripture suggests the need to go beyond just treating people with kindness. It hints at the importance of seeing people differently. President Thomas S. Monson declared: “We must develop the capacity to see men not as they are at present but as they may become.”8
Elder Jeffrey R. Holland summarized a comparable idea written by C. S. Lewis when he wrote:
C. S. Lewis once said that if we could recognize who we were, we would realize that we were walking with “possible gods and goddesses” whom, if we could see them in all their eternal dignity and glory, we would be tempted to fall down and worship. Because this is true, we need to think more highly of ourselves and we need to think more highly of each other.9
This vision of others is exemplified in the story about the four sons of Mosiah, who traveled to the Lamanites to preach the gospel to them. They did this even though the Lamanites were the enemies of the Nephites and fought against them. They did this even though other Nephites laughed at them for thinking that the Lamanites could—or would even want to—change. In fact, the other Nephites responded, “Let us take up arms against them, that we destroy them and their iniquity out of the land, lest they overrun us and destroy us.”10
The Lamanites were different than the Nephites, yet the four sons of Mosiah saw the Lamanites differently than the other Nephites saw them. Consequently, the sons of Mosiah treated the Lamanites with compassion.
For me, seeing people in this way is more difficult than treating people “a little kinder than is necessary.” However, as I try to see people differently, it seems to follow that I treat them with more kindness.
Unlike with Auggie in the story Wonder, most people’s appearances do not suggest that they might be different or that they are in need of something. For example, I have been a type 1 diabetic for forty-five years. This means that my body does not produce insulin, which is necessary to get energy from the food I eat. To compensate, I have to take a shot almost every time I eat food. Being a math nerd, I have calculated that I have taken about 100,000 shots in my life. My health revolves around balancing medicine, diet, and exercise. If one of these components is off, my blood sugar could get very low—so low that I could go unconscious and fall down. When I have low blood sugar, most people will not know. There are few visible signs that this is happening. I may look fairly normal, but I am actually in need of help. I am grateful for the kindness and patience of those who have helped me in these situations, and, fortunately, having such low blood sugar rarely happens to me.
Another example of seeing—or not seeing—someone differently comes from an experience that happened last semester. I taught two sections of Math 112: Calculus 1 to a total of 494 students. Three times a week I held office hours to answer questions that students had about the concepts of calculus and about the homework problems. In my office I keep a bowl on my desk with about a dozen different flavors of Lindt chocolate truffles. It is amazing how helpful chocolate is in getting people to drop by your office and in making them feel more comfortable talking. After visiting me several times during office hours, students often tell me about their missions or their families, and I enjoy learning more about my students.
Last semester I had one student who regularly visited me during my office hours. Sometimes she would be the only student to show up. Her name was Julia. She was not very talkative: she would ask me one or two specific questions and then leave. During the semester I never felt like I got to know Julia as well as I had gotten to know other students. With Julia’s permission, I want to tell part of her story.
On New Year’s Eve, Julia sent me an email:
I just wanted to thank you for the great semester. This is the first time I have ever understood math in my life. I struggled in high school, then got cancer. . . . Coming to BYU, I was extremely apprehensive about taking my first calculus class. . . . I was just told that my cancer metastasized, and to get treated I must stay in California for the next few months.
My heart sank as I read Julia’s email. I had no idea she had cancer. There were no outward signs that I had noticed. I expect few students knew that one of their classmates had cancer.
As we try to see people differently, it is important to be kind and treat them “a little kinder than is necessary,” because we do not know what is going on in their lives. People do not wear signs hanging from their necks that display their current struggles. No one is wearing a sign that declares, “I’m scared I am going to fail my math class” or “I had a fight with my best friend” or “My mother passed away yesterday” or “I am having a low-blood-sugar diabetic reaction” or “I have cancer.” If we knew these things, would we see people differently? Would we treat them differently?
Seeing with Heavenly Guidance
The Holy Ghost can guide us to see people differently and to help those with unseen needs. After I earned my undergraduate degree, my wife, Sarah; our young daughter, Rebecca; and I moved to Nuremberg, Germany, where I taught high school math in English. I did not serve a German-speaking mission, but I did have a minor from BYU in German.
We attended a small German-speaking congregation of the Church. I was assigned by a Church leader to periodically visit some members of the congregation. One was named Michael. Michael had not attended church for several years, and some Church members had told me that he would not come back to church.
I called him one day and asked if I could visit him and his family in their home.
Michael said that he was really busy and that he did not want me to visit him now, but in six months I could call him again. So I left it at that.
Later, one Saturday afternoon, I had some free time, and I thought that a nap would be nice. I lay down on the bed and tried to sleep, but a thought came to my mind: “Go visit Michael.”
I thought, “I cannot do that. He asked me not to visit him.”
I tried to fall asleep, but the thought that I should visit him did not leave. So I got up from the bed. As I drove to the address of Michael’s house, I tried to figure out what I could say, especially in light of Michael telling me not to visit him.
I arrived at his address. It was an apartment complex with several floors. Such buildings had a locked front door, so you had to ring a buzzer to the apartment you wanted to visit. The residents would ask who it was, and, if they wanted to, they would let you into the building. When I arrived at the front door, it was open. I rang the buzzer to Michael’s place and then started climbing the stairs to his top-floor apartment.
When I got there, the front door was open. A man was standing there. It was Michael. I introduced myself and told him I was from the Church.
He invited me in, and I met his wife. He said that they had just had a fight and had decided to get a divorce.
Now, I am a math nerd, and I am not the best talker, especially not in German. But I can listen, and that was what I did. At the end, I wasn’t sure what to say, but I told them that coming back to church would help them.
They did start attending church, somewhat to the surprise of some members of the congregation, and when my family and I left Germany two years later, they were still attending and still married. The Holy Ghost helped me to see this German family in a different way, and this blessed both them and me.
Seeing with Real Intent
I want to close with one last example of how seeing something differently blesses our lives and the lives of those around us. I did not grow up in The Church of Jesus Christ of Latter-day Saints. My mother was Irish Catholic, and we attended Catholic mass regularly. I was even an altar boy, which means I assisted the Catholic priest during the mass. When I was sixteen years old, I was interested in learning about other churches. During the summer, I was playing cello in an orchestra and met a violinist, April Meads Moriarty. She and her family were Latter-day Saints. They gave me a copy of the Book of Mormon. I read it in about ten days and started attending sacrament meeting and taking the missionary discussions. I was soon converted.
My mother was not happy about this. But instead of telling me that I could not talk with the missionaries, she decided to meet with them too in order to point out their mistakes. She was soon converted.
When my older brother, David, was home from Harvard, we gave him a copy of the Book of Mormon and asked him to read it. He said he would.
A while after David had returned to college, we were talking with him on the phone. I asked him if he had read the Book of Mormon. He said he had, and he said that it was not true.
I was shocked. After that, the topic of the LDS Church did not come up much in our phone calls with David.
In the spring, we made plans to travel to Boston for David’s graduation. One day, as we were talking with him about our itinerary for when we would be visiting him, my mother told him that we wanted to attend the LDS Church on Sunday.
David said that he would attend with us and that afterward he wanted me to baptize him.
Again, I was shocked.
As we talked, he explained what had happened. He said that he had read the Book of Mormon because he had told me that he would read it; he wanted to prove that it was not true. After telling me that it was not true, he realized that his brother—me—would not do something “dumb.” So he decided to read the Book of Mormon again. This time he read it differently, and he gained a testimony of its truthfulness. Seeing the Book of Mormon differently has blessed David’s life as well as the lives of many in his circle of influence.
Seeing as Christ Sees
I encourage you to see things in a different and positive way, whether that is mathematics, Christmas, the Book of Mormon, or the people you meet in your daily lives. Our Savior Jesus Christ sees us differently—not as we currently are but as we may become. I am awed by the love He has for me, who does not deserve it, and for the love He has for all of us—no matter who we are, no matter how different we may be from those around us, and no matter what struggles we have in our lives. In the name of Jesus Christ, amen.
1. “Christmas, children, is not a date. It is a state of mind” (Mary Ellen Chase, “Rather Late for Christmas,” Vogue 92, no. 11 [1 December 1938]: 81; see also condensed version, “Christmas Is a State of Mind,” Reader’s Digest, December 1939, 39).
2. Russell M. Nelson, “Doors of Death,” Ensign, May 1992.
5. R. J. Palacio, Wonder (New York: Alfred A. Knopf, 2012), 304.
6. Palacio, Wonder, 299; quoting J. M. Barrie, The Little White Bird (1902), chapter iv.
8. Thomas S. Monson, “See Others as They May Become,” Ensign, November 2012.
9. Jeffrey R. Holland, For Times of Trouble: Spiritual Solace from the Psalms (Salt Lake City: Deseret Book, 2012), 49; quoting C. S. Lewis, last paragraph of “The Weight of Glory,” in The Weight of Glory and Other Addresses (1949).
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Michael J. Dorff, chair of the BYU Department of Mathematics, delivered this devotional address on April 3, 2018.