In 1975, a San Diego homemaker named Marjorie Rice came across a column in Scientific American about tiling (瓷砖). There is a problem which has interested mathematicians since ancient Greek times. After Rice’s chance encounter with tiling, family members often saw her in the kitchen constantly drawing shapes. “I thought she was just drawing casually (随意),” her daughter Kathy said. But Rice who took only one year of math in high school, was actually discovering never-before-seen patterns.

Born in Florida, she loved learning and particularly her brief exposure to math, but tight budget and social culture prevented her family from even considering that she might attend college. “For Rice, math was a pleasure,” her son David once said.

Rice gave one of her sons a subscription to Scientific American partly because she could read it carefully while the children were at school. When she read Gardner’s column about tiling as she later recalled in an interview: “I thought it must be wonderful that someone could discover these beautiful patterns which no one had seen before.” She also wrote in an essay, “My interest was engaged by the subject and I wanted to understand every detail of it. Lacking a mathematical background, I developed my own symbol system and in a few months discovered a new type.”

Astonished and delighted, she sent her work to Gardner, who sent it to Doris, a tiling expert at Moravian College. Doris confirmed that Rice’s finding was correct.

Later, Rice declined to lecture on her discoveries, citing shyness, but at Doris’s invitation, she attended a university mathematics meeting, where she was introduced to the audience. Rice still said nothing of her achievements to her children, but they eventually found out as the awards mounted.

I often find myself running late on the edge of missing appointments. It’s not that I enjoy being late, but somehow, it keeps happening. A delayed train, a miscalculation in time, a wrong turn, the reasons for my lateness are many. I dislike being late, and yet, I frequently find myself in a rush or arriving behind schedule.

Michaela Thomas, a Swedish psychologist, calls people like me “time optimists” or “tidsoptimists”. We underestimate how long tasks will take and overestimate the time we have. As a result, we often find ourselves rushing, causing stress for both ourselves and those around us. It creates a domino effect of chaos, annoyance, and inconvenience for everyone involved. It can even have severe consequences.

The causes of standing lateness are complex. People, according to Jung, fall into two categories: “timekeepers” and “time enders”. Timekeepers work methodically, stay organized, and usually finish tasks ahead of schedule. In contrast, time enders, like me, push things to the last minute, feeling most energized and creative when under pressure.

Many see procrastination (拖延) as a key reason for lateness, but it’s not simply a time management issue. Fuschia Sirois, a professor of social and health psychology, believes procrastination often arises from mood management. People put off tasks to avoid dealing with emotions like anxiety, fear, or frustration. It can also be a form of rebellion when faced with boring or uncontrollable tasks.

Is there a solution for latecomers? Researchers suggest creating pre-event deadlines for important occasions like a wedding or catching a flight, so that the extra time can help you avoid being late when unforeseen circumstances arise. You can inform friends, family, and colleagues about your commitment to punctuality and ask for their support in helping you stay on time. For everyday improvement, setting alerts on phones for getting ready instead of departure time, breaking tasks into smaller, manageable parts and prioritizing time-flexible tasks can be helpful.