Imre Leader Engages Students in Simple Combinatorics Problem

The mathematics department invited Imre Leader, a British mathematician and Professor of Pure Mathematics at the University of Cambridge, to speak at Assembly on Friday, Sept. 23. He delivered a lesson on combinatorics, and later, he hosted hour-long sessions in the Academy Building. Leader attended St. Paul’s School and Trinity College of the University of Cambridge. In 1981, he won a silver medal at the International Mathematical Olympiad representing the United Kingdom’s team.

In the introduction of his Assembly, Leader posed one question to the audience: How should one vote? Though his mathematical solution relied on voting with the majority, he successfully engaged the audience in a mathematics lesson with an interesting problem. “I study mainly combinatorics,” Leader said. “It’s study of patterns if you like. It doesn’t have a lot of structure to it, just beautiful, beautiful patterns.”

“It wasn’t too difficult to comprehend, yet it was engaging, especially since it was centered around voting.”

Yannick Yao, senior and co-head of Math Club, greatly appreciated Leader’s take on combinatorics because the mathematics department does not often invite speakers for assembly. “He presented a problem in a humorous and accessible way that didn’t lose its rigor. I believe that this was a brand new experience for most Exonians, since math-related Assembly speakers are quite rare,” Yao said.

Lower Fiona Ku also enjoyed the assembly for Leader’s engaging style and seemingly hidden rigor. “Leader presented a seemingly simple problem that revealed an intriguing reality when taken apart,” she said.

Ku also, appreciated how Leader kept the audience on its toes by asking for audience participation throughout his presentation. “When he asked the audience to vote on the range of numbers in his final answer, it got me really thinking,” Ku explained. The voting was based off of guessing and assumptions, but students were still engaged when trying to pick the right answer.

Ku felt that Leader’s presentation helped her to think about mathematics from a new point of view. “Usually, we as students just type big numbers into the calculator and wait for it to spit out an answer. But this time, Leader made us think about the actual value,” she said.

Senior Eliza Khokhar found the delivery of Leader’s assembly to be refreshing. “[It wasn’t] too difficult to comprehend, yet it was engaging, especially since it was centered around voting.”

Lower Alex Mangiapane enjoyed the inclusivity of Leader’s presenting style. By working live on pen and paper that was projected onto a screen, Leader created understandable models and demonstrated the thought process behind each scenario. “The assembly was really cool on Friday. It was a new assembly directed towards math students, I also liked how he asked what other students thought the answer was at the end,” Mangiapane said.

Leader said that he has “always liked maths” and never had a specific moment when he became passionate about mathematics. “From what can I remember I liked maths as a child. I always felt a connection to it.”

When describing what he does as a professor now, Leader explained that he mostly teaches theory, logic, combinatorics, groups, rings and “just bits of pure math.” “You typically have lots of problems you’re thinking about. You can’t solve them and you’re depressed. Occasionally you have a good idea and you’re happy,” he said.

Leader also held two one-hour sessions following his assembly on Friday night and Saturday morning. Yao described the general topics of the sessions. “His session on Friday was about chasing and evasion in different scenarios. His Saturday morning was a problem-solving session between quantities ‘arbitrarily large’ and ‘infinite.’” Upper and Math Club co-head Kristy Chang added that the Saturday event, being designed towards groups three and four of Math Club, focused on more advanced topics and problems about chains and antichains.

A set of Leader’s problems focused on how a predator could evade capture or create a strategy to entrap its prey. Leader’s first set of problems described two scorpions trying to catch a beetle. With each problem, Leader changed the “playing field.” The bugs started chasing each other on two-dimensional circles, eventually moving onto a three-dimensional tetrahedron.

Leader made the students think of new solutions while applying the same basic strategy. Eventually, he changed the setting to a court in Trinity College of the University of Cambridge. “How many people does it take to stop one person from leaving the circular field without anyone catching that person?” he asked. His problems ranging in difficulty, Leader hosted a fun and challenging activity for students of all levels.

Leader also visited Yao’s real analysis class. After listening to the class discussion, Leader quickly came up with a related problem which was very non-standard and took a long time for the group to solve. “I was impressed by his wide breadth of knowledge and understanding of different math topics, and above all, I enjoyed the his style of presentation,” Yao said.

Ku felt that Leader encouraged passionate and curious students to challenge each conclusion in his presentation. “I loved that the problem appeared to be so straightforward at first, but became more complex the more I thought about it,” Ku said. “Mr. Leader’s message—that, often in mathematics problems that seem obvious are in reality not—came through loud and clear.”