July 14, 2025

Our third day on campus began with a lecture by Professor Steffen Marcus. Dr. Marcus was unable to attend in person, but he graciously agreed to deliver his talk via Zoom. Dr. Marcus of the mathematics department of The College of New Jersey discussed The Mountain Climber Problem. Each of our participants were provided with a two-meter piece of string so they could join in the activities Dr. Marcus had planned. He began with 1 peg in a mountain, a piece of rope, and a cat, Mauve, holding on to the rope. He asked how to loop the string around the peg so that if the peg was pulled out, Mauve would fall into the river below. The students quickly realized that no matter how they looped the string around the peg, Mauve would fall into the river. Next, Dr. Marcus put 2 pegs in the mountain and asked the students how to loop the rope around the pegs so that if either peg was pulled out, Mauve would fall into the water below. Students used their pieces of string and their fingers or pencils to simulate the pegs. After experimenting for a while, several students were able to find a way to loop the string around both pegs in such a way that no matter which peg was removed, Mauve fell into the river. From these two examples, Dr. Marcus showed the algebraic interpretation of these loops and then demonstrated how a solution to the two peg problem could be found algebraically. He next asked them to do this with 3 pegs, and several students succeeded in doing this. It turns out that the solution to this problem is really part of the study of non-Abelian groups.

After a short break, we held our first of two individual rounds. In these rounds, students are given seven minutes to solve difficult questions working on their own. There are seven questions on each round and each question is worth 10 points. The fun for those of us watching the students comes when we collect their answers, announce the correct answer, and hear them cheer if they get the question correct. The questions are quite challenging, but our participants continued to impress us with their ability to solve many of them.

After a break for lunch, we returned to Decker for Professor Zhengping Jay Luo’s talk. Dr. Luo is an Assistant Professor at the College of Liberal Arts and Sciences, Rider University. His topic was “The Beauty of Quantum Computing from a Mathematical Perspective.” Rather than my trying to explain anything about quantum theory and revealing my ignorance, I will let Dr. Luo describe his lecture:

Quantum computing has, in many ways, redefined our imagination about what technology can do. Unlike classical computers, which operate using binary bits that exist in states of either 0 or 1, quantum computers utilize quantum bits or qubits, which can exist in superpositions of states. This foundational difference enables quantum systems to process information in ways that vastly extend beyond the capabilities of traditional computing, offering new approaches to solving complex problems that were previously considered impossible.

In this talk, we will introduce the foundational concepts of quantum computing through a mathematical lens. We will use the language of mathematics to uncover the elegant ideas behind concepts like superposition, entanglement, and interference, and understand how these principles form the basis of quantum algorithms. By highlighting the elegant structures and abstract reasoning at the heart of quantum theory, you will discover how quantum computing challenges our classical ways of thinking and why it’s considered one of the most exciting frontiers in science and technology today.

Dr. Luo concluded his talk by telling our participants that this field is in its infancy and that they may be the ones who develop it when they are older. This was a fascinating talk at a very high level.

After this talk, we completed the second part of our individual rounds. Once again we challenged our participants with seven difficult math problems that I doubt I would have been able to solve when I was in high school.

Tonight was the second night of our talent show. Adam Raichel was back by popular demand to host our big show along with Haley Kooyman. Adam refrained from telling too many jokes, but here’s an example of one he did tell: “Why do we never see Elephants hiding in trees? (Long pause while the audience thinks about this.) Answer: Because they’re good at it!” Like many of Adam’s jokes, this one takes a few seconds to sink in. After one participant demonstrated his amazing dance skills, Haley entertained our participants with her remarkable magic act that would make Penn and Teller envious. This was a real treat for all of us. Our performers tonight included the usual assortment of singers, dancers, pianists, and Rubik Cube experts, but also included a violinist, a celloist, and a reader of Chinese poetry. We concluded the evening with some more information from our student game developer about his app, Pop The Lock X. As mentioned in yesterday’s newsletter, ou can find this game at Pop The Lock X.

Get ready for tomorrow when we hold our Speed Round and our three Relay Rounds.