On November 9th, the Middle School hosted a grand mathematical event. A themed lecture, "Math: Joviality to Practicality" was delivered at the Shuimu Theater by professor Bai Fengshan, a Director on the Board of Trustees of Tsinglan School, is currently a professor and doctoral supervisor in the Department of Mathematical Sciences of Tsinghua University. The lecture stirred up a storm of knowledge, integrating the profound aspects of mathematics into lively and engaging explanations, laying the foundation for students to ascend the stairs to the kingdom of mathematics.
Professor Bai captured the attention of all the students at the beginning of the lecture. He stated, "Mathematics is the driving force for learning, but it shouldn't be the sole driving force," sparking profound reflection among the students. This declaration prompted contemplation among the students. As they pondered this idea, the professor proceeded to elaborate on what mathematics is and its relevance to students. From basic counting to in-depth exploration, this process unveiled the essence of mathematics - counting, calculating, and proving.
When mentioning the keyword “proving”, the professor introduced the notion of "infinite" and elucidated it through practical and easily comprehensible examples. Particularly in the discourse on "fully occupied" (Hilbert's paradox of the Grand Hotel), professor proposed a fascinating hypothesis: envision a hotel with an infinite number of rooms, yet all rooms are occupied, leaving no space for new guests. However, by shifting the room number for each guest (e.g., k+1), the "fully occupied" situation can be eliminated, assuming the hotel has an infinite number of rooms. Students were deeply captivated by this concept, eagerly raising their hands to share insights or pose questions. Professor Bai attentively addressed each inquiry, guiding everyone to delve deeper into their thoughts and broaden their perspectives. At this moment, Shuimu Theater expanded like a vast sea, capable of embracing the overflowing enthusiasm of the entire middle school. Simultaneously, it resembled a distinctive little universe, where all eyes were tightly focused on Professor Bai's inspiring and exceptional explanation that ignited creativity.
Subsequently, Professor Bai introduced the concept of "dimension." While many traditionally associate "dimension" with integers like one, two, or three. Professor Bai challenged this notion, stating, "In this world, there are also 1.53 dimensions, 1.68 dimensions...". At that time, the packed theater was silent, as if this unheard-of concept were a kind of magic, and the students were the captivated audience. In the midst of everyone's confusion, the professor showcased a geometric diagram. In the diagram, a one-dimensional line was divided into three equal parts, and the middle segment was extracted, replaced by two lines of equal length, and so on. This cyclic transformation gradually approached zero. The relationship between 0 and infinity was akin to the two sides of a coin, elusive and challenging to grasp.
The lecture proceeded with fervor, as students maintained their enthusiasm and teachers immersed themselves deeply in the content. Professor Bai created famous sayings one memorable phrase after another while imparting knowledge, such as, "My abstraction has surpassed the world of reality." This statement once again describes the infinite world.
Throughout the lecture, Professor Bai not only unveiled the mystique of mathematics but also guided students to delve into the essence of mathematics through vivid language and captivating examples. From simple counting to the classic Hilbert's paradox of the Grand Hotel and geometric figures and algebra, it goes deep into the fundamental elements of mathematics - numbers, calculations, proofs—he seamlessly navigated from planar geometry to global positioning systems (GPS). Presenting a feast of thought in a relaxed and humorous manner, Professor Bai held students' attention, leaving them reluctant to depart. After the lecture, students gathered around Professor Bai, eager to engage in further discussions about their inquiries and aspirations related to mathematics.
On the evening before and the morning of the lecture, Professor Bai also held small communicating activities with L-scholars from middle school and other students passionate about mathematics, programming, or artificial intelligence(AI). In this digital era, mathematics and programming are integral to our lives, intricately linked to the contemporary world. Throughout these exchanges, Professor Bai highlighted the remarkable speed of recent artificial intelligence development, citing examples such as ChatGPT and Google. But why is AI developing so rapidly? The answer lies in the fact that human physical and mental endurance is surpassed by artificial intelligence. Whether considering cognitive ability or efficiency, artificial intelligence significantly outpaces humans, with ChatGPT serving as a striking illustration of this swift advancement in artificial intelligence.
The students mentioned the Four-Color Theorem during the conversation with Professor Bai, the idea that any map can be colored with just four colors in a way that ensures countries with common borders have different colors, meaning, in a non-confusing manner, a map only requires four colors for labeling. The students actively discussed the feasibility and correctness of the Four-Color Theorem and questioned what kind of process or characteristics are needed for a true proof. In the course of this discussion, students engaged in an in-depth conversation with the professor about Fermat's Last Theorem, a classic problem in number theory.
Fermat's Last Theorem poses an intriguing and profound mathematical challenge: When the integer n>2, the equation x^n + y^n = z^n has no positive integer solutions for x, y, z. This problem has perplexed mathematicians for centuries, and Professor Bai, through vivid explanations, guided the students to explore the deeper implications of this conjecture. Through the discussion, students gradually grasped the beauty of mathematics, realizing that Fermat's Last Theorem encapsulates profound and marvelous mathematical principles. The existence of this conjecture transforms mathematics from a mundane realm of symbols and operations into an endless journey of speculation and contemplation.
In the practical realm of mathematical learning, the professor pointed out that students might feel that the mathematics knowledge they are currently acquiring seems to have no immediate utility, may lack practical significance in future work, or they may be uncertain if it could lead to a viable professional direction. Building upon that, Professor Bai shared with the students that the knowledge itself is not the most crucial aspect rather it is the ability to learn. Math, as a language, may not immediately demonstrate its utility. It requires the gradual accumulation of knowledge until your skills become sufficiently transferable, allowing for a better appreciation of the beauty of math.
During his visit to Tsinglan School, Prof. Bai also engaged with his mentor group, students from S-Plan, Tsinglan Z-Innovative Teachers, Tsinglan-Z Club Mentors, and the Maths Curriculum Group. They exchanged views on various aspects of utilizing the beauty of Mathematics and the teaching and learning of Mathematics. Tsinglan School is privileged to benefit from the exceptional academic resources of Tsinghua University. This enables both teachers and students to engage in continuous reflection and maturation through meaningful dialogues with accomplished mentors.
Throughout our academic journey, we encounter mathematics from elementary school to advanced levels, but what exactly is it? This is a question worth pondering. Professor Bai once stated, "Mathematics is the driving force of learning," emphasizing that it is the motivation and passion that enable students to discover the beauty of mathematics. Professor Bai serves as a spark, igniting the students' yearning for mathematics; he is also like a staircase, supporting the students as they steadily climb upward, finding their future selves.
