In the afternoon of December 9, Professor Luo Shunlong, director of the Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, gave a wonderful lecture titled “Number: from Empty Set to Quantum” to the students of Kuang Yaming Honors School. By raising the questions of “Where did the number come from? Where is it going? And what is the use of it?”, Professor Luo delineated the intuitive and logical processes of how numbers evolve from empty sets to matrices from a constructive point of view, revealed the hardships and necessity of the expansion of number systems, and demonstrated the power and mystery of their applications.

Professor Luo first introduced the concept of set partitioning and equivalence relations, and then presented the Peano Curve and Stirling’s formula, following by the development from natural numbers, integers, rational numbers, irrational numbers, real numbers, and finally, to complex numbers. G. Cardano, an encyclopedic scholar of the Italian Renaissance, was a very important figure in this period. Going from the real number to the complex number meant embracing a brand-new world, with much gained and the order lost. Sir William Rowan Hamilton, an Irish mathematician, spent eight years searching in vain for ternary numbers but later discovered quaternions. He was not only a mathematician, physicist and astronomer, but also a linguist, a poet and a lovelorn man, who considered poetry and mathematics to be close relatives.

 Next, Professor Luo clarified the concepts of octonions and tensors, which led to quantum mechanics. He explained that quanta are described by matrices (operators) and introduced Pauli matrices, Gell-Mann matrices, Dirac matrices, and commutators. Then, he explained the reason why the classification of elementary particles originated from matrix group representations. After a continuous expansion of the number systems, we reached an amazing quantum world (operator world).

 Professor Luo unveiled the mysterious quantum mechanics to the students, who were intrigued and benefited from the lecture.