# The peculiar inspiration of a mathematician

Ke Zhao, a generation of mathematics master, enjoys a high reputation in the international mathematics circle. He is the founder of modern Chinese number theory and the pioneer of quadratic research. Many of Ke Zhao’s research results benefited from sudden inspiration. “Some of my mathematical results were accidentally obtained when I woke up in the morning or when I woke up from a nap. It seemed inspired.” Ke Zhao’s inspiration was once considered peculiar. Ke Zhao doesn’t think so with ability or talent.

In 1933, among more than 30 classmates, only two got the diploma of Tsinghua University, and Ke Zhao was one of them. Two years later, he entered the Department of Mathematics at the University of Manchester for a PhD. Ke Zhao’s favorite tutor is the world-famous problem-solving master, the famous mathematician Model. After carefully reading Ke Zhao’s Tsinghua University graduation thesis and asking him some tricky questions, Model found that Ke Zhao has great potential. Although Model had already acquiesced to this student in his heart, he did not agree on the surface. Model called Ke a research subject “Minkowski Conjecture”, “If you can solve this problem, I will accept you as a disciple.” In fact, before this, Model has been studying this subject for three years. For a long time, there was no breakthrough. Model did not deliberately embarrass Ke Zhao, but wanted to take this opportunity to inspire him.

For Ke Zhao, who is thirsty for knowledge, this is a once-in-a-lifetime “ticket”: Model never accepts students easily, and only by proving himself can he succeed in apprenticeship. Ke Zhao immediately immersed himself in studying, except for eating and sleeping, his focus was all on solving the problem. A week was fleeting, but Ke Zhao couldn’t figure out any idea. He was ashamed and said to Model: “Teacher, I spent a week without any inspiration.” Model asked gently, “How do you think the inspiration comes from? “Ke Zhao was speechless, who had never thought about this problem. Mordel said earnestly: “Inspiration does not fall from the sky, but it will burst out inadvertently. When will the inspiration arise? When you study hard and’walk through’ all the difficulties, you will suddenly become’willows and flowers bright’.” Ke Zhao finished listening. Enlightenment.

Model gave the students three years to complete their doctoral dissertations, but only shortened Ke Zhao’s time to two years. Ke Zhao did not flinch, nor was he afraid of pressure, but seriously experienced the teacher’s insights on inspiration. The more adversity he felt, the more he felt that his skills were poor, and the more courageous Ke Zhao went forward, he never forgot the word “tap all over”. Unexpectedly, in just two months, Ke Zhao completed his doctoral dissertation on “The quadratic form of the table is the sum of squares of the linear form”. The speed is amazing and the results are remarkable. Since then, Ke Zhao’s road of mathematics has become wider and wider. As the first Chinese, Ke Zhao appeared on the stage of the London Mathematical Society, and later published more than 10 papers in world-class journals such as Journal of Number Theory, Oxford Mathematical Quarterly, and London Mathematical Society Journal.

When others regarded Ke Zhao as a genius, Ke Zhao knew very well: Where can there be any genius? This is all the result of “walking through” various difficulties. Ke Zhao is very grateful for his tutor’s enlightenment. Whenever he encounters an insurmountable obstacle, he does not escape, but confronts him directly. After stepping through one obstacle after another, he felt the burst of inspiration at any time. After returning to China, Ke Zhao inherited this secret and trained several generations of mathematicians.

Ke Zhao likes to play Go, and he often inspires them by playing Go with his students. Professor Li Delang from the School of Mathematics of Sichuan University is a student of Ke Zhao. He often plays Go with his teacher. Every time, when Ke Zhao’s chess game is dying, he can always “kill” a bloody path and turn defeat into victory. Li Delang recalled: “Every time I look at me, I will win, but the teacher tries to find another way. No matter how difficult the game is, he never gives up.” “The teacher told us that solving math problems is the same as playing Go. After going through all kinds of difficulties, inspiration will not come to the door on the initiative.”

How can there be natural inspiration? The burst of inspiration comes from the accumulation of hard research and unremitting efforts. As long as the usual effort is in place, inspiration may come at any time.