Everyone involved in the world of mathematics realized that after Jan Liseiwicz went to China he changed a great deal, becoming a wonderful husband and father, but less and less of an original and creative mathematician. Perhaps his remarkable talents were intrinsically bound up in his undomesticated existence; and thus once he married his genius deserted him. The fact is that if anyone had thought to ask him, he would have been hard put to answer whether his actions had destroyed his talent, or whether it had just vanished of its own accord. As any mathematician could tell you, before Jan Liseiwicz went to China, he wrote twenty-seven papers which were greeted with international acclaim, but afterwards he did not write even one. On the other hand, it was during this time that his sons and daughters were born. It was as if his genius vanished in a woman’s embrace, only to transform itself into a succession of adorable babies. Looking at what happened to him, people came to believe that there might be something in the old adage about how east is east and west is west and never the twain shall meet. For such a strange man to change in such a mysterious way, in such a profound way, was really quite unbelievable. At the time no one realized quite what was going on, but we all saw the results.
Of course, though he might have lost one part of his genius, Jan Liseiwicz remained a truly remarkable teacher. You could say that while he became less and less of an original, creative mathematician, he had transformed himself into a professional and highly respected instructor. Liseiwicz taught at the mathematics department in N University for eleven years, and the chance to become one of his students was unquestionably a great honour and a wonderful beginning to any mathematician’s career. To give you just one example: of the handful of students of N University who have achieved international recognition in their field, more than half were his students during his eleven years there. Of course, being one of his students was no sinecure. First, you had to be able to speak English (after Hitler’s invasion of Austria he refused to speak German ever again). Secondly, he would not allow anyone to take notes in his classes. Furthermore, when setting out a problem he would often only give half of it, or he would deliberately set out part of it incorrectly. Having set it out wrongly he would not correct it, or at least not on the same occasion. If he happened to remember it a few days later, he might give you the problem correctly, but if not, he didn’t care. It was that little trick more than any of the others which made many of his less intelligent students give up halfway or transfer to another department. His whole educational theory could be summed up in a single sentence: An interesting but wrong theory is always better than a boring but perfect proof. If you get right down to it, the reason he used these tricks was to force his students to think, to develop their imaginations and their creative abilities. At the start of every new academic year, facing his new students, he would begin his first class with the same message, couched in a strange mélange of Chinese and English: ‘I am a wild animal, not an animal trainer. I am going to chase you deep into the mountains and forests and you are going to have to do your damnedest to run ahead of me. The faster you run, the faster I will chase you. If you run slowly, I will chase you slowly. Whatever happens, you must run, you must never stop, whatever difficulties you face. The day that you stop running, our relationship is over. The day that you run deep into the woods and disappear from sight, our relationship is also over. In the first instance, I have given up on you; in the second, you have set yourself free. Right: now it is time to start running and see who can get away from whom.’
Of course, it was very difficult to set yourself free from him, but the means of doing so was extremely simple. At the start of every term, in the very first class, Liseiwicz would begin by writing a tricky equation in the top right-hand corner of the blackboard. Whenever someone worked out the answer, he would be given 100 per cent as his grade, and for the rest of the term he would only have to attend class if he wished to do so. You could say that you had set yourself free for the rest of that term. Once that had happened, he would write a new equation in the same place on the blackboard and wait for a second person to get the answer right. If you solved three equations in a row, he would set a new problem for you alone, which would function as your graduation thesis. If you solved that too, whenever it happened, even if you had only attended the university for a couple of days, you would graduate with top marks, thereby completing your studies. Of course, in the nearly ten years that he had been teaching by then, there had never been anyone who had achieved anything close — even being able to solve one or two of his equations was a remarkable achievement.[To be continued]
Jinzhen was now sitting in Liseiwicz’s class, and because he was so short (being still only sixteen), he sat in the very front row. He could see the sharp flash and sparkle of Jan Liseiwicz’s pale blue eyes much more clearly than any of his fellows. Liseiwicz was a tall man, and standing by the teacher’s podium, he seemed even taller. His eyes were fixed on the very back row of seats. Jinzhen felt the occasional fall of drops of spittle when the professor became excited and the sudden exhalation of breath when he raised his voice. He talked about these dry, abstract mathematical notations in a voice filled with intense emotion. Sometimes he waved his arms and shouted; sometimes he walked slowly up and down, reciting. Liseiwicz, when he stood in front of the teacher’s podium, seemed like a poet, or maybe like a general. At the end of the class, he walked out without a further word. However, on this occasion, just as he was stomping out, Jan Liseiwicz’s gaze happened to fall on the thin young man seated in the front row. He had his head bent over the sheet of paper where he was working out a calculation. He seemed entirely intent upon his work, like a student in an exam hall. Two days later, Liseiwicz held his second class. When he took his place at the podium, he asked a general question: ‘Is there someone here called Jinzhen? If so, could you please raise your hand?’
Liseiwicz realized that the student who raised his hand was the young man in the front row that he had noticed when he left after his first class. He waved the couple of sheets of paper that he was holding in his hand, and asked, ‘Did you put these under my door?’Jinzhen nodded.
Liseiwicz said, ‘Let me tell you, this term you don’t need to attend class.’
There was a sudden uproar.
Liseiwicz seemed to be enjoying something, for he waited for the hubbub to subside with a smile on his face. Once everyone was quiet again, he wrote the equation out on the blackboard again — not in the top right-hand corner this time, but on the top left-hand side — and then he said, ‘Let us have a look at how Jinzhen solved this problem. This isn’t an extra-curricular novelty. His solution is going to be the subject of our class today.’
He began by writing out Jinzhen’s answer on the board in full and explained it from start to finish. Then he used different methods to produce three alternative solutions, so that those sitting in class felt that they were learning something through the comparison, tasting the strange joy of reaching the same goal by travelling different routes. The topic of this new class was developed step-by-step as he explained each method. When he had finished, he wrote a new question at the top right-hand corner of the blackboard and said: ‘I would be really pleased if someone can answer this before the beginning of the next class. That is the way to go: I give you a question in one class and you answer it in the next.’
That was what he said, but Liseiwicz was well aware that the chances of that happening were vanishingly small. If you were going to express it mathematically, you would need to use a very small fraction of a per cent, and even then you would be rounding the number up. Calculation often proves a slipshod method of determining the future — it shows the possible as being impossible. People often do not work as tidily as calculations: they can make the impossible possible; they can turn earth into heaven. That means that in actual fact there is no great gulf between heaven and earth: one fraction more and earth becomes heaven, one fraction less and heaven will change into earth. Liseiwicz really had no idea that this silent and impassive boy would be someone who could confuse him as to the nature of what he was looking at — having decided that it was earth, he could come up with a result demonstrating that in fact it was heaven. In other words Jinzhen solved the second problem that Professor Liseiwicz set him right away!