Decoded (9 page)

It was a very complicated, strange game. The best comparison I can think of is to say that it is like the two of us joining battle, only to discover that my troops are under your command and your troops are under my command. Just think how bizarre and complicated it would be to fight a battle with only the opposing army at your command – bizarreness can in some cases be a kind of complexity. Because this game was so very complicated, most people simply could not play it. Liseiwicz said that it was designed solely for mathematicians to play and that is why it was called mathematical chess. There was one occasion when Liseiwicz was chatting to me about this game and he said triumphantly: ‘This game is the result of much research into pure mathematics: given the level of mathematical knowledge required to deal with its complexities, not to mention its intricate rules, the subtle way in which the subjective role of the player transforms the structural organization – really only human intelligence can compare. Inventing this chess game was a way of challenging the limits of our intelligence.’

The minute he said this, I was immediately reminded of his current research topic – artificial intelligence. I suddenly felt alarmed and uncomfortable, because I started to wonder whether this mathematical chess might not be part and parcel of his research. If that was the case, then Zhendi was clearly being used – he was covering up what he was doing by pretending that it was all about developing this game. I then made a special point of asking Zhendi why they had decided to develop mathematical chess and how they had gone about it.

Zhendi said that they had both enjoyed playing chess together but that Liseiwicz was so strong a player that he simply had no hope of ever being able to beat him, which in turn made him depressed and unwilling to play. Afterwards the pair had started thinking about developing a new kind of chess game, whereby the two of them would both start at the same level, without one having the advantage of knowing all the set variations. This game was to be structured so that victory would be determined purely by intelligence. When they were designing the game, Zhendi said that he was primarily responsible for designing the board, while Liseiwicz worked out the rules for how the pieces would be allowed to move. In Zhendi’s opinion, if you wanted him to work out how much of the game was his own work, he would say that it was around 10 per cent. If this game was indeed part of Liseiwicz’s research, then Zhendi had made a significant contribution and he deserved some credit for it. So I asked about Liseiwicz’s work on artificial intelligence. Zhendi said that he knew nothing about it and that so far as he was aware, Liseiwicz was not working on anything of the kind.

I asked him, ‘Why do you think that he is not working on anything of the kind?’

Zhendi said, ‘He has never mentioned it to me.’

It was all most strange.

I thought to myself, the moment Liseiwicz caught sight of me he was bubbling over with news of this new research plan, but now Zhendi spends pretty much every day with him and he doesn’t say a word about it? I was sure that something was up here. Later on, I asked Liseiwicz about it myself, and the only reply was that we did not have the facilities, he could not continue, and so he gave up.

Gave up?

Had he really given up or was this just something that he was saying?

To tell the truth, I was very unhappy about the whole thing. I don’t need to tell you, if he was just pretending to have given up on this research then we had a serious problem, because only someone who is engaged in unethical (if not downright criminal) activities feels the need to hide from other people’s eyes like that. The way that I thought about it, if Liseiwicz was indeed involved in something unethical, there was only one person he could be using, and that was poor little Zhendi. The whole department was buzzing with rumours, which had already forced me to think seriously about the unusual relationship that had developed between Liseiwicz and Zhendi – I was really worried that he was being cheated, being used. He was really still only a child at the time, completely unaware of how nasty other people can be, very emotionally immature and naïve. If someone is looking for a patsy, that is the kind of person that they would pick: innocent, isolated, timorous; the kind of person where if you bully them they keep quiet about it; the kind that suffers in silence.

Fortunately it was not long after this that Liseiwicz did something truly unexpected, which completely put all my fears to rest.

[To be continued]

Jan Liseiwicz and Jinzhen finalized the rules for mathematical chess in the spring of 1949. Not long afterwards, which was also not long before the provincial capital, C City, was liberated, Liseiwicz received an invitation from the journal, the
Annals of Mathematics
, to attend an event to be held at UCLA. In order to facilitate the travel arrangements for attendees from Asia there was a contact address in Hong Kong. Everyone was to meet there and then fly to California on the final leg of their journey. Liseiwicz did not spend very long in the States, maybe a month and a half in total, and he was back at work at the university so quickly that people found it hard to believe that he could really have been to America and back in that time. However, he had plenty of proof: job offers from universities and research institutions in Poland, Austria and the US; photographs of himself in the company of John von Neumann, Lloyd Shapley, Irvin Cohen and other famous mathematicians. In addition, he had brought back the question paper for that year’s Putnam Mathematical Competition.

[Transcript of the interview with Master Rong]

Putnam is the name of a mathematician: his full name was William Lowell Putnam and he was an American – people called him ‘the second Gauss’. In 1921 the Society of American Mathematicians, in concert with a number of universities, established the annual Putnam Mathematical Competition – the focus of considerable interest in universities and mathematical societies and an important way to discover new talent at undergraduate level in mathematics departments and institutes. The competition is designed to test basic principles learned by university students, but the questions are so difficult that they require a very high level of mathematical ability. Although every year the students who take part in the competition are the very best from each university, due to the unbelievable difficulty of the questions set, the majority of people who take part will score around zero. The top thirty competitors in any one year will be picked up by the finest universities in America and indeed the world – for example Harvard offers the top three highest-scoring competitors the most generous scholarships available at the entire university. That year there were fifteen questions, whereby full marks in the competition would be 150, with forty-five minutes to complete the entire paper. The highest mark awarded was 76.5, and to get into the top ten you had to score over 37.55.

Liseiwicz had brought back the competition questions because he wanted to test Zhendi. The only person he wanted to test was Zhendi – everyone else (including the other professors at the university) would just be put to unnecessary trouble and distress by being made to sit these questions, so it was much better for all concerned if they were left in peace. Before he tested Zhendi, he shut himself up in his own office for forty-five minutes and tested himself. Afterwards he graded his own paper. He decided that his final mark should be less than the highest awarded that year, because he had only correctly answered the first eight questions – the ninth was unfinished. Of course, if he had had just a couple of minutes more he would have been able to answer this question correctly as well: the time-constraints were ferocious. But then the purpose of the Putman Mathematical Competition was to emphasize two important points:

1. Mathematics is the most scientific of sciences.

2. Mathematics is the science of time.

Robert Oppenheimer, who is often called the father of the atom bomb, famously said: ‘In science, time is the real obstacle. Given unlimited time, everyone can learn all the secrets of the universe.’ Some people say that by building the world’s first atom bomb, he came up with the best way to solve the problem of how to put an end to the Second World War. But if you think about it, if it was Hitler who had succeeded in developing the atom bomb, wouldn’t the result be that mankind was facing an even worse problem?

Zhendi succeeded in answering six questions in the forty-five minutes allotted to him. In the solution that he offered for one of the questions, Liseiwicz decided that he had made the mistake of tampering with the original question and hence he received no marks. The last question was a logic problem and he had only had a minute and a half left to look at it. There was no time to even begin working out this problem, so he had written nothing, he had just thought about it and in the very last seconds of the examination, he had scribbled down the correct answer. It was a remarkable achievement and yet again demonstrated that Zhendi had a most unusual intelligence. Grading this kind of question is up to the individual examiner – one person might give him full marks, on the other hand someone else might deduct some points: it depended entirely on the examiner’s perspective of the student’s abilities. At worst, he would still have to be given 2.5 points for this answer, so after some thought, Liseiwicz decided to be harsh and give him this mark. Zhendi’s total was 42.5 points, in a year when to reach the top ten in the Putnam Mathematical Competition, you had to get over 37.55 points.

That would mean that if Zhendi had really been able to take part in the competition, he would have been ranked in the top ten, giving him the opportunity to study in an Ivy League university, with a full scholarship and all the fame accorded to a Putnam Fellow in the world of mathematics. But because Zhendi hadn’t formally taken part, if you took his papers and showed them to someone, they would just laugh in your face. No one would have believed that this little kid from somewhere in China that nobody had ever heard of could get such a high mark – they would have thought you were having them on. A stupid attempt to take them in. Even Liseiwicz, looking at the answer papers in front of him, felt that in some way he must be being deceived. It was only a feeling, of course. Because Liseiwicz knew that it was true – he knew that Zhendi had not cheated in any way – and so he turned something that started out as just a game into something very serious indeed.

The first thing that Liseiwicz did was to go and find Young Lillie, to explain the manner in which he had tested Jinzhen on the Putnam Mathematical Competition questions. Afterwards he gave his considered opinion on the matter: ‘I tell you that Jinzhen is the best student the university has ever had, and in the future he could likewise become the best student at Harvard, MIT, Princeton, Stanford or any other world-class university. That is why I am telling you that he really ought to go abroad to study. Harvard, MIT, wherever.’

Liseiwicz pursued the matter: ‘You should believe in his abilities and give him this opportunity.’

Young Lillie shook his head, ‘I am afraid it is impossible.’

‘Why?’ Liseiwicz’s eyes were completely round.

‘We don’t have the money,’ Young Lillie said frankly.

‘You would only need to pay for one semester,’ Liseiwicz said. ‘I am sure that by the time the second semester started he would be on a scholarship.’

‘The problem isn’t the first semester,’ Young Lillie said with a bitter smile. ‘With the situation we are in right now we could not even pay for his fare.’

Liseiwicz left disappointed.

Part of Liseiwicz’s disappointment was due to a natural feeling of sadness that his dream for his student had not worked out, but the remainder was darkened by suspicion. He and Young Lillie had never agreed about Jinzhen’s academic future. Now he did not know whether Young Lillie was telling the truth, or whether it was simply an excuse because he did not want to go along with the plan. He thought that the latter possibility was very likely correct for he found it hard to believe that a family as wealthy as the Rongs could really be in financial trouble.

Everything that Young Lillie had said was perfectly true, however. Jan Liseiwicz did not know that a couple of months earlier, the remnants of the family property at Tongzhen had been seized in the Land Reform, and the only thing that was left in their possession was a few ramshackle buildings in the old mansion. One commercial property remained in the provincial capital, but a few days earlier at the welcome ceremony for the new mayor, Young Lillie (as a member of a well-known patriotic family) presented it to the people’s government of C City as a sign of his support for the newly established People’s Republic of China. The decision to select such a public occasion for making the gift might seem like he was currying favour but in fact this was not the case – it was the recipients who decided it should be done this way. Furthermore, he agreed with their reasoning that it would set an example encouraging other members of wealthy and socially prominent families to support the new government. I can say categorically that the Rong family were great patriots and that Young Lillie was no exception – he beggared himself in order to demonstrate his loyal support for the People’s Republic. His support was determined both by his appreciation of the bigger picture and his personal experience of unfair treatment at the hands of the KMT government. Anyway, of the property that Old Lillie had inherited from his ancestors, when it reached the hands of himself and his son, some had been given away, some had been spent, some had been ruined and some had been divided, to the point where it was now all gone. Young Lillie’s own personal savings had gone in the battle to save his daughter’s life. His salary had not risen to cover the rising cost of living and he had lost all other possible sources of income. Now Jinzhen wanted to go and study abroad, but even though Young Lillie supported him wholeheartedly, there was nothing that he could do to help.

Eventually Liseiwicz realized what had happened. That came about just a couple of months later, when Liseiwicz received a letter from Dr Gábor Szego, then the Head of the Department of Mathematics at Stanford University, which accepted Jinzhen as a scholarship student and included a money order of $110 for travel expenses. This had been extracted from department funds purely thanks to Liseiwicz’s persuasive lobbying. He had written a 3,000-word letter to Dr Szego, and now those 3,000 words had returned, metamorphosed into a fully funded PhD place at Stanford and a ticket for the boat. When he told Young Lillie the news, Liseiwicz was delighted to see how happy the old man was.>

Just as Jinzhen was getting ready to spend his last summer at the university before heading off to Stanford, he became terribly sick. It was this that determined he would spend the rest of his life in China.

[Transcript of the interview with Master Rong]

He had renal failure!

Zhendi almost died!

When he first became sick, the doctor told us that he was going to die – at best, he would live for another six months. During that time, death was near him all the time; we watched a young man who had always been slim swell up until he looked vast, though his actual body weight continued to drop.

He was suffering from oedema. The renal failure affected him so badly that it was as if Zhendi’s body was made of dough, constantly fermenting, constantly swelling, making him as light and soft as a cotton-boll; it seemed as though he would burst if you poked him with a finger. The doctors said it was a miracle that Zhendi survived – in fact, in his case he did practically rise from the dead. He was in hospital for close on two years and the whole of that time he was not allowed to eat any salt, it was poison to him. The struggle to live wore him out. The money that the people at Stanford had sent to pay for his journey ended up going on his medical expenses and his scholarship to study there, his diploma, his life as a student, his very future were all swallowed up by the appalling present, becoming a vaguer and vaguer dream. All of Liseiwicz’s hard work went for nothing – he had wanted to create a brilliant future for his very best student but now he had to face two unpalatable facts: One, the money was gone and there was no way that the state of the Rong family finances would ever allow us to be able to replace that $110. Two, the people Liseiwicz relied on for his own future security (including me) had suspected him of the worst possible motives.

Liseiwicz’s actions had demonstrated the purity of his intentions and proved beyond any reasonable doubt that he was genuinely fond of Zhendi. Just think about it – if Liseiwicz was really using Zhendi to get results for his own research, there is no way that he would encourage him to go to Stanford. There are no true secrets in this world – over time the truth is always revealed. Liseiwicz’s secret was that he – more than anyone else – had become convinced that Zhendi was a truly rare mathematical genius. Maybe he saw in Zhendi some kind of reflection of himself as a boy – he loved him in the same kind of selfless way as he loved his own childhood – he was completely serious and totally innocent in this.

If Liseiwicz was ever unfair to Zhendi, it came much later and came about as a result of the mathematical chess game that they had developed together. It ended up being very influential in mathematical circles in Europe and America – lots of mathematicians played it. It wasn’t called mathematical chess though, because it was named after Jan Liseiwicz: Liseiwicz chess. I got to read a number of articles on Liseiwicz chess over the years and people clearly thought very highly of it. Sometimes its significance was even compared to that of von Neumann’s theory of chess as a two-person zero-sum game. It was said that while von Neumann’s concept was of particular importance in economic theory, Liseiwicz chess had great significance in military strategy. Although the practical applications of the two games had yet to be demonstrated, their theoretical importance was supposed to be enormous. People pointed to Liseiwicz, the youngest ever recipient of the Fields Medal, and said that he was an ornament to the world of mathematics – however, after he went to China, he had really done no original research of any importance with the exception of Liseiwicz chess – the last great achievement of his later career.

As I said before, Liseiwicz chess was originally known as mathematical chess and it was developed by Jan Liseiwicz and Zhendi together – Zhendi deserves some of the credit. Once Liseiwicz called the game after himself, there was no chance that Zhendi’s role would be recognized: he was eliminated from the story and Jan Liseiwicz took all the credit himself. You could say that he was unfair to Zhendi, but you could also say that the pair were really fond of each other and that Liseiwicz really did do his best for the boy . . .