The Indian who taught in the Golden Palace was tall and old, but he fell nimbly to his knees when His Magnificence, the Emir Mahmoud Abdullah, may he live for ever, known in his student days at Oxford as David Ransome, strode in to the anteroom of the harem in the Golden Palace in Kobekistan. The Emir stopped, a little surprised at the scene before him. Instead of the usual sparsely furnished room with a small dais in the middle of the floor and a few chairs against the wall, he was transported in memory back some twenty years. There were serried ranks of school desks and facing them a larger teacher's desk and a blackboard.

"You have quite a professional set-up here," he remarked, "Do get up; that must be very uncomfortable for an old man."

"The Master is too kind," said Gupta Singh, rising to his feet rather less nimbly, and adjusting his turban, "Politeness is not so easy as it was, but I thank my Master for using my native tongue."

A perceptive listener would have identified the Sikh's origin not as India but Bradford in the north of England.

The Emir sat on one of the desks in the front row and asked, "You have a problem you wish me to solve?"

The teacher looked worried.

"Ask away. You will not give offence," he added kindly.

"Master, it is the problem of Sharifa, your daughter," the teacher replied.

The Emir smiled as he noticed that the old man had his fingers crossed; 'For luck, I suppose, ' he thought, 'He's afraid I'll have him beheaded, or worse.'

Aloud he said, "Why is she a problem? Does she disrupt your classes? Just send her back into the harem. She won't be with you for long anyway; she must be almost twelve now."

"She reaches her twelfth birthday in two days time, Master. That is the problem."

"Explain."

"As Your Magnificence, may you live for ever, surely knows, it is the custom here in Kobekistan that a child is a child until their twelfth birthday, and then, arbitrarily, they are considered young adults. A boy may no longer live in the harem with his mother; while for a girl the exact opposite happens, she is confined to the harem, no longer seen by any males but her father, and later her husband."

The Emir nodded. He had plenty of patience and pedagogues the world over delight in telling the obvious at great length. Doubtless the problem would appear somewhere along the way, and he had great respect for this man's teaching abilities.

"The problem is that she wishes to continue with her studies, and custom decrees that I cannot teach her after she ceases to be a child. This is not a problem in the area of languages, since the women of the harem teach her those skills. Even philosophy is discussed therein at some length, judging by some of her comments in class. The difficulty is mathematics."

David Ransome had been a post-graduate student of mathematics at Oxford University when a series of unlikely events had catapulted him to the throne of Kobekistan fifteen years earlier; the news that one of his children had an interest in mathematics intrigued him.

"What level has she reached in her studies?" he asked.

"I do not know how much Your Magnificence, may you live for ever, knows of these matters," the teacher said, biting his lower lip in fear at his own temerity. He had seen the Emir only a very few times, and never before spoken to him.

"I read math at Oxford and was preparing a Ph.D. thesis on the Topology of Non-Riemann Surfaces when my grandfather died and I was dumped on the throne here," his master replied.

The Sikh's face brightened, "She has already learned differential and integral calculus, Eminence, Master."

"Oh," said the Emir, quite taken aback. He had been considered brilliant, but he had been about fourteen or fifteen when he reached that level. Either his daughter was very bright, or very specialised in her knowledge.

He thought for a moment and the stood up.

"Come with me," he said and strode to the door to the harem proper.

"Your Magnificence, it is death for me to pass that door," the teacher queried, his voice rising an octave as his fear showed.

"Not if you are with me," the Emir reassured him, "just don't rape any of the women."

The teacher was on tiptoe as he passed through the forbidden door into the harem of the Emir of Kobekistan; as far as he knew no whole man except the Emir had walked in there since it was first built. Eunuchs did all the work that was needed.

The unexpected and unannounced arrival of the Emir caused a stir among the women and the eunuchs rushed about like chickens when a fox approaches. The few women who knew who the man was with the Emir were even more flustered. Only one man had ever accompanied him into the harem in fifteen years, the Princess Ayda's father; many of them had been offered as bed companions to honoured guests, but the arrangement was always that they were conducted to the man's room, never that the man came into the harem.

"Sharifa," the Emir bellowed.

The young girl came forward, clearly frightened half out of her wits. The only explanation she could think of, or any of the women could think of, was that she was to be given to the teacher as a present on her twelfth birthday.

Princess Alima, the younger of the English wives of the Emir started forward to protest but was held back by Princess Zubeydeh, the Emir's English mother, who had more faith in her son's good sense than any of the others. She knew he had tried hard to discourage the practice of child betrothals, and even marriages, before the girl was sufficiently adult to bear children safely.

The Emir looked the child before him up and down.

'Nice breasts, pretty face, ' he thought, 'She'll make someone very happy when she goes to his bed.'

Addressing her he asked, «Quelle age as-tu?»

Gathering her thoughts, the child answered, «Demain j'aurai douze ans, Maître.»

Privately she wondered why he spoke in French; in her experience, when she overheard him speak to anyone in the harem he usually used Arabic or English. He had never, as far as she could remember, spoken directly to her.

Immediately he switched to English, "Why do you want to learn more mathematics?"

She froze. Was this a trick question? Would she, or her much admired teacher, be punished if she answered wrong? Was there even a right answer?

Her father beckoned Princess Alima forward.

"Tell this foolish child that when I ask a question I want the truth," he snapped.

Princess Alima whispered in Sharifa's ear, ~Tell the truth. He'll know if you don't, and that will mean punishment for you and probably other people as well.~

As she did so one of the other women rushed forward. The Emir held up his hand to stop her, but she continued to run towards her daughter. A nod from the Emir was all it took. Two eunuchs grabbed the woman and one held her effortlessly while the other gave her three sharp blows with his dog whip. Sharifa's mother fell to the floor sobbing; it had been instinctive for her to try to help her daughter, but all she had achieved was to be whipped and to anger her Master, the child's father.

"Tell me why you want to learn more mathematics," he repeated.

The child was obviously too frightened to answer. The Emir took a handkerchief from his pocket and gave it to her.

"Do you know what this means?" he asked.

She nodded, "It means I can answer safely and will not be punished, but that only means me."

The Emir smiled and said, using Arabic so that all would understand, ~I don't have enough handkerchiefs in my pocket to give one to everybody here.~

The quip broke the tension in the room and even the girl smiled uncertainly.

"Now please tell me, before I die of old age waiting for my answer, why you want to learn more mathematics."

"It is difficult to explain. It is like an onion, only backwards. You learn a complete body of maths and it looks like everything there is, and then another layer appears which fits round that, and it seems complete again, but then there is another layer, and another, and another. I want to find the last layer, but I already know enough to know that so far I know almost nothing."

The Emir nodded. This explanation seemed to mean something to him, though most of the women were at a loss to understand what on earth she meant.

"Later on, ask Princess Zubeydeh to tell you about me, when I was your age," he said, "but for now I have some questions. First, what is the second differential of a formula?"

She was on firmer ground now, "It is essentially the rate of change of the gradient of the graph of the formula, sir."

"Who was Zeno, and why is he interesting to a mathematician?"

The answer came with confidence, "Zeno was a Greek philosopher and his paradox is an apparent proof that a fast runner will never overtake a slower one, nor even catch up."

"What does that signify?"

"That the sum of an infinite series may be finite," she replied without the slightest hesitation.

"What is Chebyshev's Inequality?"

She looked very worried, and finally said in a very small voice, "I don't know. I'm sorry."

"It doesn't matter," her father answered, "You will have to be accompanied by a eunuch and to wear an abaya." then turning to the teacher he asked, "How far can you take her?"

"Until she is ready for university, Your Magnificence, may you live for ever," that worthy replied, and then fell to the floor grovelling in obeisance as he realised the implication of what he had said. It was voicing the unthinkable that a woman from a high status harem in Kobekistan should even consider going to university.

"Get up, you fool. Some of the women here have actually been to university. It is not heresy to admit that it is possible."

He escorted the old man back to the door, and then turned to the Chief Eunuch.

"We will have to find some educated eunuchs or women to teach her literature and music and physics and chemistry. Find them and have a schoolroom set up. All the girls in this harem are to attend lessons the same as the boys from now on."

"Master," the Chief Eunuch managed to splutter in his shock at this amazing concept, but his Master had spoken and it would be done, though where he would find educated eunuchs was going to be a problem.

Then Sharifa piped up, ~Father, what is Chebyshev's Inequality?~

The Emir stared at her, then smiled broadly and switched to English, "It states that the probability that the outcome of a random variable with standard deviation sigma is no less than 'a' times sigma away from its mean, is no more than one over 'a' squared. How much of that do you understand?"

"Well, I know what a random variable is, and a standard deviation, but I would have to think about what you said."

"What did I say?" asked the Emir, curious to test how retentive her memory was.

"You said that Chebyshev's Inequality states that the probability that the outcome of a random variable with standard deviation sigma is no less than 'a' times sigma away from its mean, is no more than one over 'a' squared."