'Every even number greater than 2 can be written as a sum of two primes.'

'You surely can't prove that', said the famous mathematician.

'Not yet,' answered Petros, 'although I'm sure it's a general principle. I've checked it up to 10,000!'

'What about the distribution of the prime numbers? Caratheodory asked. 'Can you figure a way to calculate how many primes there are lesser than a given number n?'

'No,' answered Petros, 'but as n approaches infinity the quantity gets very close to its ratio by the natural logarithm.'

Caratheodory gasped. 'You must have read that somewhere!'

'No, sir, it just seems a reasonable extrapolation from my tables. Besides, the only books at my school are about geometry.'

The Professor's previously stern expression now gave way to a beaming smile. He called Petros' father inside and told him that to subject his son to two more years of high school would be a complete waste of precious time. Denying his extraordinarily gifted boy the best that mathematical education had to offer would be tantamount, he said, to 'criminal negligence'. Caratheodory would arrange to have Petros immediately admitted to his university - if his guardian consented, of course.

My poor grandfather never had a choice: he had no desire to commit a crime, especially against his first-born.

Arrangements were made, and a few months later Petros returned to Berlin and moved into the family home of a business associate of his father's, in Charlottenburg.

During the months preceding the start of the next academic year, the eldest daughter of the house, the eighteen-year-old Isolde, undertook to help the young foreign guest with his German. It being summer, the tutoring sessions were often conducted in secluded corners of the garden. When it got colder, Uncle Petros reminisced with a mellow smile, 'the instruction was continued in bed'.

Isolde was the first and (judging from his narrative) only love my uncle ever had. Their affair was brief and conducted in total secrecy. Their trysts would take place at irregular times in unlikely locations, at noon or midnight or dawn, in the shrubbery or the attic or the wine cellar, wherever and whenever the opportunity for invisibility beckoned: if her father found out, he would string him up by his thumbs, the girl had repeatedly warned her young lover.

For a while Petros was totally disorientated by love. He became almost indifferent to everything other than his sweetheart, to the point that Caratheodory came to wonder for a while whether he might have been wrong in his original appreciation of the boy's potential. But after a few months of tortuous happiness ('alas, too few,' my uncle said with a sigh), Isolde abandoned the family home and the arms of her boy-lover in order to marry a dashing lieutenant of the Prussian artillery.

Petros was, of course, heartbroken.

If the intensity of his childhood passion for numbers was partly a recompense for the lack of familial tenderness, his immersion into higher mathematics at Berlin University was definitely made all the more complete for the loss of his beloved. The deeper he now delved into its endless ocean of abstract concepts and arcane symbols, the farther he was mercifully removed from the excruciatingly tender memories of 'dearest Isolde'. In fact, in her absence she became 'of much more use' (his words) to Petros. When they had first lain together on her bed (when she had first thrown him on her bed, to be precise) she had softly muttered in his ear that what attracted her to him was his reputation as a wunderkind, a little genius. In order to win her heart back, Petros now decided, there could be no half-measures. To impress her at a more mature age he should have to accomplish amazing intellectual feats, nothing short of becoming a Great Mathematician.

But how does one become a Great Mathematician? Simple: by solving a Great Mathematical Problem.