1499 AD: Leonardo da Vinci, is painting Mona Lisa when his pupil enters his studio. The work is unfinished, but the student is charmed, nonetheless. "Your model has the smile of an angel," he says, "but, I see that she has left already; good for her because the French have entered Milan and we, too, are not safe here." Leonardo smiles at him. After they have packed their things, the lad finds that Vinci has left out the sketch. He looks at his master, who asks him, "Are you in love with her?" "Yes," says the youth, at which, Vinci smiles at him again.

They flee to Florence where Leonardo finds employment as senior military architect and general engineer of Cesare Borgia. For many years, he doesn’t paint anything because the fall of Milan is still fresh in his memory. 1513: the French are removed from Milan and Leonardo moves to Rome. Here, too, he devotes all his time to studying mathematics only. The unfinished portrait is still on his studio wall. The quiet man gets the shock of his life one day when he receives an invitation from King Francis I to enter his service in France.

"Monsieur Vinci," says King Francis on receiving the master and his pupil in his court, "I have learnt that you have quit painting and taken to useless things like mathematics. Why?" "Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar," says Leonardo. "I don’t understand you, but advise me as a military consultant what should I do to stop the rebellion here," says the king. "Find all sets of three positive integers whose product is seven times their sum," says the wise man. "Will it help?" says the king. "Just do it," says the painter, but, finding that the king can’t calculate, he decides to reveal the answer.

"We have to prove that xyz=7(x+y+z) Let x, y, z be the integers in increasing order. Then xyz=7(x+y+z)<=21z, so that xy<=21; and so, x<=4. For values of x=1, 2, 3, 4, we can use (xy)(xz)=7x(x+y+z) to get (xy-7)(xz-7)=7x(x)+49. When x=1, we get (y-7)(z-7)=56, so y=8, z=63; or y=9, z=35; or y=11, z=21; or y=14, z=15. For x=2, we get y=4, z=42; or y=7, z=9. For x=3, we get y=3, z=21; or y=5, z=7. There are no new solutions for x=4, so, there are eight solutions in all," he says. "What does it prove?" says the king. "Inequality is the cause of all local movements," says the wise man, "Imbalances lead to revolutions."

The king says, "Nevertheless, I have called you here to paint and not to do mathematics." "The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics," says Leonardo. The king says, "I am in love with your Mona Lisa. Where does she live?." The painter smiles, nods and leaves. He finishes Mona Lisa and watches the smile mesmerise the world. Many men, including the king, die with the name of Mona Lisa on their lips, but no one gets to meet her. May 2, 1519: Leonardo, on his deathbed at Cloux, Amboise, in France, says to his pupil. "I am going; ask what is on your mind." "Master, whose smile is that?" says the boy, pointing towards the portrait of Mona Lisa. The master dies with ‘the’ smile on his face, giving the pupil his answer. Mona Lisa is actually a self-portrait of Leonardo! X-rays of the painting and close comparison with portraits of Leonardo suggest that this may indeed be true.

— Aditya Rishi