Toulouse, France. 14 January, 1636 A.D.:

In the dusty calm of his study, he took down his beloved copy of Diophantus’ Arithmetica. With great excitement he turned to Book II, Problem 8, and hunted for a quill.

…On the other hand, it is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as a sum of two fourth powers, or, in general, for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain…

Bernadette Winstanley, a fourteen-year-old student from Harare, Zimbabwe, booked time on her high-school WormCam and devoted herself to tracking back from the moment of Fermat’s brief scribbling in that margin.

…This was where it had started for him, and so it was appropriate that it was here that it should end. It was after all Diophantus’ eighth problem which had so intrigued him, and sent him on his voyage of mathematical discovery: Given a number which is a square, write it as a sum of two other squares. This was the algebraic expression of Pythagoras’ theorem, of course; and every schoolchild knew solutions: 3 squared plus 4 squared, for example, meaning 9 plus 16, summed to 25, which was 5 squared.

Ah, but what of an extension of the notion beyond this geometric triviality? Were there numbers which could be expressed as sums of greater powers? 3 cubed plus 4 cubed made 27 plus 64, summing to 91 — not itself a cube. But did any such triplets exist? And what of the higher powers, the fourth, fifth, sixth…?

It was clear the ancients had known of no such cases — nor had they known a proof of impossibility.

But now he — a lawyer and magistrate, not even a professional mathematician — had managed to prove that no triple of numbers existed for any index higher than two.

Bernadette imaged sheets of notes expressing the essence of the proof Fermat believed he had found, and, with some help from a teacher, deciphered their meaning.

…For now he was pressed by his duties, but when he had time he would assemble a formal expression of his proof from the scribbled notes and sketches he had accumulated. Then he would communicate it to Desargues, Descartes, Pascal, Bernoulli and the others — how they would marvel at its far-reaching elegance!

And then he could explore the numbers further: those pellucid yet stubbornly complex entities, which seemed at times so strange he fancied they must have an existence independent of the human mind which had conceived them…

Pierre de Fermat never wrote out the proof of what would become known as his Last Theorem. But that brief marginalia, discovered after Fermat’s death by his son, would tantalize and fascinate later generations of mathematicians. A proof was found — but not until the 1990s, and it was of such technical intricacy, involving abstract properties of elliptic curves and other unfamiliar mathematical entities, that scholars believed it was impossible Fermat could have found a proof in his day. Perhaps he had been mistaken — or had even perpetrated a huge hoax on later generations.

Then, in the year 2037, to general amazement, armed with no more than high-school math, fourteen-year-old Bernadette Winstanley was able to prove that Fermat had been right

And when at last Fermat’s proof was published, a revolution in mathematics began.

Patefield Testimony: Of course, the kooky fringe immediately found a way to get online to history. As a scientist and a rationalist I regard it as a great fortune that the WormCam has proven the greatest debunker yet discovered. And so it is now indisputable, for example, that there was no crashed UFO at Roswell, New Mexico, in 1947. Not a single alien-abduction incident yet inspected has turned out to be anything more than a misinterpretation of some innocent phenomenon — often complicated by disturbed neurological states. Similarly, not a shred of evidence has emerged for any paranormal or supernatural phenomenon, no matter how notorious. Whole industries of psychics, mediums, astrologers, faith healers, homeopathists and others are being systematically demolished. We must look forward to the day when the WormCam’s delvings reach as far as the building of the Pyramids, Stonehenge, the Nazca geoglyphs and other sources of “wisdom” or “mystery.” And then will come Atlantis… It may be a new day is dawning — it may be that in the not too distant future the mass of humanity wilt at last conclude that truth is more interesting than delusion.

Florence, Italy. 12 April, 1506 A.D.

Bernice would readily admit she was no more than a junior researcher in the Louvre’s curatorial office. And so it was a surprise — a welcome one! — when she was asked to perform the first provenance check on one of the museum’s most famous paintings.

Even if the result was less welcome.

At first the search had been simple: in fact, confined to the walls of the Louvre itself. Before a blur of visitors, attended by generations of curators, the fine old lady sat in semi-darkness behind her panes of protective glass, silently watching time unravel.

The years before the transfer to the Louvre were more complex.

Bernice glimpsed a series of fine houses, generations of elegance and power punctuated by intervals of war and social unrest and poverty. Much of this, back as deep as the seventeenth century, confirmed the painting’s documented record.

Then — in the early years of that century, more than a hundred years after the painting’s supposed composition — came the first surprise. Bernice watched, stunned, as a scrawny, hungry-looking young painter stood before two side-by-side copies of the famous image-and, time-reversed, with brushstroke after brushstroke, eliminated the copy that had passed down the centuries to the care of the Louvre.

Briefly she detoured to track forward in time, following the fate of the older “original” from which the Louvre’s copy — just a copy, a replica! — had been made. That “original” was to last little-more than two centuries, she saw, before being lost in a massive house fire in Revolutionary France.

WormCam studies had exposed many of the world’s best-known works of art as forgeries and copies — more than seventy percent of pre-twentieth-century paintings (and a smaller proportion of sculptures, smaller presumably only because of the effort required to make copies). History was a dangerous, destructive corridor through which very little of value survived unscathed.

But still there had been no indication that this painting, of all of them, had been a fake. Although at least a dozen replicas had been known to circulate at various times and places, the Louvre had a continuous record of ownership since the artist had laid down his brush. And there was besides evidence of changes to the composition under the top layer of paint: an indication more of an original, assayed and reworked, than a copy.

But then, Bernice reflected, composition techniques and records could be faked too.

Bewildered, she returned down the decades to that dingy room, the ingenious, forging painter. And she began to follow the “original” he had copied deeper into the past.

More decades flickered by, more transfers of ownership, all of it an uninteresting blur around the changeless painting itself.

At last she approached the start of the sixteenth century, and was nearing his studio, in Florence. Even now copies were being made, by the master’s own students, But all of the copies were of this, the lost “original” she had identified.

Perhaps there would be no more surprises.

She was to be proved wrong.

Oh, it was true that he was involved in the composition, preliminary sketches, and much of the painting’s design. It was to be the ideal portrait, he declared grandly, the features and symbolic overtones of its subject synthesized into a perfect unity, and with a sweeping, flowing style — to astound his contemporaries and fascinate later generations. The conception, indeed, was his, and the triumph.