Alexis Lemaire

Alexis Lemaire: Seventy Seconds, Two Hundred Digits

On 10 December 2007, in London's Science Museum, a Frenchman looked at a two-hundred-digit number, closed his eyes, and after seventy-and-a-fifth seconds said the number whose thirteenth power it was. Alexis Lemaire had by then broken the same record so many times, mostly his own, that the organisations responsible for certifying such things had given up trying to standardise it. He was also, away from the cameras, a doctoral researcher in artificial intelligence.

The Thirteenth Root

The stunt requires explanation, because its difficulty is not obvious. Taking a thirteenth root sounds arbitrary, and in a sense it is — the number thirteen was chosen by the mental calculation tradition because it produces a well-behaved problem. What makes the feat tractable at all is that a great deal of information about the answer can be extracted from small pieces of the question: the leading digits of the enormous number constrain the size of the root, and the trailing digits constrain its ending. The calculator's task is to squeeze both ends toward each other until only one candidate survives.

That is a description of the method, not of the difficulty. A two-hundred-digit number must first be read and held. Then the estimation must be performed against memorised tables of powers. Then the result must be verified before it is announced. The record set on 17 December 2004 — 3.625 seconds for the thirteenth root of a hundred-digit number — was explicitly timed to include reading, calculation and verification, which is the only honest way to measure it.

A Record Broken and Rebroken

Lemaire was born in 1980 in France. He entered the record books on 10 May 2002, extracting the thirteenth root of a hundred-digit number in 13.55 seconds. The previous marks give a sense of the leap: Willem Klein, the Dutch calculator who had been the tradition's dominant figure, had taken 88.8 seconds, and Gert Mittring had brought it down to 39. Lemaire cut it by nearly two-thirds in a single attempt.

He then spent years dismantling his own results. On 17 December 2004 he reduced the hundred-digit time to 3.625 seconds. Having effectively exhausted that problem, he moved to the harder one: on 6 April 2005 he extracted the thirteenth root of a two-hundred-digit number in 8 minutes and 33 seconds.

The compression that followed was relentless. On 30 July 2007 he recorded 77.99 seconds at the Museum of the History of Science in Oxford. On 15 November 2007 he managed 72.4. On 10 December 2007, at London's Science Museum, he reached 70.2 seconds. From eight and a half minutes to seventy seconds in twenty months.

The Rival, and the Vanishing Record Book

Lemaire's career ran alongside that of Gert Mittring, and the rivalry produced the one genuine controversy in the story. In November 2004 Mittring recorded 11.8 seconds — a spectacular time — but the result was not officially recognised. The reason was not an accusation of cheating. It was that the certifying organisations had discontinued standardised records for root extraction altogether, citing the difficulty of standardising the challenge.

That decision is the most revealing fact about the discipline. The problem is that not all two-hundred-digit numbers are equally hard: some yield to shortcuts, others resist, and the difficulty of a given attempt depends on the number the organisers happen to choose. Without a way to normalise that, comparing two performances is comparing two different exams. The record book closed not because the feats were fake but because they could not be made commensurable.

The Day Job

The detail that most changes the picture is that Lemaire is not a professional performer. He holds a PhD in computer science from the University of Reims, specialising in artificial intelligence. He spent his working life on the question of how machines reason while spending his public life demonstrating a form of human reasoning that machines had rendered obsolete decades earlier. Any pocket calculator, given the right software, would beat him instantly and always. He knew that better than his audiences did.

Why Alexis Is Called a Genius

The label is applied to Lemaire constantly, and it needs to be handled carefully, because the claim rests on trained skill rather than on general intellectual power. Nothing in the thirteenth-root feat produces new knowledge. The mathematics involved is elementary; what is extraordinary is the execution. Lemaire's ability consists of an enormous memorised repertoire of powers and logarithmic relationships, an efficient algorithm for narrowing candidates from both ends of a number, and — the part that cannot be taught — the working memory to hold two hundred digits and a running calculation simultaneously while a clock runs and a museum audience watches.

That last component is the genuine cognitive outlier. Ordinary working memory tops out at a handful of items; Lemaire operated on hundreds. Whether that reflects an unusual native capacity or an unusually well-built system of chunking and mnemonics is precisely the question the discipline cannot answer about any of its champions, including Lemaire himself.

The counter-case is straightforward. This is a performance craft, closer to what a chess blindfold simultaneous player or a memory champion does than to what a mathematician does. It is improved by thousands of hours of drilling. Its records were retired because they could not be standardised, which means the numbers themselves are softer than they look. And the field is small — being the best in the world at thirteenth roots means beating perhaps a few dozen serious competitors. Lemaire's doctorate in artificial intelligence is the stronger evidence of general intellect, and it is the part nobody puts in the headline.

Legacy

Lemaire's records stand at the end of a tradition rather than the beginning of one. Mental calculation as public spectacle had a long nineteenth- and twentieth-century run, and he arrived for its last act, breaking marks set by Klein and trading them with Mittring in an era when the certifying bodies were already walking away. What he demonstrated is not that humans can outcompute machines — they cannot — but that the ceiling on trained human cognition is far higher than most people assume. Seventy-point-two seconds, two hundred digits, a museum in London, and then the record books quietly closed behind him.