You’re asked a math question you must solve entirely in your head. The answer is 2,396,232,838,850,303. What chance have you got of getting it right?

Alexis Lemaire with one of his little problems

Correct answer : zero.

Not, however, if you are Alexis Lemaire. He has broken the record for finding the 13th root of a 200-digit number. Basically, that looks like this :

85,877,066,894,718,045,602,549,144,850,158,599,
202,771,247,748,960,878,023,151,390,314,284,284,
465,842,798,373,290,242,826,571,823,153,045,030,
300,932,591,615,405,929,429,773,640,895,967,991,
430,381,763,526,613,357,308,674,592,650,724,521,
841,103,664,923,661,204,223.

Last December, at Oxford’s Museum of the History of Science Alexis broke his own record, reducing it to 77.99 seconds. Even with a calculator you wouldn’t beat Lemaire doing the calculation in his head.

How does he do it? “It is quite difficult. I did a lot of preparation for this. More than four years of work and a lot of training every day. A lot of memorizing. I need three things — calculating, memorizing and the third on mathematical skills. It is a lot of work and maybe a natural gift.”

One of the theories being put forward by researchers is that damage to one area of the brain creates compensation in another. Brain scientist Dr Allan Snyder has suggested that everyone may possess such abilities but be unable to access them.

The genius himself explains that what he does is to transform raw numbers into other structures so he can “see” the answer to the problem. “When I think of numbers sometimes I see a movie, sometimes sentences. I can translate the numbers into words. This is very important for me. The art is to convert memory chunks into some kind of structure.

“I see images, phrases, actions. It’s very tactile, sensitive. I have these associations between places and numbers. Some places are imaginary, I try to vary so I don’t confuse the numbers. It’s important to memorize. I have to be precise.”

Lemaire’s explanation is similar to that of British genius Daniel Tammet, who set the world record for reciting pi to more than 22,000 digits at the same museum in 2004. To him, he said, each number has a distinct colour and appearance, some beautiful, some not, with each complex calculation making up a landscape.

Now you know.

Knowledge is gained in pieces, but these individual pieces are not all we know. In order to understand the big picture, we put together these bits of knowledge, like pieces of a jigsaw puzzle. If we learn that A is greater than B, and that B is greater than C, we know a third fact by deduction: that A is greater than C.

Our brains demonstrate their capacity for inference by this kind of linking bits of knowledge. The ability to make logical big picture inferences from disparate pieces of information is called relational memory.

A study led by researchers at Beth Israel Deaconess Medical Center and Brigham & Women’s Hospital in Boston, MA found that this ability to link bits of directly-learned information and to make leaps of inference to construct the big picture is enhanced when we sleep.

The study involved student participants divided into three groups who learned facts about pairs of shapes they were shown. Each group was tested to see how well they were able to infer the relationship between the facts they learned about individual pairs. Group one was tested after 20 minutes, Group Two was tested after 12 hours and Group Three was tested after a full 24-hour period.

Group One, which was tested only 20 minutes after the learning period, scored the worst on understanding the interrelationship between the pairs. Approximately half of the students in Group Two slept during the 12-hour period, while the other half remained awake. All of the students in Group Three had a full night’s sleep.

Groups Two and Three showed a clear understanding of the interrelationships between the pairs of shapes.

According to senior author Matthew Walker, PhD, Director of the Sleep and Neuroimaging Laboratory at BIDMC and Assistant Professor of Psychology at Harvard Medical School (HMS), “These findings point to an important benefit [of sleep] that we had not previously considered. Sleep not only strengthens a person’s individual memories, it appears to actually knit them together and helps realize how they are associated with one another. And this may, in fact, turn out to be the primary goal of sleep: You go to bed with pieces of the memory puzzle, and awaken with the jigsaw completed.”

To Understand The Big Picture, Give It Time - And Sleep