Daniel Tammet: Mathematical Genius Visualizes Numbers, Solves Problems in Blink of an Eye

Photo: Mathematical Genius Can Solve Problems in Blink of an Eye: Daniel Tammet Can Recite Math Constant, Pi, From Memory to 22,514 Decimal PlacesCourtesy Daniel Tammet
Daniel Tammet is a mathematical genius, capable of astronomical calculations in the blink of an eye. He's also a gifted linguist, speaking nine languages including one he created called Manti.

On the outside, 31-year-old Daniel Tammet is an unremarkable young man. But behind Tammet's bookish exterior lies a superhuman gift: one of the most extraordinary brains our planet has ever seen. He is a mathematical genius, capable of astronomical calculations in the blink of an eye. And he's a gifted linguist, speaking nine languages, including one he created called Manti.

Tammet says he was born with the ability to experience numbers in an exceptionally vivid way.

"The numbers are moving in my mind," he says. "Sometimes they're fast, sometimes they're slow. Sometimes they're dark. Sometimes they're bright. That emotion, that motion, that texture will be highly memorable for me."

Photo: Mathematical Genius Can Solve Problems in Blink of an Eye: Daniel Tammet Can Recite Math Constant, Pi, From Memory to 22,514 Decimal PlacesPlay

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The phenomenon is called synesthesia, a mixture of the senses that results in a heightened sensory experience. Tammet is able to see and feel numbers. In his mind's eye, every digit from zero to 10,000 is pictured as a 3-dimensional shape with a unique color and texture. For example, he says, the number fifteen is white, yellow, lumpy and round.

Synesthesia occurs when regions of the brain associated with different abilities are able to form unusual connections. In most people's brains, the recognition of colors, the ability to manipulate numbers, or language capacity all work differently in separate parts, and the information is generally kept divided to prevent information overload. But in synesthetes, the brain communicates between the regions.

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Tammet doesn't need a calculator to solve exponential math problems such as 27 to the 7th power -- that's 27 multiplied by itself seven times -- he'll come up with the answer, 10,460,353,203, in a few seconds.

Tammet visualizes numbers in their unique forms and then melds them together to create a new image for the solution. When asked to multiply 53 by 131, he explains the solution in shapes and textures: "Fifty-three, which is round, very round...and larger at the bottom. Then you've got another number 131, which is longer a little bit like an hourglass. And there's a space that's created in between. That shape is the solution. 6,943!"

Autistic SavantPlay

Tammet first discovered his mathematical abilities as a child, the eldest of nine children in his family in England.

"I learned to count, like anyone else, at a young age, and when I did I would see colors," he said. "I would see pictures in my mind. I assumed at the time that everyone saw numbers as I did."

Tammet didn't do math as it was taught in school. Instead, the answers just came to him.

Autistic Savant Ridiculed as Youth

In addition to having synesthesia, Tammet is a high-functioning autistic savant. As depicted by Dustin Hoffman in the movie "Rainman," savant syndrome is a very rare condition in which people with developmental disorders are exceedingly brilliant in a particular area. Only 10 percent of people with autism have savant syndrome, and fewer than 1 percent of non-autistic people exhibit savant skills.

Tammet's form of autism, called Asperger's syndrome, makes him unnaturally obsessive and focused. Growing up, he felt restricted by repetitive patterns of behavior, and like most savants he found normal life and social interaction almost impossible. It's a tragic downside to the savant gift that often results in isolation and ridicule.

"Children would tease me. I would have gestures...flapping of the hands, walking in circles," he said. "The other children would repeat that back to me, call me names."

Obsession with Numbers Leads to Pi Day

It was Tammet's obsession with numbers that led to an incredible feat on March 14, 2004, known as Pi Day, when Tammet broke the European record for reciting the number Pi from memory.

Pi, the ratio a circle's circumference to its diameter is considered an "irrational" number in mathematics because it does not end. You may be able to remember the first few digits -- 3.14159 -- but not more.

Tammet says he only read through the digits once and was able to remember 22,514 of them. After a couple weeks to practice reciting the numbers back, in order, it took Tammet just 5 hours and 9 minutes to reel off the numbers while mathematicians listened and simultaneously checked every digit.

To memorize a long number like Pi, Tammet said he just forms a beautiful landscape out of the shapes he pictures in his mind: "I'm taking the numbers, I'm making them into colors and shapes. I'm able to put those into combinations which form hills…or ground or sky…It's another world that I'm able to go into, experience, live within."

Autistic Savant Masters Icelandic in One Week

Despite Tammet's limitations as an autistic savant, he is able to leave his vibrant autistic world and communicate in a way that's impossible for most savants and remarkable for any person.

"As with numbers, language is something that I have an exceptional ability, and it's something that I can perform very well in beyond most people's ability," he said.

Tammet was even challenged to learn Icelandic, perhaps the most impenetrable language on earth, in just one week. While some said it was impossible, Tammet says, "When people say to me, 'This is something you can't do,' I want to do it. I want to prove them wrong."

Simon Baron-Cohen, director of the Autism Research Center at Cambridge University, said Tammet has mastered languages by understanding them as code. "He's treating vocabulary and grammar as systems and he wants to crack the system, crack the code," he said.

After just seven days of learning Icelandic, Tammet appeared live on an Icelandic television talk show and proved his gift to the world.

These days Tammet shares his intellect in writing. He uses his synesthesia to visualize sentence structure and many have appreciated the beautiful landscape of his prose. His autobiography, "Born on a Blue Day," is a bestseller that has been translated into 20 languages.

His second book, "Embracing the Wide Sky," details how our brains really work and how Tammet overcame autism: He trained himself to make friends and tell jokes, stuff that for most of us is second nature.

"These are skills that can be learned. I'm living proof of that and there are many who are like me who have acquired those skills through effort, through the love and support of their families as well."

Tammet is currently at work on a novel, due out early next year. He spends a lot of time traveling, lecturing and sharing his gifts with scientists and adoring audiences alike.

He's learned to enjoy the disorders that caused him so much pain earlier in life.

"As a child, I wanted very much to be like everyone else, to be normal. Today, it's different. I live in a beautiful country, I have a relationship, I have a career. I travel and I do many, many things and I think my mind and the abilities that come with that way of imagining the world has enriched my life enormously."

Excerpts from 'Embracing the Wide Sky'

The following is a selection of excerpts from Daniel Tammet's second book, "Embracing the Wide Sky: A Tour Across the Horizons of the Mind."

On Memory

Imagine entering a room around which a dozen everyday objects are scattered. After a few minutes you step outside while someone else enters and removes one of the items. When you return a short while later you will likely be able to tell immediately which of the objects has been taken. As though endowed with some superhuman power, you will do this by seeing what is not there. Such is the magic of memory.

When I recited the mathematical constant Pi (3.141…) from memory to 22,514 decimal places in March 2004, it seemed like magic to many people. In fact the achievement (a European record) was the result of weeks of disciplined study that was aided by the unusual way in which my mind perceives numbers, as complex, multi-dimensional, coloured and textured shapes. Using these shapes I was able to visualise and remember the digits of Pi in my mind's eye as a rolling numerical panorama, the beauty of which both fascinated and enchanted me.

One of my fondest memories from the Pi event in Oxford four years ago is the profound sense of joy I felt at that visual experience of the numbers' beauty. The public recitation of number after number after number developed into a kind of meditation for me, as I grew more and more wrapped up in their flow. Although the digits of Pi are, mathematically speaking, strictly random my internal representation of them was anything but – filled with rhythmic strokes and structures of light, colour and personality. From this random assembly of digits I was able to compose something like a visual song that meandered through every contour of my mind, through which I was able to hear the music of the numbers.

On Language

A particular bugbear for many language learners (especially those whose native language is English) is the use of grammatical gender (the assignment of gender to all nouns) in many languages. Most European languages have two or three genders (such as the German 'der' for masculine nouns, 'die' for feminine nouns and 'das' for neuter nouns), though that number pales in comparison to the aboriginal Yanyuwa language, which has no fewer than 16 genders based on the various functions of objects used in their society ! What makes learning a noun's gender so tricky for learners is its seeming arbitrariness; for example, in French the word for 'moon' (la lune) is feminine but in German it is masculine (der Mond). Mark Twain, the American humorist, marvelled at the gendered nature of German nouns in his book, 'A Tramp Aboard': "In German a young lady has no sex, while a turnip has…(A) tree is male, its buds are female, its leaves are neuter; horses are sexless, dogs are male, cats are female...tomcats included."

Studies by cognitive psychologists Lera Boroditsky, Lauren A. Schmidt, and Webb Phillips suggest that native speakers of languages that have gendered nouns remember the different categorisation for each by attending to differing characteristics, depending on whether the noun is 'male' or 'female.' In one such study, a group of native German and Spanish speakers was asked to think of adjectives to describe a key. German speakers, for whom the word 'key' is masculine, gave adjectives such as 'hard,' 'heavy,' 'jagged,' and 'metal' whereas the Spanish speakers, for whom 'key' is feminine, gave responses like : 'golden,' 'little,' 'lovely,' and 'shiny.'

On Numbers

Various surveys indicate that as many as 10-15 percent of people report some kind of graphic mental representation of numbers. Francis Galton, a psychologist and cousin of Charles Darwin, carried out the first of these surveys back in 1880. The responses he obtained offer a fascinating glimpse into the sheer variety of mental number representations, though many number lines also displayed consistent patterns: about two-thirds were left-to-right and ran more often upwards than downwards. Some of the number lines had twists and bends, some turned upside down or back on themselves. A physicist replying to Galton's questionnaire described seeing numbers in the form of a horseshoe, with 0 at the bottom right, 50 at the top and 100 at the bottom left. Another respondent, a barrister, described visualising the numbers 1-12 as though on the face of a clock, with the following numbers tailing off afterwards into an undulating stream with the tens – 20, 30, 40, etc. – at each bend.

On the Future of the Mind

Alongside such impressive advances in medicine and technology, I hope for continuing progress in our cultures too, particularly in the way individuals with different minds are viewed and valued by society. In the not-too-distant past, autistic savants were considered of little scientific or intellectual interest and often treated as mere curiosities or performing seals. Even to this day autistic savants are too often viewed as robots, or computers, freaks, or even supernaturally endowed - in short, anything but human. And yet, as I have argued elsewhere in this book, it is our humanity that makes such abilities possible.

With all that we have begun to learn in recent decades about the intricacy and idiosyncrasy of 'normal' brains and minds, and with the growing awareness of the wide variability in conditions as complex as the autistic spectrum, such distorting and hurtful misconceptions will – I hope – decline in the years ahead. Better still, society will find ways to make best use of the talents and energies of differently able minds, maximising the depth and diversity of its intellectual capital in the face of the many challenges, and opportunities, that lie ahead for all of us.

Excerpts from "Embracing the Wide Sky: A Tour Across the Horizons of the Mind" have been reprinted with permission from the author.