The brain injury that made me a math genius Twelve years ago, Jason Padgett had never made it past pre-algebra. And then a violent mugging changed everything

If you could see the world through my eyes, you would know how perfect it is, how much order runs through it, and how much structure is hidden in its tiniest parts. We’re so often victims of things—I see the violence too, the disease, the poverty stretching far and wide—but the universe itself and everything we can touch and all that we are is made of the most beautiful geometric patterns imaginable. I know because they’re right in front of me. Because of a traumatic brain injury, the result of a brutal physical attack, I’ve been able to see these patterns for over a decade. This change in my perception was really a change in my brain function, the result of the injury and the extraordinary and mostly positive way my brain healed. All of a sudden, the patterns were just . . . there, and I realize now that my injury was a rare gift. I’m lucky to have survived, but for me, the real miracle—what really saved me—was being introduced to and almost overwhelmed by the mathematical grace of the universe.

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There’s a park in my town of Tacoma, Washington, that I like to walk through in the mornings before work. I see the trees that line its path as anyone would, the branches and the bark, but I see a geometrical blueprint laid on top of them too. I see triangular patterns emerging from the leaves, reminding me of the Pythagorean theorem, as if it’s unfolding in the air, proving to me over and over again what the ancient Greek philosopher and mathematician Pythagoras deduced thousands of years ago: the sum of the squares of the legs of a right triangle (a triangle in which one angle is a right angle, or 90 degrees) equals the square of its hypotenuse. I don’t need a calculator to know that the simple formula most of us learned in school—a2 + b2 = c2—is true; I can see it instantly in the trees all around me. To me, a tree is more than its geometry, but geometry is also far more than most people realize. I think it’s everything.

I remember reading that Galileo Galilei, the Italian astronomer, mathematician, and physicist (and one of my heroes), said that we cannot understand the universe until we have learned its language. Speaking of the universe, he said, “It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it.”

This rings true for me. I see this hidden language of the world before my eyes.

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Doctors tell me that nothing in my brain was newly created or added when I was injured. Rather, innate but dormant skills were released. This theory comes from psychiatrist Darold Treffert, who is considered the world’s leading authority on savants and acquired savants. He treated the late Kim Peek (the inspiration for the savant character in the movie Rain Man), a megasavant who memorized twelve thousand books, including the Bible and the Book of Mormon, but who had so many physical challenges that he had to rely on his father for his most basic needs. When I met with Dr. Treffert in his hometown of Fond du Lac, Wisconsin, he told me that these innate skills are, in his words, “factory-installed software” or “genetic” memory. After interviewing me in his office and in his home, he declared that my acquired synesthesia and savant syndrome was self-evident, and he also suggested that all of us have extraordinary skills just beneath the surface, much as birds innately know how to fly in a V-formation and fish know how to swim in a school. Why the brain suppresses these remarkable abilities is still a mystery, but sometimes, when the brain is diseased or damaged, it relents and unleashes the inner genius. This isn’t just my story. It’s the story of the potential secreted away in all of us.

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The first thing I do every morning is make my way to the bathroom, turn on the faucet, and let the sink fill up. I watch the water flow and wonder why it doesn’t sound like the strumming of tightly wound strings. The structure of flowing water vibrates in a specific geometric form and frequency to me, and if it were to freeze midstream, I’d see a web, but one made up of tiny crystals rather than spider’s silk. If I could hear it after it froze, it would sound like tinkling glass shards falling into the basin. I like to start my days with water. It may slip through my fingers, but it is a constant comfort.

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I look at myself in the mirror and make sure my hair’s not getting too long. I like it cropped close now. I grab my toothbrush and count how many times I run it through the water while brushing my teeth. It has to be exactly sixteen times. I don’t know why I chose that number, but it’s fixed in my mind like my street address or my zip code. I try not to worry about it too much and stare back at the intriguing water webs, working to memorize all of the angles so that I can draw a picture of the image later. I’ll probably spend hours with a pencil and ruler later on, capturing on paper every inch of the razor-sharp symmetry.

Next, I walk into the living room and throw back the drapes. If it’s a clear day, I’m in for a real show. The sun comes shining through the leaves of the trees like a million little lights, as if the leaves are blades and they cut the sun up into a million diamonds. Then the rays fan out between the leaves, falling over them like an illuminated net. Watching this, I always think of the famous double-slit experiment, in which light behaves like a particle and a wave at the same time. My friends tell me that to them, it’s just the sun shining through the trees. I can barely remember a time when I saw the world the way most everyone else does.

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On an overcast or stormy day, I pay more attention to the branches swaying in the wind. The movements are choppy and discrete, like a series of frames of a film, with black lines separating each image. At first, I got dizzy when this happened, and I had to grab the back of a chair or lean against a wall. Now I’m used to it, though I still have moments of vertigo.

Next I move on to the kitchen and put on some coffee. It’s one of my routines, but it thrills me every single time I watch the cream being stirred into the brew. That perfect spiral is an important shape to me. It’s a fractal—a repetitive geometric form found everywhere in nature, from the shell of a nautilus up to the Milky Way galaxy. Suddenly it’s not just my morning cup of joe—awesome as the coffee in the Pacific Northwest is—it’s geometry speaking to me again. And I never get tired of it.

I sit down at the kitchen table and add to whatever sketch I’m working on; lately, I’ve been drawing the coffee-and-cream spiral. I’m a real perfectionist and I can stay in my seat for hours and draw; usually, I do this until I have to leave for work. When it’s finally time to go, I put on my “uniform”—a button-down shirt and jeans. I like to look professional but I’m not really one to wear a suit and I often have to lift heavy things or repair stuff at work. I make sure I close the door behind me carefully. I always have to check and double-check and triple-check the locks. Then I can go.

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I’m forty-three as of this writing. This makes me really happy because 43 is a prime number, divisible by only itself and 1. The number 43 lives at a specific point in a sphere in my mind’s eye, as do all the other primes. I’ve drawn images of this sphere, which is consistent for me whenever I think of primes and the patterns among them. I feel such a reverence for these numbers that I recite them like a mantra when I need good luck or when I need to keep bad luck away. It’s as if the primes are so rare and so special that they’re imbued with an extraordinary power, and they act like sentinels in my mind. When I’m napping on the sofa, my daughter, Megan, sometimes wakes me up because I’m reciting prime numbers in my sleep.

But primes aren’t the only numbers I associate with shapes. Simply dialing a friend’s phone number can send up a plume of images. Numbers appear to me as a series of cubes. They are linear — three cubes across for the number 3, four across for 4 — unless the numbers are part of an equation or they’re being plotted on a graph, in which case the cubes move around to reflect what’s happening to the numbers. An equation can result in a huge, prismatic net right before my eyes. The shapes are always consistent with the specific stimulus. Numbers are an obsession, and I’m incapable of turning the fixation off. I can’t climb stairs without counting them, and I can’t eat without counting how many times I’ve chewed each bite. I never chew gum for this reason. With every number I count off, the fresh, simple prime numbers and all the other never-ending num­bers spiral into their own shapes.

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All these visions — and every shape I encounter out in the world — correlate with fractals, the elemental geometric building blocks found in nature. Snowflakes, lightning bolts, and coastlines are all fractals, meaning their subsections repeat the same patterns as their wholes. Coastlines are particularly intriguing to me because their overall measurements actually change depending on the scale one uses. For me, this underscores how understanding fractals can shed light on comprehending the nature of other things. For example, I have always wanted to know where humans come from. Now, with one quick glance at human anatomy, I see clearly that veins, arteries, and even the strands of DNA are fractals too. The human body seems to reflect the very structure of creation. The structures within the body reflect the never-ending repeating patterns found throughout the universe. The first time I noticed this, it struck me: everything and everyone is a reflection of this repeating structure.

I walk around in a near-constant state of inspiration with a great hunger for knowledge, and I read everything I can about math and physics, often developing my own theories along the way. I was even contacted by a Toronto financial firm that was interested in applying my fractal geometry to the stock market. I haven’t be­gun working with them yet, but I love the idea that my wild visions could have an application in the real world.

It’s especially important for me to keep drawing my geometry, because that’s how I’m able to share exactly what’s going on in my mind, and I think I’d go crazy if I didn’t have a way to express what I see. By turning my view of the world into drawings, I’ve found a way to explain my universe to other people.

My quest to understand and come to terms with the new me has spanned more than a decade, taking me from years of self-imposed isolation to a high-tech brain-imaging lab halfway across the world, in Helsinki, Finland. Along the way, I’ve met some of the world’s greatest experts on savant syndrome, synesthesia, and brain science. I’ve learned what my mathematical theories and visions have in common with the work of some of the most brilliant mathematicians in history. I’ve been introduced to new ways of thinking about the brain, the mind, and even consciousness, and I’ve discovered why my case may play an instrumental role in the next generation of cutting-edge brain science.

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I’ve spent plenty of time pondering the very fabric of the universe and how we fit into it. And I’ve concluded that no matter what you go through in life, in the end, there is a symmetry to it all — an or­der amid the seeming disorder. And if you could see what I see, you’d know that you’re an essential part of that order.

If I could draw the world as I see it and show every last person how he or she is enmeshed in this fine and intricate and impossibly beautiful structure, perhaps people would stop getting lost in the hurt of things and be elevated by the wonder of it all. In fact, I know they would. I know, because even though I seem like the most opti­mistic man this side of the Rocky Mountains, I’ve been to hell and back.

Excerpted from "Struck By Genius: How a Brain Injury Made Me a Mathematical Marvel" by Jason Padgett and Maureen Seaberg. Copyright © 2014 by Jason Padgett and Maureen Seaberg. Used by permission of Houghton Mifflin Harcourt Publishing Company. All rights reserved.