Jason Padgett acquired a new and unique skill/ability of drawing mathematical fractals after getting hit on the head which is known as a phenomenon called acquired savant syndrome.
Savant syndrome is a rare but remarkable condition in which persons with developmental disabilities, brain injury, or brain disease have some spectacular skill or ability that stand in definite contrast to the overall handicap. There have been a number of cases reported in which, after some brain injury/disease, savant skills unexpectedly emerge, sometimes at a prodigious level, when no such skills were present before injury or illness which is called acquired savant syndrome.
The condition can be present from birth or surface in early childhood (congenital) or can surface unexpectedly following head injury, stroke, dementia, or other central nervous system (CNS) disorders (acquired). The special skills occur most commonly in the areas of music, art, calendar calculating, lightning calculating, or mechanical/spatial abilities. Whatever the special skill, it is always accompanied by extraordinary memory of a particular type—very narrow but very deep within the area of special ability.
In many of these cases, the special abilities emerge following left hemisphere injury, particularly left anterior temporal lobe injury. Increasingly, there is speculation that these newly emerged skills, formerly dormant, are “released,” compensatory abilities rather than newly created ones.
Jason Padgett is one of about 40 known acquired savants in Dr. Treffert’s Savant Syndrome Registry. Certain objects and mathematical formulas trigger synesthetic mathematical fractals in him and he was the first to hand-draw mathematical fractals, an ability he acquired after he was hit hard on the head.
He was an ordinary fellow who had a severe concussion in 2002. Following that, he had an instant synesthesia consisting of vivid images. With no prior interest or ability in art or mathematics, he began to draw these images, which turned out to be complex fractals and other mathematical concepts. He has advanced his mathematical ability, and his drawings have become sought-after art pieces.
The study results of Berit Brogaard et.al. from the scans of Jason Padgett's brain using Functional magnetic resonance imaging (fMRI) and Transcranial magnetic stimulation (TMS) established that synesthetic imagery may be generated in areas of the brain not normally used for the creation of visual imagery.
In a series of functional MRI studies in Finland, Brogaard's team found uni-lateral left-side activity in the parietal and frontal areas when Padgett is exposed to well-formed mathematical formulas that give rise to synesthetic fractals in him and bi-lateral activation when he is exposed to nonsense formulas or formulas that don't give rise to synesthetic fractals.
They re-tested the results from the Functional magnetic resonance imaging (fMRI) using Transcranial magnetic stimulation (TMS). In the TMS study, Padgett was shown formulas and asked to rate his synesthetic sensation on a scale 1-10, relative to his "baseline" percept (i.e. without TMS). They applied TMS over the brain areas that were activated in the fMRI scan with the formulas that give rise to synesthetic experiences and found the TMS modulated two central areas.
I learned about this fellow recently and am glad I found this question through Google, since my impression has been that the media has been making a mountain out of a molehill. My short answer is that the available evidence does not demonstrate that Jason is a “math genius” in any sense that meaningfully differentiates between commonplace “math skill/ability/proficiency/talent/insight/etc” and true “math genius”.
My introduction to Jason’s case was through the following video called “The Acquired Savant” that showed up in a ‘recommended video’ list on YouTube under the title “Meet the Accidental Genius”:
As can be seen after the 1:00 mark, he was living a pretty good life but did not apply himself at school. He said “... literally everything revolved around partying and chasing girls and goofing off.”
In a TED talk called “How math saved my life” ( https://www.youtube.com/watch?v=GDU7lEmiiD8 ), he says “I was one of those kids that did not care for school or for studying”, “... my interest in school, math in particular, was completely non-existent”, “I had friends that would literally let me copy all of their homework, math, science, ...”. He also describes someone who did a spare assignment because he knew Jason wouldn’t do it, and that allowed Jason to graduate from high school.
During the initial part of an interview found on YouTube under the title “How 1 Man’s Brain Injury Turned Him Into A Math Savant” ( https://www.youtube.com/watch?v=qX6ONPQGBfo ) – which presents him as a “math genius” – Jason remembers saying “Math is stupid” and says “I used to make fun of math”.
I have no problem accepting that he dropped out of college. I vaguely recall seeing something about that prior to my first answer attempt, but I didn’t see the point of tracking down something to reference in my current answer.
From Jason's history, I see nothing more than someone who had a disinterest in school despite seeming to have everything going for him. There is nothing to suggest he had some kind of demonstrated mathematical incapability and could not have acquired mathematical proficiency if he had applied himself. Nor do we see any prior lack of exposure to math. He just did not have an interest at that point.
Then he was viciously beaten. Common sense suggests that would have been a traumatic incident regardless of his brain injury, and that it would have likely resulted in some kind of change in him in any event. As a result of his brain injury, he developed his special experience, and his interest in math emerged. Did that make him a “math genius”? Common sense suggests there is nothing special about developing an interest in something that was not interesting before. And while he ended up with a unique way of experiencing the world, I have not seen anything to suggest he has demonstrated some kind of special insight beyond what is already known. (Indeed, the fact that I, as a non-doctoral person, had some prior familiarity with and understanding of the kinds of experiences and insights that Jason described indicated to me that he was probably not in the realm of a “math genius”. My subsequent skeptical look into the matter pretty much confirmed this.)
I’m sure there are people who could debate the meaning of “genius” ad nauseam, though I myself like the part in the Wikipedia definition that says “..., typically to a degree that is associated with the achievement of new advances in a domain of knowledge” ( https://en.wikipedia.org/wiki/Genius ). Compared to the general population, Jason has a certain mathematical talent, and that might seem like “math genius” to lay people. But compared to people with a proficiency in math, is there any indication that he is beyond anyone else? Only properly qualified mathematicians could make that determination, and I have not seen anything to suggest that any have considered Jason’s abilities as amounting to “math genius”.
Compare Jason’s drawings with the work of a “software artist” with an interest in math, Jeffrey Ventrella ( http://www.jjventrella.com/ ). Mr. Ventralla might be a genius in his computer work, but do the mathematical insights on his “Divisor Drips and Square Root Waves” pages ( http://www.divisorplot.com/ ) make him a “math genius”? I’m not aware of anyone who would suggest this.
Now consider Srinivasa Ramanujan ( https://en.wikipedia.org/wiki/Srinivasa_Ramanujan ), who is widely regarded as having been a great mathematician, and who would certainly fit within my conception of a “math genius”. I’ll bet the people in the media describing Jason as a “math genius” probably know little, if anything, about Ramanujan. He was someone who accomplished so much in the field of math despite his humble beginnings. In contrast, what we get out of Jason is selling math-based drawings as art and hiring himself out as a speaker:
Jason could have potentially become a “math genius” in the sense that I am using, and perhaps still could in the right circumstances, but his track record suggests he went a different route.
A big motivation for me in writing this answer was that it exemplifies the ‘looseness’ of the media. All the media attention suggests some kind of ‘miraculous’ aspect to Jason’s story, and that seemed to be the motivation behind the OP’s question. Jason has certainly developed a special experience, and lay people may find him to be a mathematical marvel, but while he’s making the most of his situation, the evidence to support the claim that he is an indisputable “math genius” is lacking.