Sorry to be a party pooper, but I find the story of Jason Padgett (the guy who ‘banged his head and become a math genius’) completely unconvincing. From the video that you cite, here is the ‘evidence’ that he is ‘math genius’:
He tells us, with no context, ‘the inner boundary of pi is f(x)=x sin(pi/x)’. Ok!
He makes ‘math inspired’ drawings (some of which admittedly are pretty cool but they’re not exactly original) and sells them on his website
He claims that a physicist (who is not named or interviewed) saw him drawing in the mall, and, on the basis of this, suggested that he study physics.
He went to ‘school’ and studied math and physics. He says started with basic algebra and calculus and apparently ‘aced all the classes’, but doesn’t tell us what level he reached. Graduate? Post-graduate?
He was ‘doing integrals with triangles instead of integrals with rectangles’
He tells us ‘every shape in the universe is a fractal’
Some fMRI scans were done on his brain which found ‘he had conscious access to parts of the brain we don’t normally have access to’.
As far as I can tell, he hasn’t published any technical math/physics writings (peer-reviewed or otherwise). He wrote a book but as far as I can tell, this is mostly a memoir, with a bit of pop-math thrown in. From his website, this is what he’s working on:
His [sic] is currently studying how all fractals arise from limits and how E=MC2 is itself a fractal.
...
His drawing of E=MC^2 is based on the structure of space time at the quantum level and is based on the concept that there is a physical limit to observation which is the Planck length and the geometry of Hawking Radiation at the quantum level and its possible connection to describing the Holographic Universe Principle. It also shows and agrees with the holographic principle that at the smallest level, the structure of space time is a fractal.
Yep, those certainly are physics-y words! Good luck to him making progress in this area!
Its suspicious to me that he doesn’t have any writings on his mathematical works, so we are not able to judge what he’s doing. (Even time-cube man posted his writings on the internet)
This is my summary of the story:
He was hit on the head and experienced some changes after this. (Very believable )
These changes were significant enough to be visible on fMRI scans. (Also very believable )
He experienced OCD-like symptoms and other personality changes after the injury (I’m not a neuroscientist, but this seems plausible)
He experienced seeing visual distortions and ‘fractal-like’ images after the injury. (Again, I’m not a neuroscientist, but this seems plausible)
The visual hallucinations and personality changes caused him to be more interested in fractals, geometric designs, art, and math.
He took a few entry-level math classes and did ok in them.
The mugging took place in 2002 but apparently he hasn’t produced any technical writing in the subjects of math and physics.
This all leads me to believe that he is not ‘math genius’. I am agnostic about whether he is delusional about his abilities or whether he is a con-man.
Fair enough! Its just that, unless they produce technical results, or pass graduate exams or do something else tangible its quite hard to distinguish people who are very good at math from people who are not.
Obviously its hard to tell from that interview, but he seems to suggest that the reason he didn’t pass his classes was because he spent time partying, bodybuilding and ‘chasing girls’ rather than studying. It doesn’t necessarily seem like he would have been unable to pass the classes, just unwilling to put in the work. Even after he became interested in math, he still admitted to struggling with some of the classes, but he had the willpower to put in the work to understand it.
I think that your description of it being a change in ‘math attitude’ is a good one. It seems like his attitude (and willingness to persevere) changed, but not necessarily his ability.
Just to be clear: I think its super interesting that someone can have this kind of a change and it is interesting to study it! I’m just not convinced that it is a change in math ability.