“It’s remarkable that he sees the world this way without any real training”
I think it is quite the opposite. Training tends to kill original thinking, although it can turn you into a coffee-fueled theorem-churning machine... I have always hated that term when applied to research or higher education.
But Padgett is not the next Stephen Hawking. This ability allows him to see the world in a unique way — but it’s highly unlikely that his ability will land him a Fields Medal.
Well, it is not just unlikely, it is actually impossible under the prize rules, since he is over 40. It is a shame that they discriminate on grounds of age. The official reason for this policy is that the awards should not only recognize past work but also encourage future achievement on part of the recipients. So if you are over 40 they are calling you brain dead, and discouraging you of pursuing any major achievement. This is mean and goes against the goal of promoting research and recognizing contributions based on merit.
Even if it is statistically much less likely that you can make a breakthrough at a "late" age, that is not a valid justification in any case for a discriminatory policy. No woman had ever won the medal either until last year, but I cannot imagine anybody suggesting that they should have been excluded based on the statistics. On the contrary, they were encouraged and that medal of last year was widely celebrated, partially eclipsing the male awardees. Why not encourage everybody as well to try their best irrespective of their age?
It is not only mean, it is also absurd. Let's see... They can only award you the medal if you are capable of future achievements. If you are over 40, they assume that you cannot make future achievements. So if you make your breakthrough when you are over 40, they cannot give you the medal, on the grounds that you will not be making future achievements. But, wait a minute! If you are over 40, it is not possible under their assumptions that you are making any breakthrough in the first place! So the rule is useless and should be eliminated for the sake of simplicity. Brilliant, isn't it?
And those guys from IMU could not see the paradox... Talk about math genius!