The gargantuan intellectual effort behind this is incredibly humbling. I can hardly imagine the breadth of knowledge one needs to be able to keep in their mind to tackle this problem.
<<<What is worth noting about the foregoing development is that I should have seen the application of dynamic pro- gramming to control theory several years before. I should have, but I didn’t. It is very well to start a lecture by saying, ‘Clearly, a control process can be regarded as a multistage decision process in which???,’ but it is a bit misleading. Scientific developments can always be made logical and rational with sufficient hindsight. It is amazing, however, how clouded the crystal ball looks beforehand. We all wear such intellectual blinders and make such inexplicable blun- ders that it is amazing that any progress is made at all>>>
In simpler, personal terms, "oh you bloody idiot, why didn't you XYZ...?"
I was considering a problem related to a new data structure. There was a part that was plain ugly, just stank. I thought I could do better, so expressed the problem as a programmer might, and looked for regularity. There was a lot of regularity, so there was an underlying structure which I could grasp at, but not reach. Grab, grab, grab. It was like mist.
I realised it involved the edges of an n-dimensional cube. I could see the 2D case, it's trivial, so what did I do? Well I needed to generalise it so I went for the 4D cube. I spent literally weeks muttering to myself like a nutter, half the time wandering like a zombie.
And eventually it clicked. I may, just may have found something new and genuinely useful in combinatorics but that's not the point.
The point is, had I gone from the 2D case to the 3D case the structure I was looking for would have dropped out in an afternoon. Weeks wasted. It was so simple, you bloody idiot, why didn't you...
I'm not a mathematician, but I guess a lot of maths is like that.
(Edit: quoted Bellman extract to delineate it properly)
Andrew Wiles was so productive he dribbled out older results to hide the fact he was 100% on the Fermat problem for years.
Huang and Knuth are pretty smart as well it seems like.
That’s also not true about wiles productivity... he first discovered the proof in 93 but then when he talked to people about it an error was found. He eventually fixed the error in 94 and then in 95 it was published. No mathematician waits to publish the proof of one of the greatest unsolved problems in mathematics.