Huang's comment is also very interesting:
> Regarding how long it took me to find this proof, here is the timeline for those who are interested.
> Regarding how long it took me to find this proof, here is the timeline for those who are interested.
> Yet at that time, I was hoping for developing something more general using the eigenspace decomposition of the adjacency matrix, like in this unanswered MO question:
> https://mathoverflow.net/questions/331825/generalization-of-...
There's some serious stuff on Math Overflow and the Mathematics stack exchange (https://math.stackexchange.com/). I haven't figured out what the difference between the two sites is however in focus
[MathOverflow](https://mathoverflow.net/) is the sorts of math questions that will probably sound like gibberish to anyone who doesn't have a graduate-level education in Math. And I mean specifically in Math, not in Engineering or Physics.
Usually, if you want to ask a math question -- even a reasonably complex one that someone would need a lot of education to understand -- it'll go on SE.Math. MathOverflow's more of a specialty site for mathematicians.
To note it, the distinction between SE.Math and MathOverflow has at least two parallels:
1. [SE.ComputerScience](https://cs.stackexchange.com/) vs. [SE.TheoreticalComputerScience](https://cstheory.stackexchange.com/) ; and
2. [SE.Physics](https://physics.stackexchange.com/) vs. [PhysicsOverflow](https://www.physicsoverflow.org/) .
In all three cases, one site's more appropriate for most users, ranging from beginners to experts, while the other site's more specifically for research-level topics in the field.
1 x post from a cryptocurrency newbie, happy to find an audience who undoubtedly want to buy their FlappyBirdCoins. HODL HODL! We're going to the sky! Actually this post _is_ appropriate and it IS on topic and you're only saying it isn't because you don't understand digital currency is the future. (Grr)
2 x post from people who've read about the One Time Pad and are now convinced their grade school cipher is better and here's 40 characters of output - bet you can't break it. No I didn't read the instructions saying not to do this, I'm too smart to need to read instructions.
1 x post from somebody with a basic grasp who has a real but fairly trivial question, like, why is the exponent 65537 used for RSA ? This question may or may not just be their homework.
1 x post that is a good question but shouldn't be filed here, like, how do I configure Apache to enable TLS 1.3 ?
1 x post which is actually appropriate, like why does this algorithm say to use a pseudo-prime P when it only seems to be important that A isn't a factor of P ? Doesn't this 1987 journal paper I found show that it would work for other values just fine ?
I believe Feynmann said the best people always had the top unsolved problems in the top of their minds and whenever a new technique or result arrived, they would drop everything and try out the new attack on the old problem.
I am not sure thinking about technical work would help sleep, because thinking could be orthogonal to reading.
Ramanujan was like that too. He believed that a goddess sends him solutions in his sleep. Not sure if the goddess is real, but the formulas certainly were real.
http://www.oceanvivasilver.com/5-namakkals-infinity-dream-sr...
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.
<<<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)