"Is it true that you were bad at math as a kid?" "I was unbelievably slow... I always got lost... I was at least twice as slow as anybody else. Eventually I would do very well. You see, if I could do it that way, I would get very high marks."
Speaking as someone who still struggles with math, and was generally the dumbest kid in the most advanced classes, it's a huge relief to hear that someone as brilliant as Penrose experienced the same difficulties.
Grothendieck is one of the towering figures of 20th century math. He said:
"Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle–while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects."
There are many other such mathematicians who aren't flashy. (I recall that Hilbert is a famous example.) So I wouldn't be discouraged by this. Environmental factors are probably far more important.
Of course, there is a top, though it's hard to tell who's furthest ahead when all options are above your own level. It's healthier for my mental sanity to recognize that great things can still be done by those not at the top than to try and suppose the top is nearer to me than I would like or suppose that the top doesn't exist. If you asked me who I thought was at the top of humans thus far, I'd respond with von Neumann. An excerpt from an interview linked at http://infoproc.blogspot.com/2012/03/differences-are-enormou...
Fermi and von Neumann overlapped. They collaborated on problems of Taylor instabilities and they wrote a report. When Fermi went back to Chicago after that work he called in his very close collaborator, namely Herbert Anderson, a young Ph.D. student at Columbia, a collaboration that began from Fermi's very first days at Columbia and lasted up until the very last moment. Herb was an experimental physicist. (If you want to know about Fermi in great detail, you would do well to interview Herbert Anderson.) But, at any rate, when Fermi got back he called in Herb Anderson to his office and he said, "You know, Herb, how much faster I am in thinking than you are. That is how much faster von Neumann is compared to me."
Look, I'm sorry to be the one to break this to you, but if you have difficulty with any programming concept, you must not be a supergenius. You're just an ordinary genius at best.
The sad truth is that there are some people for whom programming comes as naturally as thinking, with code formed as easily as thoughts; and if it takes an effort to understand any aspect of programming, you have just learned that you are not one of those people. Alas.
Interesting. How do we know that there is a top, and who is sitting on it?
I tried answering this question with the google search: "greatest 20th century mathematician". The top link was this (http://fabpedigree.com/james/mathmen.htm). Hilbert and Grothendieck were the highest 20th century mathematicians. (Mentions that Grothendieck is "widely considered the greatest mathematician of the 20th century".) von Neumann was a bit lower, #15.
But I personally don't understand the whole ranking thing. :) Math is in bad shape if you can order people this way. I know that in software, there are a few parts which deeply interest me; while I couldn't care less if the other parts happen to have some fancy virtuosos. (They're about as interesting to me as virtuosos of building houses out of toothpicks. Which no doubt requires great ingenuity, but it's not my interest.)
So if someone were to present me a list of top programmers... it's probably the case it's dominated by these toothpick-virtuoso analogues. And even if it magically weren't, the concept is weird, because the people active in my fields of interest all have their different, interesting perspectives. They're not clones of each other which differ only in a single rankable quality. It's more about actual ideas, rather than the managerial perspective which focuses on the human as carrying units of production.
(BTW, I can't tell how much Eliezer's joking in that quote, even though I've read his fiction. One can form code virtually "as easily as thoughts", but that's like forming verse as easily as thoughts. The question is, do you find their verse interesting?)
Haha, that's an understatement, I'm sure he was light years ahead of me as early as 10. It's just inspiring to know that one can struggle with some of the basics and rebound to do great things.
I always felt I was slower than the other kids, but later I realised I was attempting to structure and understand the information whereas they were just regurgitating it. Once I did understand the information I could apply it far better than the others in class, and extend my understanding into new areas. That's just one reason someone may be "slower".
I thought I was. There's only a few dozen people on the planet who should be insulted by being told that they're not as good at mathematics as Roger Freaking Penrose.
Speaking as someone who still struggles with math, and was generally the dumbest kid in the most advanced classes, it's a huge relief to hear that someone as brilliant as Penrose experienced the same difficulties.