Let me share my personal experience: when I was 18-21 I struggled with advanced math in college. Now, at 30, when I re-open those books just for fun, everything makes so much sense and some aspects of it are even enjoyable.
I've failed to find a plausible explanation for myself. I haven't done much math (calculus, probability, statistics) since graduation, yet the exact same books are so much easier to read now.
I experienced a similar effect much earlier in my life: I struggled with understanding recursive algorithms when I was 12, but when I came back to them at 16 I laughed at myself - it suddenly seemed so trivial.
As I started getting into heavy research on recommender systems for our startup after being somewhat lax in my research reading for a few years I stumbled into some papers that were really hard for me to push through. I kept thinking, "I must be slipping, I know this stuff wasn't as hard for me in college."
Then at some point I needed to look up a couple things in some of my textbooks (I saved them all) and as soon as I picked them up I thought ... wait? That was the hard stuff? This is all so ... trivial. Since the progression from textbooks to academic papers had mostly come at some remove, I'd not noticed that I was gradually reading much harder material, to the point that the stuff that I found hard in computer science in college now seems all rather easy.
Now, I'm 28 at this point, but already I've noticed that I'm not as fast as I once was, but I've got more momentum. When I throw myself at a problem it's with the goal of crushing it rather than dancing around it. This seems to be what's awesome about smart folks that are in middle to older ages. There's like this blunt force of knowledge that can be thrown at hard problems. Great systems programmers in their 50s are awesome to work with.
Note, also, that the article also mentions that knowledge based abilities increase up until you're 60.
Once you've got an intuitive picture of how something works, you will find that the details just fall into place. But often that intuitive picture can't just be gifted to you, despite the best efforts of our best teachers to concoct the perfect metaphors. It takes time. You have to fiddle around with the concepts in your head, sometimes for years, before they really sink in. You might have to repeat them several times, or approach them from several angles, or encounter them in unusual surroundings, or find the one book that finally explains the subject in a way that clicks.
Once you really understand something, trying to remember what it was like before you understood it is like trying to forget how to read.
Well honestly, this was a statistical study. Still those of us who are 27 are glad to hear you part anyway! Damn. I don't want to have passed my prime.
Let me share my personal experience: when I was 18-21 I struggled with advanced math in college. Now, at 30, when I re-open those books just for fun, everything makes so much sense and some aspects of it are even enjoyable.
I've failed to find a plausible explanation for myself. I haven't done much math (calculus, probability, statistics) since graduation, yet the exact same books are so much easier to read now.
I experienced a similar effect much earlier in my life: I struggled with understanding recursive algorithms when I was 12, but when I came back to them at 16 I laughed at myself - it suddenly seemed so trivial.