I found it was an interesting and still incredibly valid perspective even in these days of Wikipedia and indexed research articles. Taking the time to really absorb and think about the information, and to introspect your own decisions about the material.
The point of this story, is that we are really good at identifying patterns. However there is sometimes a bit of stigma to just putting the data in a spreadsheet and plotting it. Sometimes it is worth offloading visualisation to a program designed for just that, to help your brain manipulate the concept from a grounded position.
I’ve talked before about learning as an adult, and the particular challenges that come with it. Throw in parenthood and it can be even harder to find the time. I’m going to share a few opportunistic learning strategies I’ve tried and talk about which worked (or didn’t) for me.
While doing the coursera course Introduction to Mathematical Thinking I was exposed to the following proof, which is the first I’ve understood fully. The argument is elegant and, as it turns out, over 2000 years old! Euclid’s Elements first outlines this proof.
It seems as one gets older, the less free time you have. This time (for me) is normally used for personal progress (cultural, mental gains) and downtime (games, TV, books, gym).