The life story of Perelman:
- the mathematician who solved the PointCaré Conjecture
- rejected the Fields Prize (the first and only person to do so)
- rejected 1 mil US$ prize for his solution of the Conjecture.
has left me with some realizations that I think you may find useful or otherwise thought-provoking.
If you don’t know about him, you can read my summary here.
Below are the main lessons I’ve learned:
- I used to dislike early specialization programs for young pupils. But Perelman’s story has made me more open to this.
I now accept that it may be necessary for finding and growing exceptionally talented people (esp. in Math?). Hence, it seems important to help children identify their talents as early as possible, by giving them many opportunities to get exposed to various disciplines. (This is not the same as forcing young people to follow a field decided by parents or someone else)
- Having supportive teachers and an environment of similarly talented people to learn and compete with has proven invaluable in Perelman’s case, and, I think, in many other cases. Environment does play a role, especially in identifying and providing the necessary tools for talent to grow. Anyone serious with growing and learning should therefore be very cautious about choosing associates. An environment is nothing but the people whom we often talk to and learn, exchange ideas with.
- Even geniuses such as Perelman needed a lot of practice. In his first national high school Math Olympiad, he only won the 2nd prize. This made him think a lot and helped him realize that what he needed was more practice. It seems that no one, even geniuses, can do away with practice. Talented people can still be superior without a lot of practice, but he/she probably won’t get to the top without serious practice.
- The Pointcaré Conjecture was solved through a combination of many theories devised by many other mathematicians before him.If we teach people to remember by rote instead of really understanding things, ingenuity will be hard to come by. New theories can only be developed by people with true understanding, and not superficial knowledge acquired through rote learning.To have a deep understanding of a subject takes time and efforts. There is no point in telling young people to remember by heart something that should instead be understood gradually through thinking and practice. Appear smart is not really smart. Doing so is probably going to diminishing their future creativity and confidence. And that’s the sure way to turn great minds into average ones.
- A superb researcher doesn’t necessarily make a good teacher, for most students. Perelman wasn’t a good teacher. According to the author of the book, Perelman probably suffered from Asperger Syndrome (a form of autism). This syndrome is found much more commonly among Math major and science students than other students. This syndrome adversely affects, among other things, one’s capacity for social interactions and empathy with others’ perspectives. Knowing this, we should not blame a good researcher for being a not-so-good teacher. And people in management should cater for this in assigning teaching responsibility to researchers.