Wonder and Passion
When Albert Einstein was roughly five years old, his father showed him a compass. That the needle of the compass behaved in such a determined way, made a deep and lasting impression on Einstein at this very young age. “Something deeply hidden had to be behind the thing.” (See [1], page 6.)
At the age of twelve, Einstein experienced a second wonder. In a little book dealing with Euclidean plane geometry, he discovered the miraculous concept of proofs. “This lucidity and certainty made an indescribable impression upon me.” ([1], page 9.)
When Einstein was sixty-seven years old, he still remembered these two formative events of wonder in his short autobiographical notes.
From all of my own experiences in teaching and in research, and in interacting with my collaborators and friends, and above all, in interacting with students at all levels during the last sixty years of my life, I have become convinced that igniting feelings of wonder and extreme curiosity leading to the passion of exploration and to independent critical thinking, is the primary and most important goal of teaching.
When I was twelve years old, I observed some simple, but to me fascinating, patterns of the distribution of prime numbers. A bit later I learned about Galois theory and about the amazing relations between the expressions for the roots of polynomials and the symmetries of these roots preserving the relations between them. I longed to experiment and explore, and to read and learn more about these magical worlds. These places of wonder brightened my life and took me away from the pale, grey, and sometimes sinister reality of daily life in the former Czechoslovakia. I dreamed that one day I would be able to hold in my hands the papers of Galois, Abel, Fermat and Euler. That one day I would be able to just let myself be absorbed with these great works and perhaps make some further contributions to these topics.
Even still these days I experience enormous excitement and sometimes a shiver of passion when I discover even a very small fact which I did not know before.
I observed that it is possible to share my passion and feeling of wonder with my students. Sometimes one can literally “wake up” some students and point out some hidden beauty, some fascinating mystery, and some unique puzzle. It is an enormous pleasure to see these students branch out and explore these things on their own, and to see the topics of learning with new and fresh eyes. This exploration and dedication invariably leads them to progress – sometimes very substantial progress.
We are currently living in very dramatic times where we can build mathematical models in artificial intelligence, computational neuroscience, networks, biology, and health sciences. We can try to adapt classical mathematical methods to these new and exciting explorations. Finding the collected papers of Abel, Galois, Fermat, Einstein, and others, is not just a dream any longer as it was in my youth. These works, and also the current works of many great researchers, are now freely available.
What is necessary in education is to ignite feelings of passion and of the wonder of our own students, and to encourage them to find their own individual ways to learn, to think critically, and to explore a way where their natural talent and inclination will lead them to happy and productive lives.
Not everyone needs to become a researcher, but the joy of learning and the joy of even small discoveries is accessible to the broad population of our students. Currently we are facing a complex world. This world has opportunities which only a few years ago would have been in the realm of science fiction. However, we are also facing numerous and sometimes dangerous challenges. We need to educate a new generation of students who will know how to think deeply, critically, and analytically. These skills can be acquired only by their own thinking, experimentation, and exploration. This cannot be forced – it has to come naturally.
The feeling of wonder and passion is in my opinion the “key seed” that we should try and implant into our students in order to make them critical, analytical and creative thinkers.
References
- A. Einstein. Autobiographical Notes, A Centennial Edition (translated and edited by Paul Arthur Schilpp), Open Court Publishing Company, La Salle, Illinois, 1996.
