The source is within you and this whole world is springing from it, "Rumi"

What is the one thing that you learnt at school and for your whole life you felt grateful for it? Apart from the basic skills like reading and writing or critical thinking?

For me, it was solving higher dimensions geometry problems with only imagination and without using pen and paper. Wait, what? Yes, it is school strike here in Norway and I am having a flashback to my early highschool years, we are talking about 24 years ago. God, this makes me feel so old to say!

I remember one day, our Geometry teacher walked into the classroom and said "from today we are not going to use pen an paper at all, we are not going to use anything, we will only use your imaginations!". It was the toughest and most weird thing I experienced until that day. Higher dimension geometry problems were already really really difficult for us to solve even using pen and paper. We had to map out the problem situation in our head and preferably using colors, to find a solution or a proof of a statement and then describe it for the whole class. Other students had to create the same imaginations step by step to follow the reasoning to be able to say that the solution was correct or not.

You may think, OK, what is the big deal here, everyone can imagine after all. It was extremely difficult for us in the beginning and to keep doing this over a longer period of time. Fortunately like many other skills it became easier and easier with practicing. We started building imagination muscles and it started to become fun.

It became so fun that I almost spent one summer holiday to solve all 3D geometry problems from a book with just imagination. When I got back to school I told my teacher and asked him "now what, what should I do next?". He smiled and answered "now go and try to solve real life problems this way". I was disappointed, this was not the answer I wanted to hear, it was so fun and I definitely felt I was up to something. I felt that he answered like this because he did not care that much.

It took me literally 24 years to understand his answer and what he meant at that time. The point is that imagination is the counter muscle you need to strengthen for intuition. That skill by itself helped me alot during my studies and career later on. The ability to be visionary and to see the bigger picture out of bits and pieces is a byproduct of that.

Fortunately, he had much smarter students as well whom continued this imagination game. Perhaps some of my Sampad Alumni fellows are among those. The best example of this, the late Maryam Mirzakhani who became the first woman in the history who won Fields Medal in Mathematic (equal to Nobel Math Prize) for her outstanding contributions to the dynamics and geometry of?Riemann surfaces?and their moduli spaces. You can read a simplified explanation of her work here

It takes a brilliant mind to take in the?entire?picture and look at such situations in their most general forms. That was the genius of Maryam Mirzakhani, who was unafraid to tackle major questions in mathematics—rather than cranking out solutions to simpler, more specific problems, a temptation for any researcher trying to build a resume.

It is amazing to see what kind of influence a good teacher or a good leader can make. In this era that we have AI solutions like OpenAI solving Math Olympiad problems or MIT′s AI solution that solves College-level Math problems, we perhaps need to redefine and reimagine our education systems.

In the end, the mountains of?imagination?were nothing but a house. And this grand life of mine was nothing but an excuse.

Rumi