Do it again!

My advisor was 76 years old when I decided to become his pupil.

Never I thought the great lessons I would learn from him. Although they would come with a high cost, since then, they have always positively impacted all my endeavors.

As his Ph.D. student, I was given my first task, which seemed relatively simple: to compute the eigenvectors of some three-by-three complex matrices. Easy peasy, right?

The following day, I appeared at his office. Knock-knock. “May I?” I asked him. I proudly showed him my results. After some seconds of silence, he looked at me and shot at me, for the first time, his words: “Did you do it?” It looked like a trivial question. “YES”, I said to him. To which he replied: “Did YOU really do it?” I noted the hidden meaning of his remark. “No, I didn’t. A software did it”. He suspiciously smiled. “A-ha! There you go, so YOU didn’t”. He didn’t accept any of the reasons I had for doing so. It was clear; he had asked me to compute on my own those quantities; any other kind of solution would not be accepted.

“Come until YOU have done so.”

After a couple of hours, I was back in his office. Proud of myself, I showed him my results which were the same as the previous ones.

“This is not what it should be. It’s wrong.”

Alarmed, I asked him why? “I just know it.” He handed me back my results.

“Do it again!” He kindly shouted at me.

This story repeated itself over and over and over again... In fact, FOR MORE THAN A YEAR. He would always have a reason to return my notes (which always had the same outcomes). He asked me to revisit linear algebra, to learn every possible method to extract eigenvectors: from those exact ones to those approximate ones.

At some point, I thought that maybe he was losing his mind. After all, he was old. It was the easiest explanation for that endless repetition.

Little by little, I had been learning many tools and skills. I could now see a matrix and approximately know what the eigenvalues and eigenvectors should be.

Without noticing, I was given all the tools to unravel the mysteries I would face during the following years. Those apparently nonsense efforts took me to the best of my ideas.

In a few words, I was trained to think.