Learning from Unsolvable Problems – My Time With Sol Golomb

By Sina Aboutorabi

Ever since high school, I’ve always been fascinated by number theory and discrete mathematics. What I love about this field are the possibilities – I am only limited by the limits of my own imagination.  As a student in Iran, I won a national honor in mathematics at the Khwarizmi Festival. At the time, I never thought that this interest of mine would connect me with the late Sol Golomb, USC professor of Electrical Engineering and one of the greatest minds in engineering and mathematics.

One of my best memories with him was when we first met in his office and he accepted my request for him to be my mentor. I had initially gone there to discuss my work in a sub-field which I called “sequential calculus.”  I shared the paper which won me the national honor in Iran and Sol recognized the script as Farsi right away.  He said he believed I was talented in number theory and pushed me to publish my paper in the American Mathematical Society. From that point on I started conducting research with Sol on deep space communications coding and Golomb-Costas array signals.

Sometimes the theory, although fascinating, seems to have no possible applications in the real world. This can be a hard thing for a young theorist to hear, especially when it comes from leaders in the field.  Sol was never that type of leader.  He proved to me that even theories with no clear applications can change the world. This was such an important acknowledgment of my work!

He taught me how to take joy, and even learn, from unsolvable problems.  He taught how to approach and think about open questions. He also taught me that it is very important to give chase to questioning; that curiosity has its own reason for existence. Like everyone else, I frequently make mistakes on the way to discovering a new concept or solving a problem. It is often the losers who learn more about winning than the winners.  Our mistakes always give us opportunities to learn and grow.

Sina at the Space Conference in 2015 at the Pasadena Convention Center.

Like me, Sol was a big fan of the history of mathematics and science. One day in his class on signal design, my classmates and I were sitting in the classroom waiting for Sol to show up. As a joke, I told them that the professor would most likely spend some time getting sidetracked talking about astronomy and space science. Finally, towards the end of the lecture, he actually did start talking about these seemingly off topics areas.  Of course, what seemed to be irrelevant actually ended up being associated with the applications of what we had been learning about Golomb rulers.  His ability to connect seemingly disparate disciplines never ceased to amaze me.

Prof. Golomb was an amazing example of what the human mind can do when operating at the maximum memory capacity.  I was so lucky to have seen it firsthand and I will always remember him for his great humor, kindness, forgiving spirit and generosity. Although Sol was accomplished in the history of science and technology, he was a super-man of human values. He was the humblest and most intelligent professor who I have ever come across.

Sol was a prophetic scientist who will not be repeated again anytime soon.  And yet, I have learned more phenomenal life lessons from beloved Sol than I could possibly learn from completing several PhDs.

Sina Aboutorabi is a PhD student in Electrical Engineering studying communications. He is the last of Professor Golomb’s PhD students. 

Share this Post