The Minimum of the Maximum

I recently came across a LinkedIn poll asking where it is better to work: in a leading role at a small company or in a supporting role at a large, well-known corporation. Honestly, it is not quite a fair choice, because there are many other factors to consider besides the ones stated.

In the comments, someone reduced the question to a simpler one: is it better to be the first guy in the village or the last one in the city? That is not so simple either, because ideally many different conditions should also be taken into account. But this framing does point us in a direction. If we follow it and gradually strip away all the external factors, we eventually arrive at a situation well known in mathematics: the minimax inequality.

The theorem looks like this: min max f(x,y) >= max min f(x,y)

Translated from mathematics into everyday language, it means that being last in the city is as good as, or even better than, being first in the village.

And everyday logic makes this easy to explain:

• If you are last among people who are better than everyone else in some respect, you will inevitably learn something new from them and gradually grow.
• If you are first among people who are not as advanced, you have no incentive to grow because you are already better than everyone else. You will inevitably begin to decline over time.

Before I even knew about the minimax inequality, I once had to choose between staying in my hometown for the final two years of school, where I was a star, or going to study at the Advanced Educational and Scientific Centre of Moscow State University (AESC MSU), formerly the A. N. Kolmogorov Physics and Mathematics School No. 18.

I chose AESC MSU, and I have never regretted it.

At the start, I was one of the weakest students in my year, but that motivated me to learn from my more advanced classmates. I may not have earned a gold medal, but I was admitted without entrance exams to one of the best faculties: the Faculty of Computational Mathematics and Cybernetics at Moscow State University.

At AESC MSU, I also made many wonderful friends who are close to me in spirit and share my level of intellect and knowledge. We are still in touch. The photo shows me and my classmates at AESC MSU, class of 1997.