The Mathematics of Doing


April 30, 2007
Ohad Samet

By: Ohad Samet

Paul Erdős was a renowned Hungarian mathematician who, at the age of 21 received a PhD in mathematics, and eight years after being accepted to university began wandering around the world. What do I mean by wandering? Well, it is said that upon finding a problem he was interested in (usually simple problems with complex solutions), he would schedule to work on it with another mathematician, go to his house, stay on his couch and not leave until the problem was solved. In this manner he published 458 articles with collaborators, which is a huge amount. His dedication and passion for mathematics made him a center for activity of very skilled men in the field he loved the most. His work was so significant that anyone who was associated with him, directly or indirectly, received a number describing his proximity to Erdős – those who worked with him directly were “Erdős number 1”, those who worked with his number ones, were assigned “Erdős number 2” and so on.

 

Erdős was one man with such an insatiable lust for a certain field, that his entire life was dedicated to the search for new understandings. He himself was Erdős number 0, simply zero.

 

 

Why did I go? At first for the path, then for the effort, and at last for a different reason altogether. I am not a Hungarian mathematician, thank God, and I do not intend to sleep on anyone’s couch. What I do have is this idea – “after practicing for many years, you can understand things that can only be understood from doing something physical for many years, alongside people who are doing the same thing as you”.

 

This is not a complicated concept – it concerns people like us, those who do not live to train (like Chinese monks, for example), but rather live life as well as train for long periods of time, do this actively, coming to practice every week, of course, and for many years. My math is simple as well – it is the distance in years between now and later, it is the distance between my number now and number 1 of this idea. Erdős’ idea is relevant, since, like in his case, what is unique in his desire to understand, is the relationship with people.

 

En route, I met people of all “numbers”- some who have been training for short periods of time that still have beginners’ enthusiasm, and those that train for many years and can still look back to the beginning and tell me how it was once different. Then there are those who have been training for more than a decade and those who’ve been training since before I was born. When putting all those people on an axis, you do not see a group following a leader, but rather people dispersed along a path constantly in motion. At the end everyone reaches the same point, where there’s a long way ahead, but also a long way already behind them. You don’t need more than that.

 

Getting there is not a simple task, you have to walk and carry substantial weight on your back, make an effort, sweat, and then after a long time you reach a place of understanding. This is not a very profound understanding; you cannot crack the secrets of the atom bomb with it. It is an understanding regarding how to live in a certain manner, practicing physically for many years. This practice requires preserving the past and some of which acceptance of the present.

 

In the end it is all about hard work and lots of patience, strong over-sweet tea with a smoky flavor, sparring in the desert, rain at night, practice again, and a few days and nights that go by each of us alone and for all of us together.

 

Finally, if you stick around long enough, I think that something good comes out of it all: nothing too grand or complicated, surely not an article on the number theory. Just an understanding and a meaningful reminder of living our life at this time, an ability to honestly say: “I was there back then, and I am here today, and, so it seems, I’ll also be here tomorrow”.

 

 

This is the difference between those who were “ErdÅ‘s number 1” and those who read about it in his book saying it was “very interesting”, saying they felt a strong urge to be a part of an effort such as ErdÅ‘s’ and his colleagues, yet kept sitting on the couch in their homes. This difference exists because in the DÖ we practice you cannot stand aside. The quest for understanding requires mental and physical involvement, among other things, because it is available here and now for those who are interested.