Archive for November, 2010

Dijkstra’s 3 Golden Rules for Successful Research

November 13, 2010

1- Raise your quality standards as high as you can live with, avoid wasting your time on routine problems, and always try to work as closely as possible at the boundary of your abilities. Do this, because it is the only way of discovering how that boundary should be moved forward.
2- We all like our work to be socially relevant and scientifically sound. If we can find a topic satisfying both desires, we are lucky; if the two targets are in conflict with each other, let the requirement of scientific soundness prevail.
3- Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you.
Source (with some explanations): http://www.cs.utexas.edu/~EWD/transcriptions/EWD06xx/EWD637.html

At what times is a mathematician happy?

November 7, 2010

Paul Seymour has an article titled “How the proof of the strong perfect graph conjecture was found?“, which is an informal and rather nice documentary-type article, and gives a high-level description of the process of finding the proof of the strong perfect graph theorem.

In Section 7, “What’s left?”, he writes

Having worked in Berge graphs for three years now, we have developed intuitions and skills that
took a long time to grow, and also a great fondness for the graphs themselves. Unfortunately the
main problem is solved, and there is a cold wind blowing, almost as if it’s time to go and work in a
new area … There was one other really nice question: what about a polynomial time recognition algorithm? Can one decide in polynomial time whether a graph is Berge? Is the question in NP? These were still open … We thought it would last us for another three happy years, but sadly its resistance collapsed after just a couple of months, and Maria and I managed to twist it into an algorithm.

(Bolding was done by me.) My point is that, Seymour was happy as long as there was an interesting problem to work on, and as soon as it is solved, the happiness is gone! While this may seem contradictory to a non-mathematician (who might think that the mathematician becomes happy after he solves a problem), it is SO TRUE. A mathematician has the best feeling in the course of solving the problem, and maybe a little while after solving it, but not any later!