Last week I went to Toronto to attend Erik Demaine’s talk in the FIELDS institute, which was fantastic. He had three talks in consecutive days, and I attended the first one only, titled Algorithms Meet Art, Puzzles, and Magic. He talked about his background, that he liked to design/solve puzzles from childhood, that he travelled a lot in North America when he was a kid, and that he fell in love with algorithms because he found a lot of creativity in this field. He said mathematics and art have strong relationships, and that “they are just two ways of looking at the same thing!” He also said a sentence that I really liked: “Mathematics is a kind of art, since, a mathematician does not only want to prove something; he wants to give a beautiful proof.” His slides were alternatively about math and art. He talked a lot about origami, the art of creating things by folding papers, in some slides he talked about proving mathematical results about the structure and complexity of things that can be created by origami, and whether it is possible to “reverse-engineer” and build a 2D-pattern whose folding yields a given 3D-shape. In other slides, he just showed various interesting examples of what can be done by origami and also beautiful works of his father, a glassblower.

Erik Demaine was born in Halifax in 1981, received his PhD in Computer Science from UWaterloo when he was 20 years old and immediately joined the MIT faculty, where he is now. His PhD thesis was titled “Folding and Unfolding.” He said when he was a grad student, people used to tell him to work on something “serious” if he wants to get a job; but he didn’t listen to them! He is very active and has 296 co-authors.

from: Time for computer science to grow up, Lance Fortnow, Communications of the ACM, 2009

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!

The manuscript can be found here and the online published version can be found here.

Oh boy, if you’d told me an year ago that just an year after coming to Canada I’ll write a paper with Noga Alon, I would’ve considered it as a joke. But it really happened! Thank you God!

Some technical details: There was a recent preprint by Frieze et al., where they had considered the variation of Cops and Robber where the robber has speed s>1. For every s they had given a lower bound for the maximum cop number of a graph with n vertices in that variation. In summer I had worked on this problem and improved their bound for s<7 (here). I proved the cop number of an n-vertex graph can be as large as n^{s/s+1} when s=2,4. My proof uses regular graphs with large girth, which are called cages. I had also conjectured that this lower bound holds for larger values of s as well. There is an old conjecture of Bollobas about cages that implies my conjecture. Noga told me about regular graphs that don’t have large girths, but for every two close vertices, there are a constant number of shortest paths connected them. These graphs are enough for my proof, and their number of vertices are exactly what I wanted. Hoorraay.