re: Newroz, a Math Factory, and Flexagons

MM: Can you describe what it was like to discover Newroz?/span>

KM: It was quite exciting. When I first ran the program and got the first result in less than a second I didn’t believe it. I checked it many times to make sure that there was no mistake.

MM: What role did computers play in finding Newroz? More generally, what’s the interplay in your research between doing math using computers and doing math “by hand”?

KM: Well, computers make computations a lot easier and more accurate, but no matter how much powerful computers are today, they are still limited. For example, if we wanted to find Newroz just by searching through all possible cases, it would have taken years even using all computers in the world. One important thing that I learned from my supervisor is to start with small cases when you see a complicated problem. So, we started with analyzing seven-set Venn diagrams, that were already known, to find some features to restrict the search space. Of course, even with these properties we wouldn’t be able to find Newroz without using a computer program. However, I think beyond the speed and accuracy, computers like pencils and papers are tools that you need to do the computation and you are the one who solves the problems, not computers.

MM: How did you come to be interested in Venn diagrams? What do you like about them?

KM: The first time that I heard about Venn diagrams was in high school and I found them very useful in understanding the basic concepts of set theory. Then years later while I was at the university of Kurdistan in Iran I found a paper of Stirling Chow and Frank Ruskey about generating Venn diagrams using polyominoes. I wrote a computer program to visualize their work and sent it to Frank Ruskey asking him if it is possible to do my PhD in this area under his supervision.

Venn diagrams are easy to understand and they are elegant like any other mathematical objects.

MM: What early experiences did you have with mathematics that made you interested in it?

KM: I remember when I was in middle school I had a lot of fun of drawing geometric patterns. I had a drawing kit and I had never enough of playing with it. I also liked the number puzzles and games. What I liked the most about math was that it helped me to understand other subjects in school a lot easier.

MM: Who are some of your mathematical heroes, and why?

KM: It’s hard to choose but I think one of the best mathematicians of all the time is Leonhard Euler. He is one of the most influential and most prolific mathematicians. One important thing about Euler is that he never stopped working even after he lost his eyesight. Another more influential mathematician that I like the most is Carl Friedrich Gauss. He is responsible for discoveries in different areas of mathematics. Without the amazing work of these scientists we wouldn’t be able to see the beauty of math.

MM: Many of our readers are young people. Is there any advice or encouragement you’d like to share with them?

KM: Try to understand the basic concepts and practice a lot. Problem solving is a skill. The more practice you do the more you learn.