re: Newroz, a Math Factory, and Flexagons

MM: What is it like to discover a brand-new mathematical object, like Newroz?

FR: It was quite exciting when Khalegh told me that he had found Newroz. Other researchers, some of my grad students and I had previously looked for it, and I had even spent some time trying to prove that it didn’t exist!

MM: How did you begin studying Venn diagrams? Why do they interest you?

FR: I first became interested in Venn Diagrams after hearing a talk by Anthony Edwards, who is a mathematician from Cambridge University, the same university where John Venn (1834-1923) was a professor. Anthony was talking about symmetric Venn diagrams and had discovered some with 7 curves. Eventually I finished the enumeration that he had started using computer searches.

As to why I became interested, the topic played well into my expertise in exhaustive computer enumerations and Gray codes, plus there was the attractive feature that they looked visually stunning with a little bit of drawing effort.

MM: Did you have any early experiences that led you to becoming a mathematician?

FR: As a child I found Martin Gardner’s books and the column he wrote in Scientific American to contain many fascinating topics, some of which I could actually understand. I remember building his “hexaflexagons” with my father. In high school I had a great geometry teacher, Mr. Davis; he really instilled an appreciation for axiomatic proofs. And then in university I had some really inspiring professors—that was when I first started thinking about a career as a mathematician / computer scientist.

MM: You say on your homepage that you’ve had an online presence since 1995. How have the ways that mathematicians use the internet changed since then?

FR: At the time my goal was just to teach myself something about the Internet, and make some of my research more accessible through the “Combinatorial Object Server“. The Internet plays a great role now in the dissemination of research; it is easy to envision the day when print journals are a thing of the past. And of course Email and Skype are heavily used. Finally, there is a significant number of mathematicians who study the structure of the Internet itself through such things as “power-law graphs”.

MM: Many of our readers are young people. Are there any other thoughts you’d like to share with them?

FR: Mathematics is puzzle-solving. Read a book by Martin Gardner or Raymond Smullyan—start with the older ones. Great fun!