What you will find here
This newsletter is for math and science enthusiasts who want accessible introductions to important math and science topics beyond the level found in popular books or magazine articles. It is based on a science club the authors conducted for kids and their parents in the Princeton area for many years. Ever wonder why time slows down according to the special theory of relativity? Or why Euler’s identity is the most beautiful relation in mathematics? Or why the Riemann hypothesis is considered the most important unsolved problem in all of pure mathematics? We try to answer these questions in depth but with more clarity than would a textbook by emphasizing intuition and the historical development of the ideas. We use enough mathematics to really understand a topic, but no more than that. We also throw in puzzles, just for fun.
How this substack came about
Gyan Bhanot
When I was between 10 and 15 years old, my father, who was an English and Philosophy major but loved mathematics, would sometimes pose math puzzles when we had tea in the morning on the front porch in our house in Baroda (now Vadodara) in India. Some of the puzzles he knew the answer to, and some of them he did not. I remember one of the puzzles he asked me was to bisect an angle using a straight edge and a compass. After some effort (there was no google in those days) I managed to figure that one. Then he asked me how to try to trisect an angle using the same instruments and I couldn't do it. He told me he did not know either and that he thought it was not possible (which is true). Another time, he asked me how many parts a circle can be divided into using only a straight edge and a compass. I knew this from having read about it in some book, so I told him it was possible to divide it into 3 x 2n parts, where n is a positive integer. He said that he knew it was possible to divide it into 5 parts and that Gauss had shown it was possible to divide it into 17, but he did not know the method. Much later I found the proof for 5 in a book and then learned about, but still do not understand, the deep mathematics of this, which is due to Fermat.
My father’s puzzles made a deep impression on me, and when we had children, I would (occasionally) pose puzzles to our kids at the dinner table, without insisting that the kids work them out. Sometimes they did and sometimes not, and I did not push them. However, eventually this resulted in my starting a science club, which is the genesis of this substack. With two friends, Siddhartha Sahi, a Math Professor at Rutgers and Sushama Raina, an English teacher in a nearby high school, I started the club in 1991. We would meet from ten to eleven thirty in the morning on the weekends, at various locations in Princeton, New Jersey. To make it a family affair, we had a rule: parents had to attend with the children and had to actively participate in whatever topic was discussed. The topics varied over a wide spectrum, with a preference for ideas that can be presented in a simple form, often through puzzles. Sometimes the presentations were simple enough that kids could easily follow along and other times material was more advanced, aimed at their parents.
As time passed, Greg eventually joined with his son.
Greg Hopper
Like Gyan, I had a habit of posing math or science problems to both of my children when we were getting pizza, on car trips, or when we were just sitting around not doing much of anything. After about a year of attending the club with my son, Gyan asked me if I wanted to do a session and after that I was hooked, joining Gyan to help present the topics going forward.
I often told friends about what we were doing, and a great many wished that they could join the club, but they didn’t live close enough to Princeton. Gyan and I talked about putting some of our presentations on a website over the years but professional responsibilities, until recently, always stood in the way. Now that substack has come along, we’ve decided to do it!
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