Season 6 Episode 0
In this episode, James introduces the "tree of all fractions" and demonstrates what it's like to look up something in a mathematics research paper.
If you’d like to read a little bit more about the Calkin-Wilf Tree, I suggest starting with the paper by Calkin and Wilf which we briefly looked at on the livestream. A pre-print is on Herbert S. Wilf’s website.
Then perhaps check the Wikipedia page and the (much shorter) Wolfram Mathworld page. Both refer to the Stern-Brocot tree (I prefer the Wolfram Mathworld description of this, but if you have already somehow seen continued fractions and you like them, then you might prefer the approach taken by Wikipedia).
The maths paper on row sums that we looked at is available on arXiv. I want to properly credit the authors of this paper, so here’s a little bit about each of them;
- Sandie Han is a Professor of Mathematics at the New York City College of Technology and she was chairperson there 2015-2021.
- Ariane Masuda is a Professor at the New York City College of Technology. She’s previously studied in Brazil and in Canada, and her primary research interests are in Number Theory.
- Satyanand Singh is a Professor at the New York City College of Technology. As well as Number Theory, he works in the field of Quantum Computing.
- Johann Thiel is an Associate Professor of Mathematics at the New York City College of Technology. He’s also contributed to a Number Theory paper on the arrangement of stars on the US flag.
I mentioned continued fractions at the very end of the livestream (and in the section above). Plus magazine has a great introduction titled Chaos in Numberland: The secret life of continued fractions. The article is by John D Barrow, who was the Director of the Millenium Mathematics Project https://maths.org/. John Barrow was a cosmologist and he also wrote many popular science books (The Book of Nothing, The Constants of Nature, The Book of Universes, The Infinite Book, and many more).
If you want to get in touch with us about any of the mathematics in the video or the further reading, feel free to email us on oomc [at] maths.ox.ac.uk.