TO: Ping Xu, Penn State, Institute for Gravitation and the Cosmos, Center for Fundamental Theory, University Park, PA 16802
FM: Bruce E. Camber
RE: Your homepage(s) especially within ArXiv especially with Alberto Cattaneo in Zurich, 2003 Poisson structures PDF (ArXiv-132) and with Mathieu Stiénon, also Distinguished Senior Scholar (2012), inspireHEP, and Google Scholar, and Mathematical structures (at the top of that page):
“Physics often advances when crisp mathematical structures are uncovered in a framework developed to describe observed phenomena. For example, in quantum field theory there is a vast discrepancy between the current calculational difficulty in making predictions for experiments and the simple, mathematical form of the end result. The Amplitudes program seeks to explain and exploit this surprising simplicity by reformulating the basic mathematical tools used to make predictions.“
This page: https://81018.com/xu/
Second email: 15 March 2025
Dear Prof. Dr. Ping Xu,
The header of your Mathematical Structures group reads: “Physics often advances when crisp mathematical structures are uncovered in a framework developed to describe observed phenomena.”
I don’t think there could be more crisp mathematical structures than the four primary irrational numbers, Pi (π), Phi (φ), the Square root of 2 (√2), and Euler’s number (e). Might the four hexagonal plates of the octahedron be an appropriate representation of that geometry? No experts responded so I turned to Grok: https://81018.com/irrationals/
To date, I have discussed it in these last four homepages:
• Pi Day 2025: https://81018.com/pi-day-2025/
• Today’s homepage: https://81018.com/incommensurable/
• Breakthrough: https://81018.com/breakthrough/ https://81018.com/breakthrough-indeed/
Your comments would be most welcomed. Thank you.
Most sincerely,
Bruce
PS. If you have any updates-changes-deletions within our page about your work, just say the word. :https://81018.com/xu/. An evolving page: https://81018.com/penn-state/ -BEC
First email: 21 April 2023 at 12:03 PM
Ref: GAP 2023 at the IHP in Paris
Dear Prof. Dr. Ping Xu,
Two quick questions:
1. Have you ever seen the five- tetrahedral gap (famously missed by Aristotle and documented by Lagarias and Zong, AMS-2015 Conant Award) over and under a five-octahedral gap? It’s a pretty object, but I don’t think there is anybody else who has written about it. Do you think it could be important?
2. Do you know if there are any scholars who have written about the nature of these gaps? How do such gaps manifest within space and time?
Thank you.
Most sincerely,
Editor’s Note: It seems most mathematical scholars are reluctant to open their circles to respond to people who are obviously not part of their very special domain. A special patience and tenacity is necessary. -BEC