Asking questions about the work of Levent Alpöge

Levent Alpöge, Harvard University Department of Mathematics

ArXiv (15): Modularity and Effective Mordell I; Video, 2021
Homepage(s): CV, Publications

Second email: 27 December 2022 at 8 PM

Dear Dr. Levent Alpöge:

I have been spending a bit more time reading about your work and reading your other works. As I did that, I further edited my earlier note to you and have posted it here: (this page)

You’re young. How do you answer the question, “What is the most fundamental interaction that defines the first moment of the universe? Is it the first interaction in some manner that defines space and time? ” Thank you.



First email:  16 December 2022 at 2:06 PM

Dear Dr. Levent Alpöge:

Could continuity, symmetry, and harmony be a proper description of the functional nature of pi? Years ago, I could see how it all might evolve from the most simple sphere:

Do the Planck base units define the first infinitesimal sphere? If so, is sphere stacking-and-packing a fundamental of physicality?

If base-2 is applied, there are just 202 doublings to the approximate age and size of the universe and wave-particles-fluctuations are first measured between Notations-64 to Notation-67. The first second  comes along within Notation-143. It is a description of the very early universe. Interesting?

Thank you.

Most sincerely,


PS. Along the way, we found a very interesting gap with five-octahedrons. Aristotle had failed to see the gap with five tetrahedrons! The commercial construction sets and computer programs also overlooked these gaps!  -BEC