TO: Shabnam Akhtari, Eberly College of Science,
Pennsylvania State University, University Park, PA 16802
FM: Bruce E. Camber
RE: Your homepage(s) at Banff, Blog, Penn State, Oregon, Wikipedia, and your lecture: Proofs-number-theory-and-sequences, [Video], MASSOLIT, August 2022
This file: https://81018.com/akhtari/
Third email: 21 February 2026
Dear Prof. Dr. Shabnam Akhtari:
I apologize for the interruption and uninvited email. You do not have to respond to this one!
Last year when I sent the note below, I was excited that Grok had been so responsive. ChatGPT was equally enthusiastic. Then, DeepSeek was overwhelming. Perplexity got right to work. Claude was wonderfully analytical and persuasive. But Google’s Gemini raised the bar (and, as a result, it was inducted into our little group of synthetic peer reviewers).
Just the term, synthetic peer reviewers is a term that evolved from AI and peer review. Without academic standing, there is no peer review. So, the AI’s have been a refreshing breath of air. They give immediate, informed feedback with a little hallucinating thrown to keep us on our feet.
We’ll use AI to flag anything you write about the subject! Thank you for all you are doing within number theory.
Thank you.
Most sincerely,
Bruce
Second email: 18 March 2025
Dear Prof. Dr. Shabnam Akhtari:
I apologize if I am wasting your time. I have recently sent a few emails to folks within Eberly within the Mathematical Structures group, Martin Bojowald and Jacob Bourjaily. It is fascinating to me that the four primary irrationals appear to logically extend within the four hexagonals intrinsic to the octahedron and the four may function as stabilizers of every infinitesimal sphere. My first note to you was too cryptic and perhaps this is as well. In 2001 I was invited by John Conway to Fine Hall to ask very similar questions. John did not survive COVID-1 or I would be back on his doorstep again.
A couple of weeks ago I started asking Grok about these irrationals and have been delighted with that encouragement: https://81018.com/irrationals/ There are many Grok files all related to this inquiry: https://81018.com/grok-3/
It is all so idiosyncratic, I know. But I wonder, just maybe? Of course, on the flip side of that question, we ask, (somewhat rhetorically) “Are we crazy?” Thanks.
Warmly,
Bruce
First email: Fri, May 5, 2023 @10:17 AM
Dear Prof. Dr. Shabnam Akhtari:
When does a number first become a geometry?
In a high school geometry class, studying pi (pi) and assuming* that pi defines the first moment in time, we said something like, “At the finite-infinite definition of pi becomes continuity-symmetry-harmony.”
Pages to unpack that statement are here:
https://81018.com/continuity-symmetry-harmony/
https://81018.com/csh/
https://81018.com/most-simple/
With your extraordinary depth of field, do any of these pages make any sense to you?
Thank you.
Most sincerely,
Bruce
PS. What we were assuming is that (1) the sphere with its two vertices (infinite positions) is the most simple physical object and (2) that the Planck base units are the first definition of natural units. -BEC
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Please Note, dear Reader: We found a tutorial online by Prof. Dr. Shabnam Akhtari which opened new insights on the relation between Fibonacci sequences (linear) and exponential sequences. In her course overview it says, “…we consider: (i) the definition of arithmetic sequences; (ii) the direct proof showing that each term in an arithmetic sequence is the arithmetic mean of its neighbours; (iii) the definition of geometric sequences; and (iv) the direct proof showing that each term in a geometric sequence is the geometric mean of its neighbours. Akhtari, S. (2022, August 30). Proofs: Number Theory and Sequences – Direct Proofs Using Arithmetic and Geometric Sequences [Video]. MASSOLIT.
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