Ed Frenkel, one of our heroes

TO: Edward Vladimirovich Frenkel, Professor of Mathematics, University of California, Berkeley (an expert on the Langlands programs), Berkeley, California
FM: Bruce E. Camber 
RE: Your articles in arXiv (76) especially Folded quantum integrable odels and deformed W-algebras (2021), your  book: Love & Math  (A review by Alexandra Wolfe, Wall Street Journal), even your homepage(s), especially your CV,  Personal website, X (Twitter), Wikipedia
YouTube:  https://www.youtube.com/channel/UCpF6IVIBI-UpR2taxmogj0A

This page: https://81018.com/frenkel/

References to Edward Frenkel's work within these web pages:
Eighth email: 15 July 2026

Dear Prof. Dr. Ed,

I hope this note finds you well. Your post today on the universality of mathematics — how its truths transcend language, culture, and background while connecting us all at a deeper level, of course, resonated strongly. It beautifully captures the spirit animating much of my own work.

I’ve continued my work on a discrete, base-2 exponential model of the universe (202 notations from the Planck scale to the current horizon). We recently posted a working paper proposing a concrete geometric and physical substrate for Langlands correspondences and functoriality: https://81018.com/240204/A Geometric Realization of Langlands Correspondences and Functoriality via Base-2 Sphere Packing and the Aristotle Gap

I’ve also prepared a short overview on motivic Galois groups (drawing from Jim Arthur’s recent paper) with initial bridges to our geometric framework: https://81018.com/galois/

The core idea is that the irreducible ~7.356° tetrahedral packing gap introduces topological frustration from early notations onward. This gap, replicated across successive doublings, may act as a dynamic driver for correspondences (as selection) and functoriality (as lifts), offering a geometric/physical realization that complements the abstract structures explored in the Langlands program.

I would be deeply grateful for any comments, critiques, or suggestions—particularly on intersections with motivic or exponential motives, or how this discrete approach might illuminate the unifying power of mathematics you highlighted today. This remains very much a work in progress, offered in the spirit of constructive dialogue.

Warm regards,

Bruce E. Camber https://81018.com/camber/

Seventh Message: X (Twitter) and email: 7-8 April 2026 (updated)

EDWARD FRENKEL: “We live in a volatile world, which sometimes feels hopeless, but I’d like to remind us of certain human qualities that bring us back to hope and allow us to imagine a more harmonious world, in which we can all thrive. This sense of hope comes from an unlikely source: Mathematics. Let me explain…Replying to @edfrenkel

BRUCE: “With hope and joy and love…wow, if all mathematicians had such gifts. But, they do. All of us do! Yes! https://81018.com/breakingthrough/ You are such a inspiration and delight. Uplifting. You bring your book alive, Love and Math: The Heart of Hidden Reality. I have discovered that the universe is a grid of infinitesimal spheres defined by Planck scale numbers, dimensionless constants and the irrational numbers. Yes, we are all deeply and profoundly connected! Could I interest you in taking that last homepage (linked above) to writing it up for an arXiv entry?!?

Sixth email: Sun, Nov 30, 2025, 1:15 PM

Dear Edward,

I wanted to follow up on my message (November 28) with the detailed documentation I mentioned. Since writing to you, we’ve completed several support pages that flesh out the geometric model:

Core documentation now available:

  1. The Geometric Emergence of Gauge Symmetries (homepage overview)
  2. Notations 0-24: From Planck Scale to Grand Unification (detailed notation-by-notation analysis)
  3. The 7.356° Gap: From Geometry to Physics (mathematical derivation of the geometric constraint)
  4. Testable Predictions and Experimental Proposals (falsifiable predictions for physicists)
  5. E8 and Maximum Symmetry at Notation 32 (connecting to Garrett Lisi’s work)
  6. Langlands Correspondences as Physical Mechanism ← Particularly relevant to your work

The Langlands page specifically proposes that:

  • Your geometric Langlands work describes the mechanism operating in Notations 10-40
  • The correspondences aren’t purely abstract—they’re the selection algorithm that determines which Lie groups become physical
  • Notation 24’s triple correspondence (number/scale/dimension) might be a Langlands correspondence in action
  • The 202 notations represent the finite physical completion of the Langlands program

I realize this is unconventional, and I welcome your skepticism. The work stands or falls on whether the correspondences we are proposing (FCC geometry → number fields → Galois groups → SU(5)) actually hold mathematically.

If any of this resonates—or if you see clear errors—I would be grateful for your thoughts, even briefly.

With continued respect for your work,

Bruce

Bruce Camber
https://81018.com

PS. Since March 2025, I have been slowly using AI Platforms to validate my work. Grok was first, then CHatGPT, and finally Perplexity, Anthropic (Claude), and more recently DeepSeek. Very different personalities and conclusions with each, Anthropic – Claude was key to these support pages.  -BEC

Fifth email: 15 August 2024

Dear Prof. Dr. Edward Frenkel:

Until one of you geniuses can tell me why the universe “just doesn’t work that way,” I will have to persist on this crazy path that I am on… pi generating infinitesimal spheres defined by constants like Planck’s four base units and by the perfections of pi’s continuity, symmetry and harmony. Why, if that’s the condition of the first moment, isn’t the very first automorphic forms contained therein? Couldn’t much of string and M-theory follow?

My simple logic: https://81018.com/identity/

Thank you.
Warmly,

Bruce

Quick note: 21 February 2024

Continuity-symmetry-harmony define infinity and the qualitative; and, the Planck base units are the beginning of the quantitative and define an infinitesimal sphere as a primordial building block: Reference to you: https://81018.com/reformat/#Frenkel Also: https://81018.com/reformat/#Emails

Fourth email: February 2, 2024, an update of 4 June 2023 email

Dear Prof. Dr. Edward Frenkel:

Big Bang Cosmology (BBC) has kept the Langlands programs from developing ideation about the start of the universe that would be consistent with other studies of functional analysis that are also excluded from the grid. The richness of Langlands programs needs to be part of our vision of who we are and how our universe came to be. Langlands belongs on the grid. With the growing clarity from the images of the James Webb Space Telescope, questions are raised about the smoothness of the start (which our other space telescopes have also raised). Images of well-developed galaxies within 300 million years of the start is also raising difficult questions.

The BBC’s de facto expansion of the universe is base-2. The only part of the theory that needs to be changed is its compression of “everything, everywhere for all time into a singularity.” One possible concept is to replace it with a shell sphere defined by the Planck base units or its equivalent.

A comparison with base-2 exponential notation renders virtually the same results. Obviously, it’s an alternative model. Once the BBC begins to be seriously set aside, I believe our oldest, most-ubiquitous equation will re-emerge. Pi (π) gives us a very different beginning, a smooth start, immediate star formation, and our current background radiation.

If we take as a given that the Planck base units manifest as an infinitesimal sphere with all the equations of dimensionless constants that define each, along with its deep-seated continuity-symmetry-harmony, Langlands programs can get to work and be applied as the preconditions for this moment. With base-2 and continuity-symmetry-harmony as the infrastructure even a transition from Langlands to string-and-M theory is more direct. There is room on this continuum for every study Including causal dynamical triangulation, supersymmetries, loop quantum gravity, causal set theory, hypothetical particles, and the spectral standard model.

The BBC has no concept of the first second. It has little understanding of base-2 notation and the 143 steps from the first instance to the first second of our universe. This all has to change. To that end we have started a petition to our major learned societies within every nation that has one. https://81018.com/petition/ 

Within this program, Langlands is being asked to define the first notations and the bridge between the finite and infinite. We will be asking the people within SUSY to help redefine infinity and perfection. We believe quantum causality comes later; guesstimates are within Notations 64 to 67.

So to encourage this entire process, we kindly ask you to consider signing our petition about it all: https://www.change.org/KnowYourUniverse

Best wishes,

Bruce

Third email: 6 April 2019

Dear Prof. Dr. Edward Frenkel:

Of three related articles, today’s has a reference to your work and a link to our page about your work within our website which is: https://81018.com/2013/10/13/frenkel/

These are the three related articles
https://81018.com/e8/ (Today, April 6. https://81018.com/e8/#EF )
https://81018.com/maybe/ (Wednesday, April 3)
https://81018.com/standard_model/ (Tuesday, April 2)

At some point in time, the evidence will become compelling enough, our scholarly community will have to address it; and at that time, perhaps Wheeler’s comments will become true: “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?”

Thanks.

Best wishes always,

Bruce

Second email: Wed, Nov 15, 2017 at 7:02 AM with small updates.

Dear Prof. Dr. Edward Frenkel,

Thank you for your acknowledgement back in October 2013. Today, I am digging around through your ArXiv contributions. Your work is consistently informative and inspirational. Thanks again.

Not being a mathematician or scholar, it has taken me a little time to realize that the domain we outlined with our base-2 notation from the Planck scale to the CERN-scale — that’s 64 notations — just might be a perfect place for the Langlands programs. It’s the same 64 doublings within the Wheat & Chessboard story. There’s plenty of room to build your case.

Each notation should be a domain for pure mathematics, number theory, geometry and all the functions in-between. I tried writing it up: https://81018.com/exponential-universe/

From notations 67 to 201, I would guess that all the infrastructure from each notation gets carried forward and all notations are active all the time. There is no past. We are within notation 202 today.

Just a bit idiosyncratic and probably a whole lot crazy, our chart of numbers is here: https://81018.com/chart/ I am slowly trying to interpret those numbers: https://81018.com/planck_universe/
Here’s my little chart from 2014 inspired by your first note: https://81018.com/chart2/ The first 60 notations are in groups of ten and are just wistful speculations.

I know that you have no time, but I also thought it was impolite of me to not respond to your note from four years ago. I just didn’t want to waste your time. Thanks.

Most sincerely,
Bruce
****************
Bruce Camber
http://81018.com
Austin, Texas

PS. I have copied Prof. Dr. Robert Langlands. I had sent him a note to introduce this naive (high school) work not too long ago. Although he may not remember it, this copy might help to open a discussion. I am sure, like you, he is overwhelmed with email from all the idiosyncratic folks who have studied “not-quite enough” mathematics and physics to be helpful. And, of course, within such a small world, there are a lot of us! -B 

First email: Sun, Oct 13, 2013 at 4:24 PM

Dear Prof. Dr. Edward Frenkel:

I was substituting for my nephew — “Teach them a little about the five platonic solids” — when we were observing how the tetrahedrons and octahedrons can endlessly enfold within each other and the question was asked, “How far within can we go?”

We divided each of the edges in half, connected the new vertices, and had the four half-sized tetrahedrons and an octahedron within the parent tetrahedron, and six octahedrons and eight tetrahedrons in the parent octahedron. We talked about tiling the universe, and then we did the simple math back to the Planck Length.

At that time we were not familiar with Kees Boeke’s work from 1957, or with Phil Morrison’s Powers of Ten, or Cary Huang’s Scale of the Universe. We were following geometries. We were dividing by 2. Our goal was the Planck scale.

At the 45th step within we were in the range of the size of a proton.  In another 67 steps we were in the range of the Planck Length. “Wow. That was interesting,” I observed. We then started on the path out to the edges of the Observable Universe. Another 90-or-so steps, we were there.

So, what is this thing we just created? We went to the web and found very little. Our simple geometry and simple multiplication and division was just too simple. Or, is it?

I told the kids, now over 120 of them, we’ll find out! But, we are still searching!

Why is this little effort of so little interest to the professional mathematicians? It is a wonderful ordering system for information. Its inherent geometries —  those five platonic solids — are just fascinating to see them embed so easily and readily within each other.

Of course, there is so much more to come, but perhaps our simple questions are quite enough for now.

Thank you.

Warmly,

Bruce Camber
an enthusiastic, new reader of your book, Love & Math

PS. The book will go to the school’s library when I finish and any math student will get extra credit for reading it, possibly upping their grade from a D to a C- for some! Hopefully the book will push it to an A+ for more.

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