TO: Maryna Viazovska, 
EPFL (École polytechnique fédérale de Lausanne), Institute of Mathematics, CH-1015 Lausanne, Switzerland
FM: Bruce E. Camber
RE: Your papers in ArXiv especially The sphere packing problem in dimension 8 (April 2017), the Fourier interpolation on the real line (Jan 2017), as well as Google Scholar, homepage, your Twitter your Wikipedia overviews, and your YouTube entries, especially Automorphic Forms and Optimization in Euclidean Space.
This page: https://81018.com/2020/02/27/viazovska/
Others: https://81018.com/conference/#Viazovska
Sixth email: January 4, 2026
Dear Professor Dr. Maryna Viazovska,
Since our last exchange about the Hubble constant derivation, the geometric framework has crystallized further, and I believe it intersects directly with your E8 sphere packing proof.
The claim: Gauge symmetries emerge geometrically at specific scales during base-2 doubling from Planck length. At Notation 8 (2⁸ = 256 spheres), SU(3) gauge theory—with its 8 generators and 8 archetypal gluons—appears to correspond to the eight-fold structure you proved is optimal packing in 8 dimensions.
The question: Is this mathematical coincidence, or does optimal sphere packing force specific symmetry structures?
Three specific observations:
- Your E8 result: Proved E8 lattice is optimal sphere packing in 8D
- Particle physics: SU(3) has 8 generators (Gell-Mann matrices λ₁–λ₈), 8 gluons, Murray Gell-Mann’s “Eightfold Way”
- Our framework: At Notation 8 (256 spheres), eight-fold patterns crystallize geometrically
When you proved E8 optimality, did you encounter any structures that might relate to Lie group representations? Could the 248-dimensional E8 root system have physical significance at scales where sphere counts reach ~256?
Why this matters:
If optimal packing in 8D generates the eight-fold structure underlying SU(3), then gauge symmetries aren’t arbitrary group-theoretic choices—they’re packing necessities. Your mathematics would be the proof.
Similarly, at Notation 24 (16.7 million spheres), the observed grand unification scale (~10⁻²⁸ m) corresponds precisely to SU(5)’s 24 generators. And at Notation 32 (4.3 billion spheres), full E8 (248 dimensions, close to 2⁸ = 256) might appear between GUT and electroweak scales.
Framework documented here:
- Notation 8 analysis: https://81018.com/notations-0-10/
- E8 at Notation 32: https://81018.com/notation32-e8-maxsym/
- Full gauge emergence: https://81018.com/gauge-symmetries/
I know your work focuses on pure mathematics, not physics applications. But if optimal packing geometrically requires eight-fold structure at 2⁸ spheres, that would be profound—it would mean SU(3) is inevitable, not chosen.
Would you have thoughts on whether sphere packing theory predicts which symmetry structures must appear at which scales?
Thank you for your time, and again congratulations on that Fields Medal — it is well-deserved.
Most sincerely,
Bruce
Bruce Camber
https://81018.com/2020/02/27/viazovska/
Fifth email: 3 October 2025 at 3:45 PM
Dear Prof. Dr. Maryna Viazovska:
I think you will find this of interest. Yesterday I asked Grok to convert our 18.5 tredecillion PlanckSpheres per second to the standard Hubble constant units (km/s/Mpc) involves multiplying by the distance conversion factor (1 Mpc ≈ 3.086 × 10^{19} km). It yields approximately 71 km/s/Mpc—remarkably close to observed values from supernovae measurements (~73 km/s/Mpc).
Meaningful? We’ve been touting the 18.5 figure for years.
Thank you.
Most sincerely,
Bruce
PS Our page about your work is here: https://81018.com/2020/02/27/viazovska/ *************************
Bruce E. Camber
Austin, Boston, Winter Park
http://81018.com/bec/
*************************
Fourth email: 5 July 2022 at 4:57 PM
Dear Prof. Dr. Maryna Viazovska:
Many geometers, chemists, and physicists know that five tetrahedrons sharing a common edge create a gap: https://81018.com/gap/ Most do not know that five octahedrons create the same gap; and that stacked, that gap is a beautiful thing to see: https://81018.com/15-2/ * My initial study of that gap is here: https://81018.com/geometries/
I have unsuccessfully searched for studies that explore the very nature of that gap. Have you studied it? Could it be associated with quantum fluctuations? Might there be a geometry for quantum fluctuations? Do you have any insights that could help us grasp these realities more profoundly? Thank you.
Most sincerely,
Bruce
*PS. Those are models we created and photographed. The face to face vertical alignment from tetrahedron-to-octahedron-to tetrahedron would necessarily create a horizontal alignment much like that pictured. -BEC
Third email: 27 July 2020 at 4:28 PM
Dear Prof. Dr. Maryna Viazovska:
With the world falling apart at the seams, your answers to mathematical questions about the very nature of life and the universe are more important now than ever.
I think that you have so enlivened mathematical discussions, I sent Oprah a recommendation that she interview you about the (1) scientific nature of infinity, (2) the first moment of physicality, and (3) the very nature of quantum fluctuations. Oprah is a talk show host in the USA.
Within so much of your work online, I am right now seeking answers to eight key questions to help Oprah and our readers to better understand your work. The URL for it is here: https://81018.com/conference/ and our specific page about your work is here: https://81018.com/2020/02/27/viazovska/
You are currently pictured on today’s top level page where there is a link to our overview page about your work. I started these kinds of pages a few years ago on my 70th birthday because I was getting a little forgetful.
Thank you.
Most sincerely,
Bruce
Second email: 8 May 2020 at 11 AM
RE: Given your most-foundational thinking about forms and functions…
Dear Prof. Dr. Maryna Viazovska:
Would you have a look at the latest version of my February 2020 article
that I referred to in my last email to you? Here are the links into FQXi:
Overview: https://fqxi.org/community/forum/topic/3428
Article: https://fqxi.org/data/essay-contest-files/Camber_3u.pdf
Do you think that it could have some merit?
Thank you.
Most sincerely,
Bruce
First email: 27 February 2020 at 11 AM
References: Sphere-packing problem
Dear Prof. Dr. Maryna Viazovska:
Congratulations on all your awards and recognition. Sensational.
You are not very far away from your earliest successes; I am hoping you might have some patience for a naive high school teacher and his students. We have been asking ourselves about a most simple progression from a tetrahedron and its octahedron going within by dividing our edges by 2 and connecting the new vertices.
We’ve asked, “How far within might we go?”
We assumed the Planck base units of length and time were good answers. It took 45 steps within to get into the range of CERN’s measurements and another 67 steps within to get into the Planck scale. https://81018.com/home/ is our back story. When we went in the other direction, multiplying the edges by 2, in 90 steps, we were out beyond the approximate size and age of the universe.
202 steps encapsulate the universe. What a crazy conclusion! It only got more crazy.
If those Planck base units manifest as the first moment of space and time, what would these units look like? We assumed the sphere — https://81018.com/perfection/ — and then sphere-stacking as the first functional operation within space-time.
Have you ever imagined your spheres as “primordial infinitesimals”?
I am writing about it here: https://81018.com/3u/ It’s a work-in-progress; perhaps you might have some advice? Thanks.
Sincerely,
Bruce
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