Hales, Thomas Callister

Thomas C. Hales

University of Pittsburgh
Pittsburgh, Pennsylvania

Articles: Computer related
________•  A formal proof of the Kepler conjecture (Jan. 2015) (PDF) (PDF-Princeton
ArXiv (27)The Kepler conjecture (Nov 1998) (PDF)
Dense Sphere Packings: A Blueprint for Formal Proofs (2012)Review
Blog: Jiggerwit  Sloppiness of NIST
Google Scholar
Homepage   Another

References to Thomas Hales work within this website:
https://81018.com/couplet/ (July 2020)
https://81018.com/duped/#Hales  (May 2020)

Most recent email: 8 April 2020

Reviewing some of your work, I noticed problems with my reference/resource page for you, so just updated it. Just so you have the last word, here is that reference: https://81018.com/hales/  (this page) Essentially because I am older now — part of the high risk pool — and my acuity is not so acute, I have had to resort to such postings just to remind me, keep me on track, and be polite. Any changes? Your requests will be quickly honored.

Again, I thank you for all your most brilliant work,


Third email: Aug 1, 2019, 1:18 PM

Dear Prof. Dr. Thomas Hales,

Because it was called idiosyncratic and it has not been encouraged,
and I did not want to be responsible for misleading our high school
students with crackpot concepts, I’ve pulled our base-2 exploration
out of the classroom. Some of our old web pages are still up
including https://bblu.org but I have continued on my own:

Not to taint your work in any way, because it is so important and
spheres, Kepler, conjectures, and cubic close packing of equal spheres,
is all so important, I continue to study your work and still encourage
people to visit your site: https://81018.com/transformation/#1b and
https://81018.com/transformation/#1f (with links to you).

I thought you might appreciate hearing from me after three years.
If not, I’ll hold back further notes!


Second email: Thursday, July 7, 2016, 10:53 AM

References: https://en.wikipedia.org/wiki/Kepler_conjecture

Dear Prof. Dr. Thomas C. Hales,

In 2011 we divided the edges of the tetrahedron, connected the new vertices to find the half-sized tetrahedrons in each of the four corners and the octahedron in the middle. We did the same with the octahedron and found the half-sized octahedrons in each of the six corners and the eight tetrahedrons, one in each face, all sharing the common center point.

We continued dividing by 2 and in forty steps we were down in range of the proton and fermion. In another 67 steps we were in the range of the Planck base units. To normalize the process we used the base-2 exponential notation from the Planck base units and went out to the Age of the Universe and the Observable Universe in just over 201 notations. Kees Boeke’s base-10 work is interesting; this simple model was fascinating.

Just high school people, we thought we had a great STEM tool. As we studied it, it became more. The first 67 notations challenged us to see this very small universe in new ways. In time, we began to think it could be a possible paradigm shift in the way we look at our universe. Our working model is here: https://81018.com/chart/

We have done a little work with your proof of Kepler’s conjecture.
The first reference is here: https://81018.com/number/#Kepler
Might you give us a little feedback? We would be most grateful.

Most sincerely,


First email: 17 January 2016 @ 9:56 PM

References: https://en.wikipedia.org/wiki/Kepler_conjecture
A proof of the Kepler conjecture – Annals of Mathematics

Dear Prof. Dr. Thomas Hales,

We are high school folks wrestling with issues that are way beyond our training. I need a really good mathematician to help with what we consider to be a possible paradigm shift in the way we look at our universe.

In my very rough-draft paper, working title, “On Building The Universe From Scratch,” I have made several references to your proof of Kepler’s conjecture. It is my second-most important number (after pi).

The first reference is here: https://81018.com/number/#3
“The Feigenbaum constants, Buckingham Pi theorem, the fine-structure constant, dimensionless quantities and physical constants were cited less often. We have added two numbers not cited at all: mathematician Thomas Hales‘ number from his proof of the Kepler Conjecture and what we call the Pentastar 7.38 degree gap.”
The primary reference is here: https://81018.com/number/#Kepler

I know you are a busy person with the highest credentials; I humbly ask if you could you take a look and give us a little feedback? We would be most grateful.

Most sincerely,