Philip J. Davis (January 2, 1923 – March 14, 2018)

Philip J. Davis, once a Professor, Division of Applied Mathematics, Brown University, Providence, Rhode Island Also: Chief, Numerical Analysis Section, National Bureau of Standards (NBS) and National Institute for Standards & Technology Note: 1901–1988, NIST was named the National Bureau of Standards (NBS)
Standards Eastern Automatic Computer (SEAC)
NBS Electronic Computer Laboratory

ArXiv: Unity and Disunity in Mathematics, Bernhelm Booss-Bavnbek, Philip J. Davis, 2013
Books: The Mathematical Experience, Descartes’ Dream (with Reuben Hersh of the University of New Mexico), Interpolation and Approximation (1963), Numerical Integration (with Philip Rabinowitz, 1967), The Schwarz Function (1979) and Circulant Matrices (1979).
Homepage SIAM (PDF)

NOTE: Davis left the National Bureau of Standards (NBS) in 1963 to become a faculty member in the Division of Applied Mathematics at Brown University.

HOME: Phil Davis grew up in Lawrence, Massachusetts, the same town as Leonard Bernstein. Long ago, I had lived in the abutting town of Andover and its abutting town of Wilmington. Davis is my grandmother’s father family name, so we had some things about which to discuss besides the foundations of mathematics and physics. On my last visit, he had returned home. His wife had a serious relapse and died. Not long thereafter, Phil followed her. Phil hammered home that the sphere (2-vertices) was more fundamental than the tetrahedron (4-vertices).

Key email: Sun, Mar 15, 2015, 1:37 PM

RE: You’ll probably bristle with this statement…

“Pi is the first ratio, holding that circumference with the two vertices (within a point-free geometry) such that the simplest three-dimensional figure is created, the sphere, which becomes the building block of all things within the finite universe.”

I am working on it. But, without question, you are the one who opened this door. Do you want to see more as I attempt to unfold these thoughts?

Thanks again.


Email: March 11, 2014, 4:20 PM

RE: Rather late in life, I am picking up where I left off in 1965, i.e. on your path to learn as much as possible about the sphere, pi and transcendental numbers

Your comments about the simplicity of the sphere stuck with me. I began doing a little research. And, you know how “a little” can open dozens of paths. Now, I need to focus.

It is quite fascinating that pi has been such a mystery, all the way from the days of Archimedes, then I suppose Cavalieri, then John Wallis and his infinitesimals. I am working through David Richeson’s book, Euler’s Gem. There is so much to read and digest.

Notwithstanding, I write to thank you for opening the door on pi and the sphere.

With warmest regards,


Email: Jul 18, 2014, 1:39 PM

RE: You are one of the few people who might help to interpret this data.

Dear Prof. Dr. Philip J. Davis:

Back in December 2013 I got an email from a fellow who is part of an online discussion group about geometry. He had been doing some work with the Planck Length and he thought I would be interested to learn more about his work with constants and NIST values and measurements.

He sent me two primary references to his work:

Have you seen work like this in the past? Does it make any sense to you at all? What does it say about ratios?

Thanks, Bruce

Phil replied: “There are always people who wish to sum up or create the world using a few principles. But it turns out that the world is more complicated. At least that’s my opinion.” P.J.D.

The more I looked at it, the more I thought, “Ratios are what are primarily real. The subject and object are derivative. We need to grasp the essence of the relation!

Early email: Tuesday, May 8, 2012 at 4:48 PM

RE: In an earlier note to me, you challenged me with the notion that a sphere is more fundamental than the tetrahedron.

Dear Prof. Dr. Phillip J. Davis:

May I agree with you? The sphere it is! It must have something to do with the Planck length, the smallest possible radius?

Here are my simple calculations:
Here is my simple reflection about it all:

With the Planck length applied across the entire spectrum in about 202 notations, it opens up a number of interesting challenges for the mind.

I would be honored to hear from you.



 An early email: Sat, Mar 31, 2012, 9:58 PM

PJD – Have you worked with Frank-Kasper coordination polyhedra? -BEC

Also, see work by Jean-François Sadoc (ArXiv) and Rémy Mosseri (CNS)

My de facto homework assignment as a result of reading your work:

Define and grasp the following:
Lagrange Polynomial Interpolation
Newton’s Divided-Difference Formula
Hermite Polynomial Interpolation
Cubic spline interpolation
Bezier curves
Cubic B-splines
Orthogonal functions
Trigonometric functions
Chebyshev polynomials
Legendre polynomials
Laguerre polynomials
Gamma functions
Beta functions (Euler integral of the first kind)
Bessel functions ♥

“Thank you PJD for your years of encouragement.” -BEC