On learning about the work of Stephen Smale

Steve Smale, University of California, Berkeley, Berkeley, California

Articles. Wolf Prize, Fields Medal, Breaking the Dimension Barrier
ArXiv: The Emergence of Function, 2016
Books: The mathematics of time, Springer-Verlag, New York-Berlin, 1980. ISBN 0-387-90519-7
Google Scholar
Homepages: Berkeley, 90th birthday celebration (Recording-Zoom, July 15, 2021),
• City University of Hong Kong
YouTube: On the Mathematical Foundations for the New Sciences

Within this website: https://81018.com/gravity/#Footnotes Also see: John Willard Milnor

First email: 23 April 2022 at 7:00 PM

Dear Prof. Dr. Steve Smale:

I have been working within the Planck scale since December 2011. We started with the tetrahedron in our classroom, divided the edges by 2 and connected the new vertices. We discovered the four tetrahedrons in each corner and the octahedron in the middle. Following the spirit of Zeno, we went down inside 45 steps to find ourselves in the range of fermions. In another 67 steps we were within Max Planck’s scale. 

We then decided to start with Planck’s length. We multiplied by 2 and in 112 steps we were back in the classroom, and in another 90 we were out to the approximate size and age of the universe. It was great fun for high school people and our classes of new geometers to discover base-2 and the 202 notations

What a steep learning curve, and then to discover we were idiosyncratic and out of step with academia! How could mathematics be so capricious? We had so much to learn! This homepage and letters to David Kaiser and Karen Uhlenbeck in part summarize our dilemma.

But then today, I discovered your work!
It certainly took me long enough!

I was starting a study of Attractors and you are the first contemporary person cited. So, to say the least, I have started following your work. Yes, you’ve become a new mentor! https://81018.com/smale/ will be where I document what I am learning from you. In our cave, I am hoping that you are that little gold vein that widens into what some might call the mother lode. 

I thought you’d smile to learn that you have a new groupie who happens to be 74 years old!

Best wishes,



Research: 5-manifold, Axiom A, Geometric mechanics, Homotopy principle, Mean value problem
Also: Cycle detection, Hyperbolic set, Stable manifold, Wada basin, Hidden oscillation, Rössler attractor, Stable distribution, David Ruelle, John Willard Milnor 

•  John Willard Milnor (1985). “On the concept of attractor”. Communications in Mathematical Physics99 (2): 177–195. doi:10.1007/BF01212280S2CID 120688149.

•  John Willard Milnor is one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize (the others being SerreThompsonDeligne, and Margulis.)

•  Bell’s Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity, T.N. Palmer, arXiv:2108.10902, August 2021

•  What can Koopmanism do for attractors in dynamical systems?, Viktoria Kühner, ArXiv, March 2019

Every hypothetical particle holds clues. Every formula within Langlands programs and string-and-M theory hold clues. They all have to work together and be part of a continuum.