Karl Schwarzschild: My letter to a legend


9 October 1873 – 11 May 1916, Ludwig Maximilian University of Munich PhD in 1896 extending the work of Henri Poincaré. From 1901 to 1909 as a professor, Göttingen ObservatoryUniversity of Göttingen, he came under the influence of David Hilbert and Hermann Minkowski. Wolfgang Pauli says that he was the first to introduce the correct Lagrangian formalism of the electromagnetic field. The focus of our work here ultimately is on the conceptual working relation with the Compton scattering.

In 1916, Einstein commented to Schwarzschild:

Albert Einstein to Michele Besso: Physics Today: Vol 58, No 7(opens in a new tab)

I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next Thursday I shall present the work to the Academy with a few words of explanation.— Albert Einstein (Eisenstaedt, “The Early Interpretation of the Schwarzschild Solution,” D. Howard, J. Stachel (eds), Einstein and the History of General Relativity: Einstein Studies, Vol. 1, pp. 213-234. Boston: Birkhauser, 1989]

  • Articles:
    1. Habison P. (2007) Schwarzschild, Karl. In: Hockey T. et al. (eds) The Biographical Encyclopedia of Astronomers. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30400-7_1247
    2. Straumann N. (2004) The Schwarzschild Solution and Classical Tests of General Relativity. In: General Relativity. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11827-6_4
    3. Einstein letter about Schwarzschild, 1917
    4. Stuart G. Clark, The Unknown Universe: A New Exploration of Time, Space, and Modern Cosmology, Pegasus Books, 2016 (References to Einstein’s letter about Schwarzschild)

A Note from Bruce: Permit me please dear readers to ask some hypothetical questions that perhaps you might answer for Karl Schwarzschild. In a rather less esoteric way, I asked scholar Chiara Marletto at Oxford’s Wolfson College (and their New Frontiers Quantum Hub) some of the same questions.

Letter to a legend: First email: January 9, 2022

RE: Your calculations, Arthur Holly Compton’s commensurate calculations

Dear Prof. Dr. Karl Schwarzschild:

Ever since Pythagoras we have had growing confidence that all things can be encapsulated by numbers, geometries, and equations. Eugene Paul Wigner carried on that tradition. He was barely 14 when you died, but he did study at Göttingen with a very old David Hilbert. Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. With your very special calculations, especially the one now called the Schwarzschild radius, how might you answer the following questions:

  • Do mathematics, logic, geometry and equations describe a real reality? I think you’d say, “Yes.”
  • Where should we start to build our universe? At this point I should like to introduce you to a very different look at the universe. I would ask that we work with the calculations that Max Planck did in 1899 (and George J. Stoney in 1874) of natural units of space, time, mass and charge and to think of quantization in rather new ways.
  • Might a rather whimsical, Lewis Carroll (Charles Lutwidge Dodgson) open a base-2 hole, with Zeno acting like our pied piper, take us from our desk at school all the way down to the Planck scale in just 112 steps? Might we then go out (by multiplying the edges by 2) to the edge of the universe in just 90 base-2 steps?

Now that hole was a tetrahedral face and our first step within was because we divided the edges by 2 and connected those new vertices. Multiplication by 2 is indeed somewhat magical. Having a scale of the universe from Planck Time and to the current time all on one chart (2016) is also magical. We initially started in 2011 with a relatively crude board based on Planck Length.

  • In what ways could those 202 notations be real? If the range of the quarks and other elementary particles is from Notations 65-to-67, what manifests between notation 1-and-64?
  • If we were to make the wild speculation that it is the domain of all the hypothetical particles, strings, automorphic forms and the Langlands programs, dark matter, and dark energy, would it further inform the Schwarzschild radius and the mathematics of relativity theory and black holes?

Now, I’ll be going through all the references to your work that I found above, but particularly I will be looking most closely at the two references within ArXiv. I’ll continue to update this letter, but in thinking of black holes and its deepest history, I’ll send another note to you. Thank you.

Most sincerely,



Stuart G. Clark, The Unknown Universe: A New Exploration of Time, Space, and Modern Cosmology, Pegasus Books, 2016

Direct quotes with this book: “By 1998, Hawking was ready to concede the bet” (with Kip Thorne) about the status of Cygnus-X-1. Kip thought it was a black hole. Also regarding Schwarzschild: “Einstein’s paper announcing general relativity to the world.”