✅ Summary: Stephen Hawking did not publish on the following topics
1) Langlands programs and automorphic forms
There is no record of Hawking publishing on or writing about the Langlands program, automorphic forms, or related number-theoretic/mathematical frameworks in his research papers or books. His scientific work focused on general relativity, black holes, cosmology and quantum gravity—not advanced number theory or Langlands conjectures.
2) Geometric gaps of 7.356+ degrees beginning with Aristotle
This specific geometric concept does not appear in his scientific literature. Hawking’s research and writings do not explore historical geometry in that detailed way, nor reference Aristotle or later geometrical measurements tied to degrees or such gaps.
3) The role of π and irrational numbers (π, e, √2, φ)
While Hawking occasionally references the importance of mathematics in physics, there is no academic publication where he systematically studies irrational numbers or their properties as a central topic. His works mention mathematical constants to explain physics, but not mathematical foundations of these constants themselves.
4) From base-2 exponential notation to “18.5 tredecillion spheres per second”
Hawking’s scientific research does not cover speculative base-2 notation systems, numerological counts of spheres, or exponential notation in this context. His physics papers do not delve into large combinatorial models of numbers or spheres per second.
5) Planck Base Units, Stoney units, ISO numbers
Although Hawking’s work in cosmology and quantum gravity naturally involves Planck units (e.g., Planck length, Planck time) as physical constants, he did not publish new foundational theory about different base unit systems (e.g., Stoney units or ISO numbering systems). Discussion of Planck units appears in physics contexts, not as a foundational comparative study of unit systems.
6) E8 and Sophus Lie (Lie groups)
Hawking’s academic work includes general relativity and spacetime geometry, which uses mathematical tools like differential geometry. However, there are no papers or books by Hawking on exceptional Lie groups such as E8 or detailed work on Sophus Lie’s theories. These are outside his publication scope.
7) Functional analysis
Functional analysis (a branch of pure mathematics) is not a subject of Hawking’s scientific research or publications. His technical works in theoretical physics do not include functional analysis as a central research topic.
8) Perfection and the infinite
Philosophical themes such as “perfection” or metaphysical discussions of infinity may appear in popular science narratives, but Hawking does not have academic papers on metaphysical concepts of perfection or infinity in the philosophical or mathematical sense. His work deals with mathematical descriptions of the universe (e.g., cosmological singularities), not philosophical interpretation of infinity in an abstract sense.
📌 Published Areas of Hawking’s Actual Work
Stephen Hawking’s verifiable academic focus (from his list of scientific publications) includes:
- General relativity and cosmology
- Singularities and cosmological models
- Black hole physics (Hawking radiation, entropy)
- Quantum gravity and early universe theories
- Popular science books explaining physics to broad audiences
None of the eight topics above are found in his formal research articles or books as primary subjects.
🧠 Important Distinction
It’s possible for Hawking to mention mathematical ideas or constants in a conceptual context in books like A Brief History of Time or The Grand Design (e.g., references to Gödel’s theorem or the role of mathematics in physics) — but that is very different from him publishing research on those topics.
✔️ Conclusion for Your Homepage Draft
Based on known and documented publications by Stephen Hawking, he did not author scientific or academic commentary on any of the following:
- Langlands program
- Geometric gaps of ~7.356°
- Deep studies of π and irrational numbers independent of physics
- Base-2 exponential notation as applied to large number counts
- Comparative natural unit systems beyond standard Planck units
- E8 group theory or Sophus Lie extensions
- Functional analysis
- Philosophical notions of “perfection and the infinite”