Readings

Week 1. Hall of Fame Examples of Counting in Science and Math.

Amedeo Avogadro by Cyril N. Hinshelwood, Linus Pauling (1956) . These articles are based on addresses given by Cyril Hinshelwood, then based at Oxford University, and Linus Pauling, then based at Caltech, on the commemoration of the centenary of the death of Avogadro.
Photosynthesis by Eugene Rabinowitch, Govindjee (1969)
Atmospheric carbon dioxide variations at Mauna Loa Observatory, Hawaii by Charles D. Keeling, Robert B. Bacastow, Arnold E. Bainbridge, Carl A. Ekdahl Jr., Peter R. Guenther, Lee S. Waterman, John F. S. Chin (1976) . Figure 5 depicts the variation of atmospheric carbon dioxide from 1957 to 1972.
On the Equilibrium of Heterogeneous Substances, Part I by Josiah Willard Gibbs (1874) . Gibbs’ treatise on thermodynamics. Under the section “Criteria of Equilibrium and Stability”, Gibbs formulates thermodynamical equilibrium as a variational statement.
Translation of Ludwig Boltzmann’s Paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium” Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. by Kim Sharp, Franz Matschinsky (2015) . Translation of Boltzmann’s seminal works introducing a probabilistic basis of entropy.
Translation of Einstein’s Paper proposing the notion of the photon. by A. B. Aronst, M. B. Peppard (1964) .
Serengeti Shall Not Die by Bernhard Grzimek, Michael Grzimek (1973) .
The First 50 Million Prime Numbers by Don Zagier (1977) .
Thinking outside the 10-dimensional box by 3Blue1Brown (2017) .

Week 3. Counting by light.

Charles David Keeling and the Story of Atmospheric CO2 Measurements by Daniel C. Harris (2010) .
On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground by Svante Arrhenius (1896) .

Week 7. Counting Prime Numbers.

The First 50 Million Prime Numbers by Don Zagier (1977) .
Mathematics, A Very Short Introduction by Timothy Gowers (2018) .
Mathematical Education by William P. Thurston (1990) .
On Proof and Progress in Mathematics by William P. Thurston (1994) .
Geometry and the Imagination in Minneapolis by John H. Conway, Peter G. Doyle, Jane Gilman, William P. Thurston (1991) .
A Mathematician’s Lament by Paul Lockhart (2002) .
The Shape of Space by Jeffrey R. Weeks (2002) . In Exercise 2.2, Weeks introduces playing tick-tack-toe on a torus.
Prime Numbers and the Riemann Hypothesis by Barry Mazur, William Stein (2016) .
Euler, The Master of Us All by William Dunham (1999) .
The Euler Archive by originally compiled by Gustaf Eneström (1913) .
Variae observationes circa series infinitas by Leonhard Euler (1744) .
Leonhard Euler’s Integral, A Historical Profile of the Gamma Function, In Memoriam by Milton Abramowitz (1959) .

Week 8. The Riemann Hypothesis.

Are theoretical results ‘Results’? by Raymond E Goldstein (2018) .
On the Number of Prime Numbers less than a Given Quantity. by Bernhard Riemann (1859) . Translated by David R. Wilkins.
A Study of Bernhard Riemann’s 1859 Paper, Second Edition. by Terrence P. Murphy (2025) .