18 Major Scientific Statements not Usefully Expressed as Equations

Ernest Davis
January 8, 2024

1. The motions of the planets and the moon in the sky have regularities. (Ancient astronomy)
2. The ratio of the diagonal of a square to its side is not the ratio of two integers (Pythagoras).
3. Jupiter has its own moons (Galileo).
4. There are microscopic organisms, some of which are involved in the spread of disease. (Leeuwenhoek and precedessors)
5. Some fossils are the remains of long-extinct species. The earth long predates recorded history. (Nicholas Steno, Robert Hooke)
6. Heat is molecular motion. (Daniel Bernoulli)
7. Matter is made of atoms (Dalton and predecessors).
8. The quintic equation cannot be solved by combinations of arithmetic operators and radicals. (Abel-Ruffini).
9. Species evolve by natural selection. (Darwin).
10. There are meaningful non-Euclidean geometries (Bolyai/Lobachevsky)
11. The chemical properties of elements are a roughly periodic function of their atomic weights (Mendeleev).
12. Living beings are composed of cells.
    (Theodor Schwann, Matthias Schleiden, Rudolf Virchow, Robert Remak)
13. Large collections exhibit statistical regularities (Galton).
14. There are multiple infinite cardinalities (Cantor).
15. Continents drift. (Wegener)
16. There are subatomic particles. (Thomson)
17. There are unprovable true statements about the natural numbers. (Gödel)
18. Genetic information is largely carried via DNA (Alfred Hershey, Martha Chase)

Thanks to Pat Hayes for correcting the wording of Godel's theorem and the attribution of cell theory.

This is in response to Ian Stewart's popular list and book 17 Equations that Changed the World.. With all due respect to Stewart and the wonderful equations he discusses, it is important to keep in mind that there is a lot of science and even of math that does not consist in equations.