Tortoise Tuesday: Significant and Scientific — What science and mathematics can teach us about thesis

As a Writing Center Fellow, I believe that good writing is necessary in all fields. However, it can be easy to conceive of writing (as I’m sure most people do) as an inherently humanistic act or practice. Writing in STEM fields is only a necessary way of communicating ideas, not intrinsically part of the discipline.

However, as I read G.H. Hardy’s essay “A Mathematician’s Apology” and Karl Popper’s lecture “Science: Conjectures and Refutations” for ENG 401 Literature and Science, I discovered that both Hardy and Popper describe “good” mathematical and scientific ideas in ways strikingly similar to how we at the Writing Center describe good theses. The foundation of a good argument, it seems, is consistent across disciplines, and we can use the standards provided by Hardy and Popper to inform our writing as much as our scientific or mathematical research.

In “A Mathematician’s Apology,” Hardy discusses what makes a mathematical idea “significant.” Hardy writes: “We can say, roughly, that a mathematical idea is ‘significant’ if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas” (89). While we can quibble with exactly what Hardy finds significant or not in his essay, this basic definition of significant — “connected, in a natural and illuminating way, with a large complex of other mathematical ideas” — can be useful when thinking about a motivated thesis. Ask yourself: Does your thesis connect to a larger conversation of ideas? What exactly does it illuminate in that conversation? 

In “Science: Conjectures and Refutations,” Popper articulates what makes a theory or idea “scientific” (versus “pseudo-scientific”) and, like Hardy, describes a good thesis statement in the process. Popper summarzies his conclusions in one line: “the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability” (37). Here, Popper describes an essential element to a strong thesis: arguability. For a thesis to be good, someone must be able to argue against it; it cannot describe a factual state of being. Theses which rely heavily on plot summary or observable facts tend to veer into inarguable territory. Check yourself by asking: is there a counterargument to my thesis? If I had to write another paper disagreeing with myself, what might I say?

    Hardy’s definition of a “significant” mathematical idea and Popper’s conception of a “scientific” theory can be used to understand what makes a good thesis. These criteria relate to Keith Shaw’s four-step thesis test:

  1. Is the thesis arguable? Can a reasonable person argue against it? Popper uses this standard for determining whether a theory is scientific.
  2. Is the thesis manageable? Is it responsive to the evidence at hand and suitable for the size/length of the paper?
  3. Is the thesis interesting? Does it address a question/puzzle/contradiction and go beyond the obvious?
  4. Is the thesis important? How is the claim significant in the context of the field? Hardy uses the term “significant” to describe an important mathematical idea.

The questions we ask at the Writing Center about what makes a good thesis statement are the same questions mathematicians and scientists ask about what makes a good argument in their fields. Rather than simply a form of communication, argumentative writing is in the same category as scientific hypotheses and mathematical theories, another form of the effort to argue and prove a new way of thinking about the world.

— Paige Allen ’21


Hardy, G. H.. A Mathematician’s Apology, Cambridge University Press, 2012. ProQuest 

Ebook Central,

Popper, Karl R. “Science: Conjectures and Refutations.” Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge, 2002, pp. 33–41.