Contributed by Sue Geller
Professor of Mathematics
Professor of Veterinary Integrative Biosciences
copyright 2016
It is a common myth that people in STEM fields do not write with the same needs as people in non-STEM fields. This arises from everyone's experience in math and science in their first 12 or 13 years of education during which all of math and most of science seems to be simply a set of equations to be solved. Even in the days of the dinosaurs when the teaching of geometry included proofs, these were taught using two columns, one for the symbols and one for a sentence fragment or simply a noun to give the reason. It didn't look like writing did in other subjects, so was relegated to not writing. But this is not true. First, an equation is a properly formed sentence with = the verb. After all we say ``equals'' when we read the = sign and equals is a verb. In fact, one reason many people have trouble with math is that they don't realize that they are writing sentences. Many people leave out the equals sign in their computations, leaving a series of nouns and making as much sense as ``Civil War President Lincoln Robert E. Lee.'' In fact, it is this lack of seeing an equation as a sentence which makes word problems so problematical for many people, something I find strange since every problem I've ever faced has been a word problem.
Enough about my pet peeve on mis-writing algebra. Writing in STEM fields is much like writing in non-STEM fields, namely, each article, essay, etc., is telling a story. In fact, one of my statistical colleagues puts it when teaching or working with non-statistician colleagues, ``What is the story you are trying to tell the reader?'' If the writer focuses on the message of the story starting in the introduction, the writing is easy, organized, and smooth. Without a coherent story, the article tends to be disjointed and confusing. Does this sound familiar for non-STEM writing? It should. The fact that STEM writing often contains charts, graphs, equations, and statistics, doesn't change the essence of good writing, telling the story clearly and interestingly.
What do we use? Actually, we use the same things as non-STEM fields: spelling, grammar, logic, connections between paragraphs, attention to the intended audience, ease of reading, catching the reader's attention, etc. It's the way we use them that seems foreign to newbies and to non-STEM people. To add to the confusion, there is a big difference in writing up experiments and in writing papers containing proofs. I think writing up experiments is actually easier because there is an accepted outline to be filled in: abstract, introduction, materials, methods, results, discussion, references. Yet within this seeming rigid format, there is tremendous room for creativity.
But what about theoretical topics? Yes, we tell a story too, starting in the introduction. It just seems incomprehensible to the non-specialist because, as my father said about my dissertation, ``I recognize all of the verbs, adjectives, and adverbs, but none of the nouns.'' One interesting part of writing with so many symbols is that we need to start each sentence with a word so as not to have the symbols run together. Since we are often writing a logical argument, our connectives include so, thus, therefore, hence, whence. I think mathematics is the only subject in which the word whence is not archaic. To give you an idea of what a mathematics proof looks like, I give you one attributed to Euclid many millennia ago, but in Geek instead of Greek. Recall that a prime is a positive integer bigger than one whose only divisors are one and itself,
e.g., 2, 3, 5, 7, 11. The proof is by contradiction,
i.e., assuming the what you want to want to be false and showing the assumption leads to a contradiction or false statement.
Theorem: There are an infinite number of primes.
Proof: Suppose there are a finite number of primes
. Let
By the Fundamental Theorem of Arithmetic, x can be factored into a product of primes. Since none of the listed primes divide 1, none of them can divide x. Thus, there has to be another prime, contradicting that there are a finite number of primes. Therefore, there are an infinite number of primes.
See, that didn't hurt a bit and even looks like the writing you are used to.