2/

In 2021, I remedied this by taking Philosophy 201, Plato and Aristotle, at SUNY Binghamton. At one point, I mistook the endpoint of one of our readings in an exceedingly tedious dialog of Plato's titled Parmenides and plowed on into what appeared to be an interesting bit about numbers. Plato seems to say that all the numbers (the positive integers) can be generated from 1, 2, and 3 by multiplication.

3/

As Aristotle pointed out, this process leaves out all of the prime numbers (as well as all of the composite numbers with factors other than 1, 2, or 3, beginning with 10, 14, and so on).

Scholars have puzzled over this ever since. Plato loved math, and it's difficult to imagine him making such an obvious mistake.

4/

After poking at this for a bit, I realized that in fact there is a way to generate all of the numbers (the positive integers) from just the first three without using multiplication. In fact, without even going so far as counting or using arithmetic as we understand it at all. It just depends on what you mean by "number." To the ancient Greeks, "number" meant what we would call a "set."

5/

So I wrote a little paper about my discovery. And then it occurred to me to try to get it published. A couple of early reviewers were encouraging, so I spent the next year (seriously slowed by the pandemic) doing the necessary search of the literature and putting the piece in proper scholarly form.