By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social

Here are two groups of Western philosophers.

Group A: Plato, Epicurus, Plotinus, Aquinas, Duns Scotus, Francis Bacon, Hobbes, Locke, Spinoza, Newton, Leibniz, David Hume, Herbert Spencer, John Stuart Mill, Schopenhauer, Kant, Kierkegaard, Nietzsche, Wittgenstein, Jean-Paul Sartre, Kurt Gödel, Karl Popper, Jeremy Bentham, Alan Turing, Saul Kripke.

Group B: Aristotle, Socrates, Descartes, Bishop George Berkeley, Rousseau, Heidegger, Hegel, Marx, Frege, Bertrand Russell, John Dewey, Albert Camus, Frantz Fanon, John Rawls, Willard Quine.

What distinguishes these two groups?

I came across this intriguing teaser on Cambridge (UK) academic and journalist John Naughton’s March 23 Memex post.

Naughton got it from a March 17 blog post by the eclectic commentator Doug Muir.

Muir in turn was inspired by reflecting on an article about the deceased British philosopher Mary Midgely (died 2018), whose observation that a philosopher’s work is akin to that of a plumber demonstrates that she had a gift for communication.

Like Naughton, I was unable to solve the puzzle until I read on and was sucked into the above three-step regression.

[There is of course an issue of how to define the categories with precision and how you obtain your lists; Muir addresses that.]

The answer to the puzzle is that the philosophers in Group A never had children, whereas those in Group B did. Now you have to provide an explanation. Muir provides his. He also addresses the same question for physicists and music composers. The comments thread for his post presents a variety of suggestions.

I’ll let you chase that one down through the three links I gave.

Even as I was reflecting on the philosophers, however, I was asking myself about mathematicians. Doing so brought to mind an analogous observation I had made last Fall, after I co-taught a masters level history of mathematics course at Southern Denmark University in Odense, Denmark. (I did my part from my home office in California via Zoom).

I had neither given nor taken a history of mathematics course before. (In Denmark, future math teachers have to pass such a course in order to graduate with a teaching credential; a splendid idea in my view.) But my co-teacher had. So I was a student in the course as much as an instructor.

What struck me as I listened along with the rest of the class, as my co-teacher gave brief biographies of the usual list of mathematical greats, was how many came from broken homes (of one kind or another).

There is, to my mind, a highly plausible explanation for that, which I’ll leave as an exercise for the reader. (Someone has probably written a master's dissertation on it.)

In my case, my childhood home was not broken, but as was the case for many of us growing up in a working-class family in the UK in the early post-WWII era, it was decidedly lacking in kindness and emotional closeness. I threw myself into math as a way to escape the world I was living in.

When I went off to Kings College London in 1965 to major in mathematics, I met many students whose path to university had been similar. (Kings took the smart students who did not have the schooling that would propel them to Oxford or Cambridge.)

The fact is, life experiences can have a profound effect on our choice of career and how we pursue it, experiences that, on the face of it, have nothing to do with the work we choose to do and how we go about it. As instructors, we should be aware of the possible effects of the life-context that comes with every student we teach.

It was at Kings that I had an experience that completely changed my life and career as an academic mathematician; in particular, my approach to college-level mathematics teaching. But it was only when I was chasing down that philosophers and children puzzle that I became aware of that early influence. (That’s like a week ago!) In fact, it was more than “became aware”; it hit me like a thunderbolt.

What was that life-changing experience? I met a girl. Not any girl. (I was at a university; I met many girls.) This was the one who, at the end of my sophomore year, became my wife. But here’s the math part.

Not long after we met, she told me she was never good at math. (“If I had a nickel, etc.”) I told her the problem was not hers; she had not been taught properly. “It’s all just logical thinking,” I said, “formalized common sense.” If it is presented properly, anyone can learn it.

For the record, we were talking about how binary arithmetic works; I have no recollection how that topic came up, especially at that stage in our relationship – we’re talking days, not weeks. But here’s the rub. Despite several attempts to explain place-value and how you perform calculations, this well-educated, smart person (she was one year older than me – still is come to that), who wrote short stories, monologues, and poetry and was completing a dissertation on Percy Shelley, simply could not get it.

I was stunned. How could anyone not get it? (Many years later we had two daughters. One of them was a math ace, the other not only could not grasp mathematical reasoning, she had dyscalculia to boot.)

Given our intense interest in each other, we were both highly motivated to make as many connections as possible. But there I met a barrier -- a barrier regarding the subject that was the intellectual passion of my life. I really, really wanted to get her to see what I could, and she was just as motivated to do so. But it never happened.

The result was, when I started teaching university mathematics some years later, I realized that there were intelligent, motivated people who simply cannot grasp math. Period.

When I got my first regular teaching position in 1977 (until then I was wrapped up in research, with a series of postdoc positions in Europe and North America), I immediately asked to teach a section of the big “Elementary Mathematics” first-year course designed for poorly prepared students who needed to gain some required math credits. (The university mounted the course with a substantial government grant, and hired a former school math teacher, who had obtained a Ph.D. in mathematics education, to run it.)

My new colleagues were staggered. Why would a research “high flyer” churning out scholarly papers want to do that? Surely, I would prefer to teach upper level courses to classes with maybe 5 or 6 students?

True, I did like doing that, since most of those courses were in parts of mathematics I was not fully familiar with. I would be paid to learn more math! Plus the teaching was easy; just explain it to them and help them with the problems.

But that early experience with my soon-to-be wife had had a profound effect on me. I had an equal (if not greater) passion to try to teach and explain math to as many people as I could. My wife may have been an extremal case (she was, and is), but there were many more who, with some effort on the part of the instructor, could eventually “get it”. I wanted to help them do so.

And I have remained passionate my entire career about teaching non-majors courses and engaging in “mathematical outreach”.

I’m doing it right now.