The Key Question

Why am I here? What do I want to find out?

I’ve been thinking about this post for weeks now not knowing how to approach it. One problem is that I’m no journalist. If I had been, I could just have asked the question, noted the answer and been done and gone. I’m not conducting interviews – though I at one stage played with the idea – and some Colleges asked if that was what I wanted to do. But that’s not my style – I can be systematic when that is an appropriate approach – but in general I mostly work in an intuitive, almost impressionistic way.

This means that I’ve had many highly interesting conversations these weeks and now there remains the work to sort it all out. Below, and in the next post, I will connect points of views with people I’ve been talking to, as truthful to my memory and understanding as I can. I do this at the risk of misrepresenting what you said – in that case let me know and I will correct or remove!

Let me first state the key question in three possible ways:

1. Vague and general:
I’m basically just curious about how mathematics is taught at Liberal Arts Colleges.

2. Jokingly:
I’m searching for the perfect mathematics class.

3. Seriously:
In what ways do the Liberal Arts context influence the way mathematics is taught as compared to other colleges?

This is how I phrased it in a talk today at Bryn Mawr College. The first version was my basic motivation for planning this trip. About the second version, I was asked (jokingly) if I had found it during my visits. I said no, and that I did not expect to find it as one single course, but rather as an amalgam of bits and pieces from many classes.

The first person I asked the third, serious version, was David Ellis at Beloit College. He said that Mathematics is a Liberal Arts subject.

That is a good answer even if it begs the questions a little. Mathematics is indeed the Liberal Arts subject. Just remember the old classification of the seven liberal arts.

Trivium: Grammar, Logic, Rhetorics

Logic has been a mathematical subject at least since Boole, certainly since Frege & Russel, perhaps even since Leibniz.

Grammar, widely interpreted not just as grammar of natural languages, also includes grammars of programming languages.

Quadrivium: Arithmetic, Geometry, Astronomy, Music

The first two has always been mathematics. The third was mathematics at the time but is now natural science. Music, at the time of Pythagoras was mathematics.

So, apart from rhetorics, all the original liberal arts were mathematical!

Let me stop here. I got many more answers, but I will collect them in the next post. Now I have at least posed the question and drawn the base line:

Mathematics was Liberal Arts – it still can be. Because, slowly a picture is developing – a subtle picture it is.

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