Monday, July 23, 2007

ESU5 Day 5

The first part of day 5 was a very interesting and engaging talk by Leo Corry on a bit more recent history of mathematics. He explored the connection between David Hilbert and the "new maths" in the US and "modern maths" in France. Hilbert has been portrayed as a proponent of "mathematics as a game" and axiomatics as the most important thing in mathematics. Leo Corry gave an important quote of Hilbert that suggests otherwise. I don't have the quote here, but the meaning was something like this: When mathematicians build their theories, they do not start by working for years on the foundations, before going on to build the theory on the foundations. Quite the contrary: mathematicians build beautiful spaces and corridors, and only when they start seeing signs that the foundations are not strong enough for further developments, they start to worry about them. Hilbert's opinion was never that axiomatics was the main thing in mathematics, but that axiomatics was important to put the beautiful theories already developed on a stronger foundation. Corry asked if this is maybe also what we should do in schools - develop (with our pupils) wonderful mathematics to let them see the beauty, and then only later worry about the details of the foundations. This is, of course, quite the contrary to the ideas of New Maths, which was so inspired by axiomatics.

The second thing I took part in today was my own workshop. It did turn out quite well, in my opinion - to the extent that the participants' activity is a measure of success. Most of the people there took part in the discussions, and some people told me that they appreciated a focus on primary and lower secondary pupils. What my workshop did was to look at some of the activities I do with my students, and to discuss whether they are meaningful. I added a subtitle to my talk: "If you can't do very much, can you still do something?", and I could actually also add: "If you don't KNOW very much, can you still do something?" After all, my knowledge of the history of mathematics is inferior to that of most people at this conference, but if I am to wait until I'm an expert before I start working on this with my students, they will never learn anything on history of mathematics. So my answer is clear: it is usually better to do something (and maybe make someone interested) than to wait until what you do is flawless...)

And of course, by presenting my stuff here, I've already removed some mistakes because of the comments of the participants...

Now, I've had a wonderful lunch, and will enjoy an afternoon of mathematics in the knowledge that I'm done with my presentation...

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