Sunday, January 04, 2009

How Not to Communicate Mathematics

My colleague David Goss, who is the Editor-in-Chief of one of my favorite journals, the Journal of Number Theory, has started a new and unusual feature: video abstracts for accepted papers.

In a recent message to the NMBRTHRY mailing list, he suggests the following video as a "terrific example of what is possible with this technology". The video is of the renowned number theorist, Alain Connes, discussing his paper, Fun With F1.

Although I think the use of video abstracts is a clever idea that could be quite useful, I'm afraid I have to differ with David about this particular video. I think the video exhibits many of the problems inherent in trying to communicate advanced mathematics:

1. Assuming too much. What percentage of viewers will even know what A1, A2, B2, and G2 are? My guess is that, even among number theorists, only a small percentage will know what is being referred to here.

2. Not explaining enough. In the video, Prof. Connes talks about his paper, but never says explicitly what F1 actually is. (He says it is the field with characteristic 1, but of course there is no such field; we are meant to understand that it is not an actual field, but some sort of degenerate analogue of finite fields.)

3. Not giving any examples. It's often hard to grasp abstract mathematics without a simple example that one can manipulate.

Finally, it doesn't help that Prof. Connes has a very strong French accent that makes much of the video difficult to understand. (He also breaks into French in several sentences, seemingly without noticing.)

Alain Connes, a Fields medallist, is a much better mathematician than I am, but I don't think this video will be at all useful for the vast majority of mathematicians who view it.


isohedral said...

I would heartily support you in an attempt to create your own video abstract of a recent paper, whether for that journal or otherwise. More generally, this is something we'd like to do in the department as a form of public outreach.

Takis Konstantopoulos said...

This poses a more general question about the correct use if multimedia in mathematics and sciences more general. While people think that multimedia is the way to go, it is not easy at all to give a good presentation of your work if you have too many bells and whistles available. Take for example a mathematical talk created in power point with lots of colors, words that appear and disappear, formulas that move, etc. I maintain that you need to have abilities beyond mathematics to do it properly so as it is not offending to the (my) eyes and ears; otherwise, stick to chalk and board.

As for the video abstracts, I don't think that the example of Alain Connes is the worst one. I watched a few and had a hard time understanding what was being said. Look at this: Arithmetic of the Ramanujan-Gollnitz-Gordon continued fraction. First, the accent (very strong Korean) is hard to understand--harder than the French of Connes. Second, he says (I think he does--it's impossible to hear the words continued fraction): "Let nu of tau be the continued fraction defined as follows" and then he moves his hand over a formula. Now, I can hardly SEE what the formula is. The whole video suffers from similar problems. What is the point?

Jeffrey Shallit said...

Takis, I'm sure you're right that there are worse examples. I was only commenting on Connes' because it was picked out by the editor as a particularly good example of the genre.

Anonymous said...

The problem typified in the video is common in Physics too. At university we had wizards of the field teaching us - the only problem was that they skipped so many steps in their lectures that only the students in their tutorial classes could have a hope of understanding their lectures. For the lecturers it was as simple as A...Z - we were wondering what happened to B-to-Y!

This was exacerbated later by the UK government insisting that only research ratings be the judge of university excellence in the country. A lot of good teachers were shown the door...

Takis Konstantopoulos said...


There is a big difference though between university teaching (at, say, undergraduate level) and presenting an abstract of your paper. Presumably, the latter is for a technical specialized audience. So we don't expect the authors to explain every little detail. Despite this, we notice that the the video abstracts may be unintelligible even to specialists due to, say, poor articulation, but also poor exposition of what the paper is about. It requires some skill to explain your paper in 2-3 minutes.

Now, about your comment on UK education, I happen to be professor at a UK university. It is clear to me that many (not all, but very many) UK universities have reduced education to money-making business, especially by introducing programs at a vocational level. The issue is not the research ratings (RAE); this is not what hurts the system most. There are other, more major, problems which I cannot discuss here.

Anonymous said...

nice blue eyes O:

Anonymous said...

Thanks for the info Takis. The push to money-making was well under way when I was doing my PhD at Uni in the mid-90s. An interesting tale was told to me about a certain department at my Uni having a very generous electricity contract cancelled as they were using some of the electricity for commercial purposes...

On the RAE thing, point taken. I certainly seemed to be a larger problem in the eyes of the students in my Uni at the time.