Mathsy people try very hard to like mathematics documentaries. They will frequently claim that they like them. But they don’t, really, not often, not much. For non-maths people it is much simpler: they don’t like maths documentaries and, if not so intimidated as to hold their tongues, they are generally happy to say so.

The sad reality is that most mathematics documentaries are bad. They are bad art, and they make for bad education.* This was brought to mind by a new Netflix documentary, *A Trip to Infinity*, and by a recent invitation. The invitation I’ll get to later. The documentary is bad.

*A Trip to Infinity* goes where about a hundred documentaries have gone before. It attempts to explain mathematical concepts of infinity with Hilbert’s Hotel and the other standards, and then goes on to consider the possibility of infinity in the physical world. Both the mathematical and the physical are done poorly, with too much “Wow!” and too little crafted explanation, and the two are inevitably muddied together. The many interviews are conducted in a casual, “just chatting” style, and are intercut at very short intervals. This is presumably done in an attempt to make the topic more human, but the result is simply confusing and frustrating. In instances where spare, careful wording is essential, the viewer is instead bombarded with clumsy and emotive language, cheap philosophy and lapses into jargon. The excellent Steven Strogatz comes across badly, the not excellent Eugenia Cheng comes across worse, and the many other mathematicians and physicists and philosophers even worse. Very little is said with sufficient depth or clarity to be of much interest.

*A Trip to Infinity* is also self-indulgent and way too cute, over-egged by about infinity eggs. The old-style cartoons and trippy animations and many other gimmicks are clearly intended to be playful, but are merely annoying and distracting. The music is intrusive, insistent on telling the viewer what they should feel. *A Trip to Infinity* works too hard on impressing and manipulating, and too little on explicating, thereby failing on all counts.

Not that it matters. That another bad mathematics documentary has appeared is not news. But it is also not reported. Mathematician Dan Rockmore reviewed *A Trip to Infinity *for the *New Yorker*. Rockmore tries hard to sell the film, writing of the “engaging experts” and the “moments of math magic”, but he is not convincing. It feels as if Rockmore is trying, and failing, to convince himself.

We maths guys want so much for others to like, to love, mathematics as we do. We want them to see mathematics through our eyes. They cannot. A mathematics novice, even if very keen, necessarily looks at mathematics differently. For a film to encourage any deeper understanding, it must be very good teaching or very good art. The standard badgering of the novice with “Wow!” is neither.

It can be done. The Eames’ famous *Powers of Ten* is very good art, as is the beautiful *Hotel Infinity*. The Open University’s *Hotel Hilbert* is very good art and very good teaching. These films, however are the exceptions.

A few months ago, Burkard was approached by a mathematics publication, inquiring if he was interested in contributing an article on the films of George Paul Csicsery. Csicsery has made a number of documentaries about mathematicians, beginning in 1993 with *N* *is a Number*, his well-known film about Paul Erdös. Csicsery’s most recently completed film, *Secrets of the Surface*, is about Maryam Mirzhakani, and he has more in the works.

As he usually does in such situations, Burkard asked if I was interested in collaborating on such an article. It was then a question of whether we thought we could write something sufficiently interesting to warrant the effort, and that immediately raised an amusing difference of approach: for Burkard, the question amounted to whether Csicsery’s documentaries were sufficiently good; for me, it was whether they were sufficiently bad. The final judgment was that the documentaries were clearly not good enough for Burkard, they were arguably bad enough for me, but not enough to convince Burkard. We decided against writing the article.

After Burkard flagged the project, I sat down to watch about ten of Csicsery’s documentaries.** They are infinitely better than *A Trip to Infinity*. Nonetheless, I didn’t much like them. I will briefly try to explain why.

First, I should indicate what is obviously good about Csicsery’s mathematician documentaries. Csicsery tends towards elegant simplicity, letting the mathematicians talk. Csicsery’s fundamental style is to be unobtrusive, to let the subject be themselves and tell their story. This works very well for films based around interviews with natural characters such as Erdös, and Paul Halmos and Yitang Zhang. It works less well when Csicsery must resort more to secondary interviews, as with his films on Mirzakhani and Julia Robinson; the secondary (for the purposes of the film) characters tend to be more self-conscious and awkward, overly concerned with selling the subject.

These films can be very interesting for mathematicians, or at least some mathematicians. We get to see some of the human side of some mathematics legends. We don’t get much else, however, and non-mathematicians won’t get much of anything.

To the extent that Csiscery’s films tell some stories of mathematicians’ lives, they work. But these stories are of limited interest unless the viewer is also told, or already knows, the underlying importance of the story. That requires also explaining some of the mathematics and/or how the mathematician thinks about this mathematics. In most of Csisery’s documentaries there is only a minor attempt at this, and so the documentaries can only be minimally successful. In recent films, Csicsery has resorted more to computer animations and popularisers in order to explain concepts, but this only detracts from his films: the explanations tend to be boringly redundant for mathematicians and standardly useless for non-mathematicians, and they dilute the human charm of Csicsery’s filming of mathematicians doing their thing.

It is not clear how, or if, a straight, expository mathematics documentary can succeed. Csicsery’s films are interesting and valuable attempts, are about as good it gets, but they do not really succeed. *A Trip to Infinity*, despite what some evangelising mathematicians might claim, is the much more typical, abject failure.

*) There is no simple dividing line, but I’m concerned here with stand alone documentaries intended for a general audience. Dedicated maths channels, such as Mathologer and Numberphile and 3Blue1Brown are also bad, and for broadly similar reasons, but they are a separate category. Mainstream movies are still a third category, and are also typically bad (but with some notable exceptions), although the source of the badness tends to be different.

**) The most interesting, *Hungry for Monsters*, has nothing to do with mathematics. It is a 2004 documentary on a child abuse witch hunt from the early 90s.

Would you be willing for me to share the criticism by marty with members of a mathematician education discussion group?

Sure. I imagine I’ll get whacked, but the whacking might be entertaining for others.

Have you seen the BBC Horizon documentary on Andrew Wiles and Fermat’s Last Theorem? I thought they did an amazing job.

Thanks, Nordin. Effectively, no. I think I may have watched it long ago, but my memory of it has melted into general memory. Rockmore also mentions and praises highly a Nova documentary on Wiles, which appears to be different. I will try to check them both out.

I’ve now watched it. I didn’t like it.

I recall an historian being asked “What do you prefer – historical dramas or documentaries?” The historian preferred historical dramas because they were not presented as something that sticks to the truth.

Thanks, Terry. Interesting. History is tricky, and I won’t offer an opinion, but interesting.

Documentaries are to my mind primarily works of art. They have some subject matter content for sure.

If they mess up either of these then the documentary doesn’t work.

I genuinely dislike most presentations of mathematical ideas. I feel like they often miss the point, or are misleading, or … .

Thanks, Glen. I could have been clearer about that point, and am still pondering this all. (I would have polished more for a proper publication, but one eventually tires when writing a lowly blog post.)

Of course any documentary has an artistic element. As you say, if they mess that up then the documentary cannot work well. But I’m wondering if a mathematics documentary can only work well as more abstract art, that it might be better to attempt Picasso, or at least Monet, rather than Rembrandt. Fundamentally, I think video is the wrong medium for mathematics exposition.

I feel as though there is a strong human physicality to learning mathematics. In a video this is clearly impossible, so to emulate it you can try to give your video interactive-type elements. Obviously in a documentary this is impossible. So, the conclusion here is that having actual mathematics teaching in a documentary is not going to work.

However I do not think it is all doom-and-gloom. Some things can be made to work well. I’m thinking primarily of visual stuff like proofs without words (like the AM-GM) and dimensionality stuff like flatland.

Talking heads in my view can’t be made to work well, unless they are talking heads only for the audio aspect and the main viewing is in some other graphic element.

I must confess, I’d be unable to make anything like what I’m describing, so perhaps I shouldn’t comment too much on it.

Can you explain why dedicated math youtube channels are bad? I know that numberphile is pretty bad from that 1+2+3… = -1/12 video, but I thought Mathologer and 3Blue1Brown weren’t that bad.

Thanks, Z. My footnote was too strong, but I think only a little. I think Mathologer is better than the other two (of course …), but I honestly don’t like any of them much. But that’s not really the point.

The problem I have with all these channels, even when the videos are accurate and polished, is that they trick novices into thinking they understand more than they do. If they encouraged people to go read, to fill in the details, that would be great. But I doubt very much that is happening more than epsilon, except maybe at the top end.

The consequence of these videos is that watching is replacing reading. That is very not good.

I enjoyed the movies “The imitation game”, “The man who knew infinity”, “Hidden figures”.

I didn’t.