Comment j'ai détesté les maths (2013)
Directed by Olivier Peyon

Film Review

'How I used to hate maths!' is a sentiment that many who have been through the West's education system in the past forty or so years will doubtless readily share.  Olivier Peyon's documentary Comment j'ai détesté les maths begins with a depressing vox populi of maths-hating teenagers that makes the experience of having had to endure mathematics at school appear to rank a close second to the Nazi Holocaust in the league of inhuman atrocities.  The fault lies not with the subject but with the way in which it has been traditionally taught - this much is made apparent in the first (and most illuminating) part of the documentary, which contains many wise and thoughtful contributions from educationalists and academics, including the maths historian Jean Dhombres.

The underlying thrust of this disjointed but intensely likeable documentary is that mathematics is something that should inspire wonder and excitement, not fear and loathing.  If only it were taught in a more imaginative way, by teachers who were genuinely enthused with the discipline and not constantly burdened with the chore of continual assessment, children would grow to love mathematics as much as sport and other creative activities.  A better approach to teaching mathematics is what the film militates for - not the kind of faddish tinkering about that has alienated teachers and pupils alike for the past four decades, but something far more radical.

Instead of merely programming schoolchildren to pass exams, we should be training them to think for themselves, helping them discover what is great about mathematics - not just its practical use in solving real problems, but its inherent power, as a universal language that allows us to make so much sense of our world.  Peyon's film is highly pertinent - mathematics is now recognised as a crucial driver in future economic growth, and yet, in spite of this, the developed West continues to fall behind the developing East in school attainment levels in mathematics.  By teaching out children to hate maths, we are destroying their future prospects.

The case for why maths matters is eloquently made by such colourful characters as Cédric Villani and François Sauvageot, who become the stars of the film - as much by their visual impact as their obvious enthusiasm.  Looking scarily like Albert Einstein reincarnated as Jean-Pierre Léaud, Villani is one of France's leading mathematicians, yet when he attends a conference in India to receive the Fields Medal (the equivalent of the Nobel Prize in mathematics) he has the distrait air of a freshman who isn't quite sure he is at the right university.  Even though most of what Villani says is inelegantly draped in cliché (a case of a great intellect struggling to communicate in layman's language), the way in which he expresses his love of mathematics makes him an adorable mascot for the subject.

And the same goes for François Sauvageot, another screen-filling eccentric whose tee-shirt (embossed with the slogan 'I am not a number, I am a free man') fits with his highly individualistic approach to teaching maths.  Judging from the level of involvement he manages to get from his class of lively teenagers as he uses graphic design to get across some hard geometrical concepts, Sauvageot looks as if he has the makings of a great reformer - the kind that our education system desperately needs to make mathematics attractive to school kids.

Contributions from other (less flamboyant but equally passionate) educationalists make the same point.  For maths to be taught effectively, it must be founded in everyday experience, not served up as some abstract alien concept that is as irrelevant today as Latin or some other dead language.  Images of children not only engaging with maths but actually enjoying it, deriving pleasure from solving problems through structured, logical reasoning, must surely put paid to the myth that the subject is inherently dull and uninvolving.

Committed educationalists and pure mathematicians go some way to making the case for why mathematics is so important, but the point is only really made when the so-called applied mathematicians come on the scene and start talking the kind of language that most people understand.  With a passion that occasionally comes across as fanaticism, they convince us that what makes maths so important is its value in solving a huge variety of complex problems of immense practical importance - such as the laying of underwater cables or developing algorithms for internet search engines.  And where would stock markets be without ultra-sophisticated mathematics?  Where indeed...

This leads us neatly into the film's cautionary final section, which shows up the risks facing a society that allows itself to become dependent on increasingly complicated forms of mathematics.  Maths offers spectacular opportunities for those who apply it wisely, but it also brings the possibility of even greater failure if someone gets his or her sums wrong.  As he proudly reveals, the trader Jim Simons made his fortune (which currently stands at over 15 billion dollars) by applying his mathematical skills to the buying and selling of shares, revolutionising an industry that had previously been conducted along the lines of an exclusive gentlemen's club.  Today, banking is so dependent on advanced mathematics that it could not continue without it.  It is this numerical wizardry that keeps the world's economy ticking over, ensuring an acceptable level of growth in the pension funds and personal fortunes of big and small investors alike.  To put it crudely, without maths we'd all be broke.

But what if the mathematics becomes so complex, so abstruse, so impenetrable that no one - not even the bow-tie wearing boffins that programmed it into their computers - has an adequate understanding of the implications of using it?   We've already had one taste of what can go wrong when the skyhigh IQ eggheads try to be too smart - in the financial crisis of 2008, which originated from the buying and selling of dodgy financial instruments that parcelled up risky investments in such a convoluted way that it was impossible to adequately assess their overall level of risk.

When the crash came, the smart Alec mathematicians who had dreamed up all these weird and wonderful products became an easy scapegoat - but the actual fault was elsewhere, with those fund managers who, desperate for increased yields, seized on these exotic money-spinners without any willingness to understand the associated risks.  In the last part of his film, Peyon deals pretty superficially with the 2008 crash and the lessons to be drawn from it, although he does effectively make the point that whilst clever maths does bring great opportunities, it also comes with immense risks, and that understanding and quantifying these risks is essential if we are to avoid further calamities.

As if the prospect of a mathematically contrived Apocalypse wasn't bad enough, Comment j'ai détesté les maths raises the spectre of an even more worrying scenario - namely that there will soon come a time when human beings will stop doing mathematics altogether.  (If that prospect makes you cheer then you really do need to watch this documentary.) Such has been the progress in computer technology, one young mathematician confidently asseverates, that it seems likely that computers will one day completely take over the job of doing all mathematics.  All that will be left for humans to do will be the mundane task of setting the computer the task of the problem to be solved.  No need to master differential calculus and learn about Laplace transforms or Bessel functions.  All of that will be taken care of by the thin sliver of microscopic circuitry built it into your coin-sized iPhone.  Just ask your question, and the computer will output the answer.  When this day comes, no one will hate maths because maths will have ceased to be!

Thankfully, there are others in the film who put the counter-argument, that mathematics is such a thing of inherent beauty that human beings will always be drawn to it, as they are to music and other forms of art.  Of course, mathematics matters because our technology and industries depend upon it, but shouldn't we also love it for its unique aesthetic qualities, which seem to be so intimately bound up with human creativity?  We don't need to see Helaman Ferguson's marble statue of The Eight Fold Way to visualise the beauty of mathematics.  The contributors to Olivier Peyon's thought-provoking documentary all convey a sense of wonder for their subject, and this adds up to something far more tangible.  And here's the upshot: if you hate maths, then you simply do not know what maths is.

Film Synopsis

So you've always hated maths?  You're not alone - it is a subject that has brought misery to countless schoolchildren and left irreparable scars.  All that mucking about with fractions and long division and algebra and calculus and stuff with logarithms - what is the point of it?  No one ever uses it in their day-to-day  lives.  It's just pi in the sky.  Au contraire!  Our way of life, indeed our entire civilisation, depends on mathematics to a degree that you can hardly imagine.  Without maths, there would be no internet search engines, no mobile phones, no iPads, no Sat-Navs, in fact none of the technological innovations we have come to take for granted over the last thirty years.  Maths has become crucial not only to science and technology but also to commerce.  There is not a single business on the planet that is not reliant on mathematics to a greater or lesser extent.  Why is it then, given it is so important, that mathematics is still inflicted on children more as a form of Medieval torture rather than a pathway to enlightenment?  And does it matter if humans give up maths altogether - surely computers can be relied upon to do the job for us?  Just what kind of civilisation are we creating that is becoming so intrinsically bound up in complex mathematical formulae which no one really understands?  Are we right to loath maths - or should we learn to love it?