Maths phobia is older than you might think. A hundred years ago, German physicist Felix Auerbach, lamenting the phenomenon and hoping to find ways to address it, wrote a little book called . Maths, he said, has so much to contribute to society that addressing this fear is a challenge of the highest importance.
Auerbach was a fascinating character – a scientist but also a patron of the arts. Edvard Munch painted his portrait and Bauhaus School founder Walter Gropius designed his house. For a mathematician like myself, the pleasure of reading his book, now published in English for the first time, is accompanied by a sigh of regret that the topic is as relevant today as it was a century ago.
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Why do we fear mathematics? At heart, says Auerbach, it comes down to a fundamental misunderstanding of what maths is. The fear of messing up a calculation may be real, but the fact that there are many excellent mathematicians who are terrible at arithmetic proves that numeracy and mathematics aren’t the same thing.
We understand this about writing literature. The art of creating a compelling narrative in beautiful prose is different from the technical skill of getting the spelling and punctuation right. The same is true with maths. It isn’t mere calculation.
What, then, is mathematics? Auerbach says it is three things: a science, a language and an art. For me, part of the issue is that we are stuck in the first box. The incredible utility of maths in the sciences and engineering has meant that it is possible, though undesirable, to teach it only with this utility in mind. A focus exclusively on technical skills misses the joy and excitement that can come from finding patterns and understanding them, from seeing the true beauty of mathematics. That beauty lies in wonderfully elegant thinking that allows us to understand the infinite, explore the sublime symmetries of art and nature, and delight in the perfection of an abstract world of ideas.
As a language, what sets maths apart is the universality of its truths – you can become fluent wherever you are from. As Auerbach memorably puts it, you cannot do “German mathematics with a Japanese accent”. But it is the case for maths as an art that is closest to my heart. In researching my book Once Upon a Prime, about the beautiful connections between mathematics and literature, I have found many examples of mathematicians and poets praising each other’s disciplines. This is no surprise, as mathematics is, says Auerbach, “without exception, a poetic art”. If we can be shown the beauty of mathematics, we will forget to be afraid of the technical details underpinning it.
Today’s self-help gurus like to point out that, physiologically, we experience anxiety the same way we experience excitement. So, if your heart is racing and your palms are sweating before a big event, you simply have to tell yourself that you are excited. In the same way, fear can be negative (dread) or positive (awe). Our goal should be to try to move people along a continuum from a view of mathematics as a collection of calculations whose impenetrability engenders dread to an appreciation of a profoundly beautiful language whose complexity inspires awe.
A hundred years on, Auerbach’s writing is as pertinent as ever. It is a timely reminder that “maths anxiety”, as it is now called, remains as much a challenge in 21st century as it was in the 20th.
This is an edited extract from the foreword of The Fear of Mathematics and How to Overcome It by Felix Auerbach, published by Mathematical Society Archimedes, 2024
Sarah Hart is professor emerita of mathematics at Birkbeck, University of London
