Comment Marcus du Sautoy on… the importance of the history of maths “History can be a powerful ally in teaching difficult mathematical ideas for the first time” hen I learnt my mathematics at gence during the Renaissance. But I discovered how school it was taught in a very much exciting mathematics was being done in India ahistorical manner. The people, the long before Fibonacci (c1175–c1250) kickstarted the cultures, the politics were all mathematical revolution in Europe, and that there W missing. It was the ideas that were inklings of the calculus bubbling away in India counted. I learnt how negative numbers worked. in the 14th century, well before Newton and Leibniz What to do with a sine and a cosine. How to calculate articulated their theory. But these historical vignettes volumes of solids. I knew little of the history of these aren’t just interesting curiosities. ideas. Personally, the abstract ideas were enough to Witnessing the way teachers have used excerpts excite me, but the missing stories of where these ideas from the Story of Maths in the classroom, I’ve seen came from could have engaged so many more in the Marcus du how history can be a powerful ally in teaching wonders of mathematics. Sautoy is the difficult mathematical ideas to those encountering For example, sines and cosines were our best tools Simonyi them for the first time. A historical perspective for navigating the night sky centuries before Galileo Professor for has even helped me in my own journey to create ever had a telescope in his hands. The ancient Greeks the Public new mathematical knowledge – appreciating could use triangles and angles to tell the relative sizes Understanding how a completely new mathematics appeared of the earth, moon and sun without ever leaving the of Science, from the old has given me the tools to make my comfort of their observatories. I think that knowing professor of own breakthroughs. this history gives life to concepts that might other- mathematics at A historical narrative is actually hiding beneath the wise feel like they’re invented to torture students at the University of educational trajectory we take students on as they exam time. Oxford and the learn their mathematics. It’s not dissimilar to Or take the formula for the volume of a pyramid. author of What building those pyramids in Giza. Each year at school You could simply learn that it’s a third the area of the We Cannot Know we construct a new layer of the edifice on top of the base times the height. Or you could show students the (Fourth Estate, ideas we encountered before. And this is exactly how Egyptian papyrus where this formula first appears. 2017). mathematics evolved through history. What distin- The scribe was motivated by the very practical guishes mathematics from the rest of science is that challenge of wanting to know how many stones the the mathematics that was discovered 2,000 years ago architects would need to build the pyramids in Giza. is as true today as it was when the likes of Euclid The papyrus also contains the ideas of how to derive recorded the ideas in his Elements. The resilience of the formula by approximating a pyramid by mathematics to the effects of time is due to the power constructing a tower of rectangular boxes. of proof. Mathematical proof allows us to access Suddenly, with context, a dry equation comes alive. truth in a manner that is almost impossible in any I must admit that it was only when I started other subject. exploring ways to bring mathematics to the masses The other important role that history can play for through the books I have written and the TV my subject is to reveal that it is still a living, programmes that I have made that I myself breathing subject. For most students, became aware of where my subject came mathematics seems to live in some from. In 2008 I made a series for the BBC timeless, never-changing textbook that called The Story of Maths. It charted in has been handed down from generation four one-hour episodes the origins of to generation. With such a picture, it’s mathematics in ancient Egypt and no wonder that many don’t realise Babylon, through to the amazing break- that there are still so many chapters throughs of the last century that are the of the mathematical story still to be ingredients for the technological revolution written. But what gets me up in the we all enjoy today. morning to run to my desk are all It was while making that programme that the unsolved problems. It’s the I understood how Eurocentric our view of mathematical enigmas – those mathematics is. The story most people are fed is whose solutions will become the that mathematics began with the ancient stories of tomorrow – that are the Greeks and then went quiet until its resur- lifeblood of mathematics. OXFORD UNIVERSITY IMAGES/JOBY SESSIONS IMAGES/JOBY UNIVERSITY OXFORD 114 The Story of Science & Technology.