Having read a few of the science-based Very Short Introductions (VSIs), I have become more inclined to read those on subjects which I know little or nothing about, or where my knowledge is somewhat scatty. This volume falls squarely in the last of these. Having studied maths at university and read quite a few books *about* maths (for some reviews see here, here, here and here), I have picked up snippets here and there, but have never before read anything like a formal history.

Stedall opens with something of a case study: that of Fermat’s last theorem. To anyone who has a GCSE in maths, this is an understandable problem, even if the solution is still only understood by a handful of “elite” mathematicians in the world. It is through this problem that the author looks at various approaches one might take to mathematical history. At this point the unwary reader might start to get a little confused.

The reason for that is that Stedall takes her history seriously. Though the book is interspersed with the stories of some of the problems that have puzzled men and women for millennia, their friendships and rivalries, a history which is limited to dates and discoveries is one that would be superficial and misleading, as Stedall points out. An additional problem is highlighted, in that some of our sources are extremely sparse, with very little known about the likes of Pythagoras or Diophantus and even less about the development of the science outside Europe.

This begs the question: what is mathematics? It might sound like a stupid question, until you actually think about it. Much of what I did as part of my masters degree might well have been considered theoretical physics; and that was mostly studying scientific developments from the 18th up the 20th century. Most of this has been developed in western Europe. So what about the rest of history and the rest of the world? To answer that Stedall looks at a wider scope than many readers will be familiar with. Of particular note is the look at Arabic science, a topic I hope to follow up later this year with Jim Al-Khalili’s book, *Pathfinders*.

The next two chapters look at the spread of mathematical ideas. The first, from the perspective of the mathematician to the mathematician, the second, from the perspective of teacher to student. I must confess, I’d not really considered the dissemination of mathematical ideas from an historical perspective. The insight we get into an English Victorian education is something I probably ought to have known, but which was nonetheless a revelation to me. Less surprising, though sadly so, was the discussion on women’s mathematical education, which is a sad indictment on our education system until far too recently.

It’s only after all this that the reader who, like me, expected a more conventional story of some individual’s lives, get what they were expecting. Piecemeal, we have already had some insight but here we fill in some of the more obvious gaps, such as the lives of Euler and Lagrange. Though these are dealt with in a brief manner, that is kind of the point of this series of books.

Only towards the end do we actually see any maths. For some readers, this may come as a relief, for others, it may leave us wondering how good a history of ideas might be without the explicit statement of some of those ideas.

Stedall’s writing is perfect for the job. She is engaging, insightful and thought-provoking. As ever, we are provided with a great list for potential follow-up reading. I can’t say that I now have an encyclopaedic knowledge of the history of maths, but I have been able to glimpse some extra insights. Yet I don’t feel rushed to follow these up, but follow them up I may well do, but all in good time.