Top critical review
Reviewed in the United States on March 22, 2019
There is a lot to like about this book. It is engagingly written and teaches some basic aspects of calculus from a unified perspective, through a series of historical vignettes and practical examples. But this is a crowded field, with excellent similar works by authors like Ian Stewart, William Dunham and Isaac Asimov.
This book is distinguished by a useful organizing principle for explaining calculus, it consists of slicing things up into infinitesimal pieces and reassembling them into more tractable forms--all the while avoiding the dangers of what the Greeks called a "completed infinity."
My objection to this book published in 2019 is it's nearly identical to works I read as a kid published in the 1950s. The story of civilization runs from the Greeks to the northern Europeans and stops. There is a brief mention of one Hindu and one Moslem mathematician, but no rich stories to make the reader care about them, or see how mathematics played out in their cultural contexts. There are the same women mathematicians mentioned in my 50s books, but the focus seems more on their personal struggles to be taken seriously than on the depth of their thinking, or how their social conditions might have affected the problems they chose. There is one more woman, Katherine Johnson of Hidden Figures, but this fits awkwardly into the book and seems more like an attempt to add relevance by referencing a popular movie than a part of the story.
On one hand, there's plenty of material to fill a book this length without bringing in global perspectives or making sure there representation is proportionate to mathematical contribution rather than familiarity to math teachers a few generations back. Probably few modern students have closer genetic or cultural ties to, say, a 10th century Iraqi living in Cairo than to a 17th century Frenchman living in Amsterdam; nevertheless in my experience Moslem students are more engaged if Islamic scholars are included, Asian students are more engaged if Asian mathematicians are included and so on. And certainly women students are more engaged when the stories include women.
The examples also have a dated feel, although more to the 1990s than to the 1950s. Compressing fingerprint files for faster transmission over dial-up modems will not impress many young people today. And some of them are more likely to think about illegal government surveillance, or the revelation that the FBI examiners of that era were giving systematically fraudulent testimony, rather than celebrate with the author that the G-men will get the criminals faster. The mobile phone and AIDS examples are also very 1990s. They make calculus seem musty, like handheld calculators or cassette players.
So I'm of two minds about this book. If it had been published 60 years ago, I would say it's an excellent history, teaching some profound and useful mathematics in a pleasant way. It will still do those things, and there are plenty of other places to learn about non-European mathematics and up-to-date applications. On the other hand, I can't recommend this book unreservedly when there are more inclusive equally good books out there.