The Unreasonable Effectiveness of Mathematics review – why can’t maths be taught like this in school?
For a subject that lies behind nearly every advancement in modern living, mathematics is surprisingly absent from most of our lives. We know that it works behind the scenes, making computers tick, as well as predicting the real world in terms of economics, science, and even sport. Yet with this awareness comes a lack of respect. It’s a habit that has left us indifferent to the magnificent achievement of mathematics, which is too often treated as a dull but reliable tool.
The premise of Ian Stewart’s inspiring book is that we’ve fenced off mathematics, thinking it an abstract concept that only has a bearing in even more abstract industries. In 300 pages, Stewart presents an eclectic collection of mathematical ideas proving that maths is most certainly not dull. If, at times, it’s humbling to realise how little you know, that is multiplied many times as you realise the interconnectedness of it all.
Stewart begins with the business of elections and, specifically, “gerrymandering”. Much spoken-about in the US, this is the process whereby partisan control of state elections sees parties manipulate the electoral maps to give them more seats for their share of the vote. It’s a good starting point that exemplifies the pattern of the rest: Stewart takes something routinely dismissed as straightforward and shows why it is hugely, sometimes staggeringly, complex.
Even the notion of “fairness” turns out to be subjective and depends on which model you pick. Stewart explains all this in helpful terms, breaking down the maths into granular detail and employing valuable analogies. Often, the simple problem results in elegant solutions that are delightful to discover, such as the solution to how to ensure that two children divide a cake evenly: one cuts and then the other picks.
From there, Stewart launches into other simple yet surprisingly complex areas, such as the challenge of tracing the most effective path over a map, something that is highly relevant in the age of home deliveries, which also takes us into the area of computer image recognition and the extremely modish area of adversarial networks.
Then it’s onto kidney transplants, MRI scanners, fire-optic networks and the problems of data transmission, GPS, cryptography (along with cryptocurrencies), and a fantastic chapter on data compression (even for a self-professed geek and computer graduate who thought he understood the science). Just when you think you know where he’s going when he’s describing the way your phone reduces images to JPEGs, he moves on to the far less well-known use of “wavelet/scalar quantisation” by the FBI to store fingerprints.
Arguably, Stewart’s argument about the unreasonable effectiveness of maths is slightly undermined by the sheer reasonableness of his choice of subjects. It’s hard to believe in the “unreasonably effective” of mathematics when it leans so heavily upon technology and the hot work of silicon. A look at the role of maths in the humanities would have been welcome – language processing and language reconstruction, perhaps, but also textual analysis where so much work is being done.
Stewart goes some way to addressing this with a chapter about the role of numbers in the work of film special effects, but this is where the book probably comes closest to representing familiar information if the reader is in any way computer savvy. That, however, is to nit-pick. As Stewart acknowledges himself, there were dozens of areas he could have explored. Those he does pick offer the reader a glimpse into the deeper work of mathematicians. He even manages to make the problems of making springs entertaining. Yes. You read that correctly. Springs.
It’s another of the slightly understated beginnings that Stewart exploits to good effect. If it’s self-evident that good wire should make good springs and bad wire make bad springs, what’s less obvious is the problem that engineers have in spotting good and bad wire. Yet identifying the difference takes us into a light primer into chaos theory, fuzzy logic, but then into a much bigger lesson in the portability of mathematical solutions, or, as Stewart describes it, the “basic principle in mathematics […] that once you’ve found something that does the job, you work it to death”.
By the time you’re reading about how understanding the topology of a lobster’s eye might help unlock the secrets of “self-driving vehicles and machine interpretation of satellite images”, you’ll be ready to agree with Stewart’s statement that “mathematics is at its most useful in conjunction with everything else that humanity can bring to bear on the problems that it faces and the objectives it envisages”.
At times, Stewart makes a staggering jump from the simple to the complex, the micro to the macro, but it’s to his credit that he rarely strays so far (for too long) into the theories and formulas that might lose the non-mathematician. Certainly, it’s the kind of book that sometimes highlights gaps in the reader’s understanding (in other words, as a non-mathematician, there were moments when I felt like I needed a responsible adult to hold my hand) but never to the point where it becomes unreadable.
Rather, it warms up long-dormant muscles to the point where you should feel like exercising them again. It also makes one wonder why mathematics can’t be made this fascinating when we’re all taught in schools.
And that, ultimately, is the elephant in the room here. Unless you’ve taken a higher qualification in mathematics or work in a select number of fields, you are most likely to be returning to much of the material here for the first time in decades. That mathematical illiteracy shames a nation that can otherwise boast some of the best talents in terms of technology, coding, as well as innovation.
By writing such an engaging defence of his subject, Stewart has done mathematics a great service in ensuring that we begin to recognise mathematics as the rich and creative subject that it is, and not the low-level caricature that so many imagine.