Pluses and Minuses: How Math Solves Our Problems

by Stefan Buijsman

A guide to changing how you think about numbers and mathematics, from the prodigy changing the way the world thinks about math.

We all know math is important: we live in the age of big data, our lives are increasingly governed by algorithms, and we're constantly faced with a barrage of statistics about everything from politics to our health. But what might be less obvious is how math factors into your daily life, and what memorizing all of those formulae in school had to do with it. Math prodigy Stefan Buijsman is beginning to change that through his pioneering research into the way we learn math. Plusses and Minuses is based in the countless ways that math is engrained in our daily lives, and shows readers how math can actually be used to make problems easier to solve. Taking readers on a journey around the world to visit societies that have developed without the use of math, and back into history to learn how and why various disciples of mathematics were invented, Buijsman shows the vital importance of math, and how a better understanding of mathematics will give us a better understanding of the world as a whole.

Stefan Buijsman has become one of the most sought-after experts in math education after he completed his PhD at age 20. In Plusses and Minuses, he puts his research into practice to help anyone gain a better grasp of mathematics than they have ever had.

Genres: Nonfiction, Mathematics, Science, Philosophy, German Literature, Swedish Literature

209 pages, Paperback

First published October 1, 2018

Reviews

[Johanna Lemon · Rating 3 out of 5]

When I attended graduate school, I was required to take a statistics class. I was terrified, because I knew I did not like math and I was certain that math did not like me. I did, however, end up with an A+ in that class, because I spent hours pouring over my textbook, working out formulas, again and again and again, until something finally clicked.

This book was a little like that.

That is not to say that I had to read this book multiple times to understand the points the author was trying to make. I did, however, have to reread multiple paragraphs in multiple chapters, just to follow the mathematical lines he was laying down - especially in the chapters regarding mathematical philosophy, calculus, and statistics.

I had expected this book to contain more text and analyses on the social, political, and environmental ramifications that math creates in our daily lives. That is why I - an occasional reader of non-fiction - picked up this book. The author does speak to this, but his main goal, in the end, is for the reader to get a glimpse of the nuts and bolts of how these forms of math work, so that WE can then think more critically about the information presented to us in the larger world.

I’m sorry to say that I don’t feel as if I understand calculus or statistics any better, much less really see how organizations like Google are using them to enhance the quality of Google Maps. Graphs I understood a bit better, but it’s still murky.

I did, however, truly enjoy the anthropological aspects of this book - where the author discusses cultures that don’t use math. And reading about the history of math (as well as the academic spats it caused) was very interesting. I also really liked the tone of this book. You can definitely tell that the author is passionate about math. He wants to help you understand it. Does he succeed? He didn’t with me, but then again, that could just be me.

This book, in my opinion, comes in at 2.5 stars.

[M · Rating 4 out of 5]

I’ve been having fun reading books on math lately. The first was Zero: The Biography of a Dangerous Idea by Charles Seife. The second was Humble Pi: A Comedy of Math Errors by Matt Parker. Both made me wonder why I wasn’t a math teacher. So then I took an online algebra class during the pandemic and got my answer. Still, I liked reading about math, so when I saw Pluses and Minuses available as an ARC on NetGalley, I was pretty excited.

In the introduction it became clear what kind of math I was going to be reading about -- not the calculation drudgery (which I both love and loathe) but the kind that solves problems. And the first problem it mentions was this: “We can only learn how to combat fake news if we understand how internet services strengthen our opinions and why it’s not easy to change the way they do that.” This is the kind of thing I’m trying to communicate to my students when I’m telling them that math really, truly, sincerely IS important in every aspect of their daily lives, but it’s what I have the hardest time communicating because my pedagogical realm is so divorced from math. Then I was promised that the “ideas behind [statistics and calculus] are often unexpectedly simple and much more useful than you might suspect from what you learned at school”. I’m decently comfortable with statistics, but I’ve always wanted to actually understand what the heck calculus is for.

I didn’t expect to start with the how babies think about quantity and shape, but that’s where the book went pretty early on, and it was fascinating (and might even explain why I find geometry easier than algebra). That moved on to the history of the development of math (including some word problems from 1740 B.C. -- not much has changed!) A little historical tidbit I enjoyed: “The head of a temple [in ancient Egypt] was paid exactly thirty times more than the lowest laborer.” If only we had a cap like that on CEO salaries…

My main beef with the book is that sometimes it makes references to mathematical principles without any explanation of what that principle is. Here are a couple examples: 1.“Archimedes...discovered his famed principle of fluid dynamics.” I know I learned what that is, but off-hand, I can’t remember.
2. “Ratios are in fact fractions… but, instead of ⅔, they wrote them in a more complicated way.” I want to see that way!
A little parenthetical or footnote would erase the need to have Google at the ready while reading. It is entirely possible that footnotes and end notes were not available in the advanced reading copy (that happens), and if that is the case, then you won’t have to worry.

The discussion of pi was great. The author argues that “no one finds it strange if we talk about pi. We’ve become so used to numbers like this that they only seem peculiar when we think about them a little longer.” To that, I say, speak for yourself. Pi and other numbers that can’t be expressed completely have always given me a headache. It doesn’t matter if I’m just plugging it into a simple expression like A=πr2, I still end up spending at least ten minutes wondering things like, “If this calculator only uses a portion of pi in the calculation, then can we ever get a truly accurate answer to what the area of this circle is?” These meanderings are probably why I rarely ended up finishing my math homework. He writes about how 0.999… is actually equal to 1, and my brain explodes. At least he acknowledges that “[i]nfinity soon makes your head spin.” I have a lot of respect for people who can spend their days calculating to create actual, physical results (like getting a plane to fly or, his example in this chapter, making cruise control on a car work) while grappling with numbers and ideas that cannot be expressed. Sure, you can make a little symbol for it, but can you really imagine infinity?

This topic led to what I was most excited about going into this book: an explanation of calculus. I can’t now do calculus, and if you asked me to explain how and why it came to be, I would likely just quote from this book, but I feel satisfied that I have a much better understanding of what it is and how it works. I’m still stuck with the Greeks, though, in having “a problem with infinity” and thinking no one can calculate with that. Understanding calculus, to me, requires a leap of faith that my brain seriously struggles with. When I read the explanations for calculus, I get it momentarily, and then it fades away, and I have to remind myself why it works. I’m hoping to brush up my math sills and take an introductory calculus class soon (once schools meet in person again; I’m not sure I could handle it in a distance-learning situation). I even already purchased the calculator for it. Maybe with daily exposure, I’ll finally be able to hold on to my understanding for more than a fleeting moment. (A plus from this book that will serve me well: I learned what differentials and integrals are.) The author makes a good argument for understanding the ideas behind calculus even if we choose careers (as I have) that do not require that we use it. It’s not far from the reason I tell my students why they need to understand at least the very basics of science even if they won’t be pursuing science in the future -- it’s a matter of understanding how our world works, and if we don’t have a basic understanding, then we are much more likely to be fooled by lies and poor (or intentionally misleading) reasoning which affect who we vote for and what those people who decide the quality of our daily lives choose to do. They can easily choose to benefit themselves over us if we are not both skilled and informed.

We move on from calculus to statistics, a subject I am infinitely (I have infinity on the mind) more comfortable with. I’m no expert, but I enjoy the topic, especially the analysis of what people think data implies versus what data actually implies. It has taught me to be critical of any implications and assumptions I see extrapolated from statistics shared in the news, and that has proven very useful. I did appreciate that this section, but for two, used examples not beaten to death in other books on statistics.

Then we go on to graph theory, which, to be honest, is something I didn’t know was a theory. I thought graphs were just visual representations of data. Who knew? Not I, obviously. It turns out this is the theory behind what Google searches recommend, how to predict the effectiveness of certain cancer treatments, and how computers “learn”. (I had a bit of a War Games flashback during that last section.) This all, unfortunately, leads to abuses of the information gathered with this tool, and they are way scarier than what is possible with statistics (and the manipulation of statistics are scary enough!). I didn’t know I didn’t know about graph theory, and it ended up being my favorite part of the book.

I’d definitely recommend this one. It’s not exhaustive on any of the subjects, but it provides an explanation, examples, and the importance of different fields of math with some interesting history and an overview of the problems in each. I think it’s a good starting point for anyone interested in learning more, and I wish this were how math was introduced to me in school. If I knew why certain skills were useful, I would have spent a lot more effort trying to master them.

[Kerry Pickens · Rating 5 out of 5]

This is British book on applied math, which is how I think all math(s) should be taught.

[William Schram · Rating 2 out of 5]

What is the use of mathematics? It's a timeless question asked by many a schoolchild. What's the point of learning trigonometry or geometry if you aren't going to use it?

I think that Stefan Buijsman wrote Pluses and Minuses for a younger audience. He doesn't go in-depth with any subjects. He lists the uses of it, though.

The book is a series of stories brought forth by Buijsman. He discusses the Cholera outbreak in London that we fought with mathematics. He talks about what ancient cultures knew about mathematics and what happens when you don't use mathematics.

"Pluses and Minuses" is okay. There isn't much more to say about it. Thanks for reading my review, and see you next time.

[André · Rating 4 out of 5]

Ein sehr gut verständlicher Überblick, wie die Dinge, die ich im Matheunterricht nie so richtig verstanden habe, im Alltag wirken.

Einfach zu lesen und interessanter als es auf dem ersten Anschein klingt!

[Erin · Rating 2 out of 5]

Pluses and Minuses is a non-fiction book by Stefan Buijsman, themed about math and its uses in history and modern day life. The subheading of the book is, “How Maths Solves Our Problems”. Basically the book gives a variety of examples about how old cultures developed maths in their societies, for reasons such as trading. It also shows modern examples of how math is used in so much of life today. Some early examples in the book are the way map websites use mathematics in order to determine the best routes to take from one location to another. It also talks about the way streaming websites use algorithms to determine recommendations for users. The book was translated from Dutch to English by Andy Brown.

I think the main reason I chose to read this book is because I have an interest in math. I’m not good at it, admittedly, but I definitely want to learn more about it and to appreciate it more. Without mathematics, modern day society would not have a lot of things. And the aim of this book is to educate people a bit more about several types of math, how they came about and how they’re used around the world in the modern day.

My first real thought about the book is that it is often vague. The book mostly skims over topics, and I feel like it doesn't give enough information about any of them. It's one of those types of books that you might use to learn a very basic understanding of the topic. And, if you want to learn more, you will need to find other sources to research the topic in more depth. In that way, I do definitely appreciate the thoughts of the author. I like the way they gave varied examples. Such as talking about the way we use math as well as talking about a few other cultures who don't learn maths, but still have a little bit of use of it (even if they don't realise they're using it). But I would have appreciated if the author had spoken more of such cultures. Because, again, it's one of those things where the author sort of gives a basic understanding, but I feel there's more to it.

Another issue is that there are a variety of aspects throughout the book where there's an assumption that you already know a bit about topics. Such as references to famous people, like Plato. I feel like these Plato things could have been better explained. As someone who did not know the stories referenced, I had to look them up separately; in order to have a better understanding of what the author was actually talking about.

Overall, I think it’s a decent book. I wouldn’t necessarily think it well done, personally. But I appreciate that the author has made a good attempt at trying to educate people. There’s a decent amount of examples and imagery so that many people can indeed get a fair idea of what the author is talking about. Though, there are definite points where some of you may need to research further on the topic, if you’d like to try and understand it better. Because a lot of it is somewhat vague and basic.

[Víctor Cid · Rating 3 out of 5]

Stefan Buijisman es un filósofo matemático y con este libro pretende mostrarnos como las matemáticas nos rodean en nuestro día a día, ya que el mundo moderno está construido a golpe de números.
Todos los capítulos nos muestran la aplicación práctica de algunas ramas de la ciencia matemática, a situaciones cotidianas, como la teoría de grafos y las sugerencias de Netflix, los errores de la estadística en los sondeos electorales, o los supercomputadoras y el pronóstico meteorológico.
Algunas historias son realmente buenas como la de Newton, Leibniz y el cálculo diferencial. Otras sin embargo son un poco pesadas y alargadas absurdamente para llegar a las 200 páginas.
El libro en general está bien, pero noto mucho contraste entre unos capítulos y otros.

[Text Publishing]

The following reviews are shared by Text Publishing – publisher of Pluses and Minuses

‘From Netflix’s Numbers to the Maths of Manhattan, Buijsman’s book gets one big plus from me!’
Adam Spencer

[Maurizio Codogno · Rating 2 out of 5]

non capisco il punto dell'autore

La pubblicità italiana a questo libro descrive Buijsman come un enfant prodige, che a poco più di vent'anni è un filosofo della matematica. Tutto è possibile, ma di filosofia in questo libro (non ne troviamo poi molta: giusto un accento iniziale alla diatriba tra platonisti e formalisti, senza che ufficialmente l'autore prenda posizione. (Occhei, questo depone a favore del suo essere un filosofo: se non hai una tua posizione, non affiliarti a nessun'altra.) Per il resto, c'è un po' di storia della nascita della matematica, direi la parte più interessante del testo perché Buijsman mostra come non sia poi così necessario usare la matematica... a meno che non cominci a essere in gruppi molto grandi, e un po' di spiegazioni sul perché anche argomenti che appaiono astrusi come integrali e differenziali (io avrei usato derivate, ma cambia poco) o statistica siano comunque importanti, anche se a noi non capiterà mai di usarli nella vita di tutti i giorni. Secondo me il risultato finale non funziona nemmeno per il pubblico di non matematici, anche a causa della traduzione. Immagino non ci siano molti traduttori dall'olandese: ci sono però troppi punti dove Stefano Beretta sballa completamente il significato di una frase. Chi di matematica ne capisce può immaginare quale fosse il vero significato: ma probabilmente non leggerà il libro. Chi non ha una cultura matematica continuerà a non averla, e anzi si farà delle idee sbagliate...

[Alec Cohen · Rating 4 out of 5]

A short and to-the-point book that took me way too long to read, “Pluses and Minuses” dives into the the history, utility, and relevance of math in our daily lives. While not an essential aspect for a human society to function, it becomes essential when societies form in larger numbers. Otherwise, how would we track and distribute resources effectively on such a large scale. Buijsman also points out how nebulous the benefits of math can feel, despite its utility generally being praised and prioritized. The truth is that math is useful, but also abstract and removed from reality in many ways. It’s also curious how many brilliant mathematical discoveries were accidental. It’s doubtful that Newton envisioned calculus being used in modern cars or that early adopters of statistics foresaw our ability to collect and analyze massive amounts of data. Ultimately, the book concludes with encouraging readers to at least have an appreciation of the major branches of mathematics in order to live more conscientious and thoughtful lives. We may not use something like calculus in a daily basic, but we can appreciate how often we engage with it on our phones’ algorithms. Math has some incredible benefits, as well as limitations, and knowing both allows us to be more aware citizens of the world.

[David Cohen]

Stefan Buijsman got his PhD in the philosophy of mathematics at 20. Since then he has continued research on how we learn mathematics and has written three popular science books on mathematics and AI, one of which is available in over 20 countries. Stefan now works on the philosophy of AI at TU Delft, focusing on examinability and the information that different stakeholders need to responsibly develop and use AI systems.

Onto the book review: HIGHLY ACCESSIBLE. I wish I could be as concise and reachable in my description of the (extra)-ordinary as this book covering
* Cultures with no (need for) mathematics
* Human physiology of counting several, more than a few, and higher concepts
* Arithmetic operation applications
* How calculus just arrives at a point or an amount in time (the engine behind our engines) ; And,
* Statistics impacts our lives for efficient decision making and in explaining anomalies.
Not really 207 pages, due to references and a great index, but an easy read.

[Olivia · Rating 3 out of 5]

Dieses Buch legt dar, warum Mathematik für jeden von uns relevant ist und das auf eine verständliche und anschauliche Art und Weise. Schade, dass diese Hintergründe in der Schule meistens untergehen, ich bin sicher, dass es viele Schüler*innen motivieren würde.

Den Inhalt des Buches fand ich persönlich sehr spannend (zugegebenermaßen, ich als Maschinenbauerin befasse mich eh mehr mit Mathematik als der Durchschnittsmensch und habe auch nicht die Abneigung gegen sie, die viele empfinden). Leider war der Schreibstil des Autors nicht meins. Es wurden viele Erkenntnisse häufig wiederholt oder auf Beispiele immer wieder Bezug genommen. Für mein Empfinden, wäre das nicht nötig gewesen.

Alles in allem trotzdem ein lesenswertes Buch, dass für alle von uns relevant ist!

[Shaen · Rating 5 out of 5]

I enjoyed it. Finally got a grasp on what Calculus is. Generic overview of Math, from historical usage to current age. Especially enjoyed for the philosophical ideas regarding the relation of Statistics&Graphs to politics and privacy.
Privacy: Facebook, like weather forecasts, knows what you'll buy before you do.
Politics: understanding statistics so you won't be misled.
cultivating scepticism related to statistics, steming from basic understanding of math and how easily "science" can be used to manipulate ("how to lie with statistics" referenced)
The book has many more thoughts, some on politics, some on math.

[chris · Rating 3 out of 5]

"...why did people start using mathematics in the first place? In Mesopotamia, it was needed to organize city-states. Math made it easier to collect taxes, plan food supplies, and build houses. With so many people, it had become very difficult to do these things without it. But not all math was useful. Solving mathematical word problems with no practical value was a status symbol, to show others how clever you were. Even King Shu-Sin did them: his subjects weren't allowed to know everything, but he, of course, knew everything." (p. 66)

[Richard Thompson · Rating 1 out of 5]

I remember a few years ago one of my colleagues complained to me about having been forced to study algebra in high school. He said it was completely useless. I tried to be kind in the way that I pointed out to him that it was only useless because he didn't remember it so that he missed out opportunities for applying it and that I had used algebra in figuring out a spreadsheet formula that very morning. This is a math book for people like that guy, though I doubt that people like that guy will have enough interest to pick a book like this up to begin with.

Everything here is beyond simplistic. Anyone with the most basic mathematical knowledge knows all of this already. Maybe this book would be good for somebody, but I'm not sure who. In any case, it was not for me.

[Vovka · Rating 2 out of 5]

The hardcover version of this book may be good for throwing at mathphobic teens in answer to their whining “when am I ever going to use this in real life?”

But for anybody else paying attention to how the modern economy works, how technology is evolving, or how politicians and the media abuse statistics, it’s not a question we were asking or needed answering. The book is too basic for this audience.

[Inge Hulsker · Rating 3 out of 5]

Interessante info, waarom wiskunde belangrijk is. Nu en in het verleden tijdens het ontstaan van wiskunde.
Af en toe haakte ik een beetje af in de details. Tegelijkertijd had ik het gevoel dat er meer meegenomen had kunnen worden, in de breedte. Nu leek het op een paar gebieden toe te spitsen en daar vrij veel van te herhalen.

[Nani Lacrima · Rating 3 out of 5]

Grade zu Beginn hat das Buch viele spannende historisch mathematische Aspekte aufgegriffen. Die letzten 50 Seiten waren eher anstrengend zu lesen, da sie die Tiefe der Mathematik nicht mehr gerecht wurden. Es war anstrengend zu verstehen, ohne die Mathematik überhaupt zu beschreiben, das liegt also am Schreibstil.
Ein nettes Buch, dass aber kein Highlight darstellt 1/12

[Annarella · Rating 4 out of 5]

An informative and well written book about applied math.
I liked how clear the explanations are and the style of writing.
Highly recommended.
Many thanks to the publisher and Edelweiss for this ARC, all opinions are mine

[Norman Weiss · Rating 4 out of 5]

Das Buch unternimmt es, den Lesern zu erklären, warum Mathematik notwendig ist und wozu sie dient. Das gelingt nach meinem Eindruck gut. Zwar gelte:

Man kann sehr gut ohne Zahlen leben. (S. 49)

Aber möglich ist dies, wie der Autor darlegt, nur in kleineren, wenig komplexen Gesellschaften. Die Verwaltung von Städten und größeren gesellschaftlichen Verbänden läßt sich mit Mathematik einfacher bewältigen. Buijsman zeigt dies am Beispiel verschiedener Hochkulturen.

Mehr auf meinem Blog "Notizhefte": https://notizhefte.com/2020/09/06/esp...

[Max van IJsselmuiden · Rating 3 out of 5]

Pretty basic overview of how maths came to be, what theories have had a big influence on our daily lives. The book provides an overview of several math theories. I was hoping for more deep-dives into correlations or example scenarios.

[Bob Rubbens · Rating 2 out of 5]

Wiskunde in vogelvlucht, in beide historie en hedendaagse toepassing. Als je al het een en ander hebt gehad in vakken of hobby interesse is het technische gedeelte soms wat minder boeiend.

[Ingrid Krüs · Rating 3 out of 5]

Het idee is leuk, maar er valt nog wel wat te verbeteren aan zijn schrijfstijl en manier van uitleggen.

[Isabelle · Rating 2 out of 5]

Je m'attendais à plus interrogateur et complexe.

[Barrette Plett · Rating 2 out of 5]

It was okay. It felt a bit vague, and there were places where it felt clearly translated. I would have liked simpler, more concrete examples.

[Martin Ljungqvist · Rating 5 out of 5]

Superintressant bok om hur matematik används och vad den är bra för!

[Serdar Yalçın · Rating 3 out of 5]

Özetle matematiğin ne işe yaradığını anlatıyor, bunu çok derin bir şekilde yapmaması hem avantajı, hem de dezavantajı.

Rahatlıkla bir ortaokul, lise öğrencisine tavsiye edilebilir.

[Leo Elbourne · Rating 2 out of 5]

A randomly arranged bunch of chapters with randomly arranged paragraphs on random subjects that might vaguely be about maths.

[Olivia · Rating 3 out of 5]

Graph theory is something, that’s all I have to say

[Lilly Bradford · Rating 5 out of 5]

I 100% believe everyone should read this book. Incredibly well written and a great explanation of why and how math matters! Eye opening!