In Pursuit of the Unknown: 17 Equations That Changed the World

by Ian Stewart

The seventeen equations that form the basis for life as we know it. Most people are familiar with history's great Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives. Using seventeen of our most crucial equations -- including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time -- Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries. An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.

Genres: Science, Nonfiction, Mathematics, Physics, History, Popular Science, Stem

362 pages, Kindle Edition

First published January 1, 2012

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.

Reviews

[Ahmed Samir · Rating 2 out of 5]

So for a while now I’ve been wanting to read a popular math book and Ian is a well known mathematician. I must say I was quite disappointed.

The book has 17 chapters according to the 17 equations that are listed on the front. However, my only concern with this book is how poor the “popularization” was. Although the topics were very well written and extremely interesting, I still think he did a poor job in simplifying the math. As an engineer, most of the time, this was not an issue. But I can imagine that for a non-math/science major, this book would be quite problematic and quite unclear. Sometimes I had to repeat a chapter to understand fully what was going on. And that is usually not the case.

Also, towards the end of the book, chapters started losing that element of excitement that kept you going through the first chapters. The ending chapters felt like I was pushing myself to finish just for the sake of finishing.

Although I’ve gotten many ideas for my YouTube channel from the book, I wouldn’t recommend this book to anyone but a core popular education reader. Other than that, it’s just a dense read.

I would give it a 2.

[Brian Clegg · Rating 3 out of 5]

There's been a trend for a couple of years in popular science to produce 'n greatest ideas' type books, the written equivalent of those interminable '50 best musicals' or '100 favourite comedy moments' or whatever shows that certain TV companies churn out. Now it has come to popular maths in the form of Ian Stewart's 17 Equations that Changed the World.

Stewart is a prolific writer - according to the accompanying bumf he has authored more than 80 books, which is quite an oeuvre. That can't be bad. He is also a professional mathematician - a maths professor - and that potentially is a problem. The trouble is that, much more so than science, mathematicians are not ordinary people. They get excited about things that really don't get other people thrilled. And it takes an exceptional mathematician to be able to communicate that enthusiasm without boring the pants off you. It's notable that the most successful maths populariser ever, Martin Gardner, wasn't a mathematician.

So how does Ian Stewart do here? Middling well, I'd say. The equations he provides us with are wonderful, fundamental ones that even someone with an interest in science alone, who only sees maths as a means to an end, can see are fascinating. In most cases he throws in quite a lot of back story, historical context to get us interested. So the meat of the book is excellent. But all too often there comes a point in trying to explain the actual equation where he either loses the reader because he is simplifying something to the extent that the explanation isn't an explanation, or because it's hard to get excited about it, unless you are a mathematician.

The section on the Schrodinger equation, for example, is presented in such a way that it's almost impossible to understand what he's on about, throwing around terms like the Hamiltonian and eigenfunctions without ever giving enough information to follow the description of what is happening. (I also always get really irritated with knot theory, as the first thing mathematicians do is say 'Let's join the ends up.' No, that's not a knot any more, it's a twisted or tangled loop. A knot has to be in a piece of string (or rope, or whatever) with free ends.)

Inevitably, to give the book real world interest, many of the equations are from science, and Stewart proves, if anything, better at getting across the science than he is the maths (probably because it is easier to grasp the point). The only section I'd argue a little with is the one on entropy, where he repeatedly says that entropy always increases or stays the same, where it's more accurate to say that statistically it is very, very likely to do so. But there is always a small chance that purely randomly, say a mixture of gas molecules will partly unmix. (He also uses an unnecessarily complex argument to put down the creationist argument that uses entropy to argue for divine intervention, as it's easiest to explain that you aren't dealing with a closed system, something he doesn't cover.)

Overall, then, I am not sure who will benefit from this book. There's not enough detail to interest people studying maths or physics at university, but it becomes too obscure in a number of places for the general reader. A good attempt, but would have benefited from having a co-author who isn't a mathematician and who could say 'Sorry, Ian, I don't get that. Let's do it differently.' Bring back Simplicio. (One for the Galileo fans.)

Review originally published on www.popularscience.co.uk and reproduced with permission

[Bryan Higgs · Rating 5 out of 5]

I am a fan of Ian Stewart. I think he is one of the best writers about Mathematics and Science in general -- certainly one of the most approachable to a layman, albeit a layman with a scientific/mathematical bent. I own and have read a number of his books, and have enjoyed them all. You can find a number of my reviews of his books on Goodreads.

As the subtitle says, this book is about 17 equations that changed the world. As one who has a Ph.D. in Physics, I was familiar with all but one of these equations, but the author certainly broadens one's appreciation of the effects of these equations on the course of human history. The one I was unfamiliar with is the Black-Scholes Equation, about which more, later.

Each chapter begins with a summary page, showing the equation in question, with little lines pointing to the major elements of the equations, and labels identifying them. Then, on the same page, the author lists three items: 1) What does it tell us? 2) Why is that important? 3) What did it lead to?

This forms the basis for the rest of the chapter, and sets the tone. While the author talks a little about the mathematics behind the equation, he adds some history, some related anecdotes, and then a discussion of more details about why the equation is important, and how it has affected humans, sometimes over millenia. While I was familiar with almost all of the equations, I learned something new about each one, from the author's coverage. His writing style is light, and often amusing. He often refers to things in today's society that are relevant to the equation and its consequences.

I was particularly delighted with Stewart's discussion, in the introduction to the chapter on the Second Law of Thermodynamics (a topic that I always found challenging, even as a trained physicist), of C. P. Snow's "The Two Cultures"Two Cultures (http://sciencepolicy.colorado.edu/stu...), a lecture given in 1959 that has long rung true to my ears. Snow's premise was that, while society expects "educated" people to know, for example, the works of Shakespeare, and other literary and historical works, it is rare for those so-called educated people to know even basic science, least of all understand it. He used the Second Law of Thermodynamics as an example, as it is a very fundamental physical law that should be familiar to everyone. Snow bemoaned the low level of scientific education at the time, and it is my belief that the situation has only become worse -- so many people today ignore scientific results, often preferring political statements to those of science. The issue of climate change is the obvious example, but there are many more. Stewart's explanation of the Second Law of Thermodynamics and its ramifications were extremely lucid, and his discussion right on target.

The last chapter is entitled "The Midas formula: Black-Scholes Equation". This was the only equation I was unfamiliar with, and for a very good reason: it relates to Finance, and financial derivatives in particular. The author not only provides a very good explanation of the equation and how it has become the "sine qua non" of Wall Street and the big financial organizations, used to justify their reckless actions that caused the 2008-9 financial crisis and the resulting Great Recession, which is far from over as I write (despite all the glowing reports of economic growth). This chapter is a strong and authoritative indictment of what has happened in the Financial sector, and continues to happen, with no sign of any accountability ever being applied. If "regular" people read this chapter and fully understood it, they would (and should) become enraged over what has happened and continues to happen. Unless the financial sector is reined in, we are no doubt headed for more catastrophes in the future.

One further point about this book: I have felt for some time that there is a real need for students (from middle school, high school, and college) not only to learn mathematics, but to learn how it is useful and relevant in their lives. Too often, mathematics is taught in a rote manner; too many students are turned off by repetitive problems ("Solve the following 40 quadratic equations", and the like), and with too little understanding of the concepts and the true meaning of the many aspects of mathematics.

I would love this book to become required reading at, say, the upper high school and/or college level, as I think it could help with this necessary deeper understanding of the relevance of mathematics. Unfortunately, I doubt that most students would have the necessary sophistication to fully understand many of the concepts in this book. This is not to say that the book is written at a very deep level, but it would take a relatively sophisticated reader to get the best out of the book. However, perhaps someone could teach a mathematics course with this as a supplementary text, with the necessary "translation" being performed by the teacher. I suppose I am forever optimistic...

[Sean · Rating 5 out of 5]

Great book. Ian uses the equations as a launching pad to dive deeper into subjects that surround the equation. I greatly enjoyed his selection of equations. His last paragraph on each equation usually had some great personal commentary about society. I was a little disappointed in the discussion of Maxwell's Equations, as he tried to get a little technical, but then said a couple times that it would be too hard to explain correctly in this book. I'm a physics teacher, and I've seen very good, short explanations of Maxwell. But Ian finished the book on an equation that caught me off guard. The Midas Formula (Black-Scholes Equation) for investment modeling, was analyzed in how it led to the equation winning the Nobel Prize, to only then be greatly misused without full understanding, and thus leading to the banking debacle of the current century. Easy to just pick one of the 17 equations and read it. I read it cover to cover at the beach.

[Michael Huang · Rating 4 out of 5]

Written by a math professor, the book discusses 17 equations summarizing key intellectual achievements in science and math. These are not always recognizable as famous equations (e.g., Maxwell’s equations). Some of them are really just concepts. For example, the equation in the chapter on imaginary numbers is just i*i=-1.

In the book, you hear about background stories, simplifications, and anecdotes. In general, the discussion is not too technical but still better than most pop-sci books. Probably the most hardcore section is about a page (p 260) of discussion on Everett’s “many-world” interpretation. This interpretation addresses Schrodinger’s cat by claiming that the cat is indeed both alive and dead (already exaggerated). This is later even more grossly exaggerated as that there’s a world where Hitler won the war. Everett’s interpretation is legit. The later exaggeration is just that, exaggeration.

[Summer · Rating 3 out of 5]

Never have i understood so little. Too above my head

[Ashley Reid · Rating 3 out of 5]

There were parts of this book that made me want to rate this at least 4 stars, but there were also quite A few boring parts that made me want to skip over them completely.

Overall it was A very interesting book and one that I will probably still recommend to some of the more dedicated math/science students in my GenEd classes.

[Marnie]

A divulgación non ta divulganding. Parece un libro de texto e cada vez é máis complicado. Ao mellor volvo a el cando leve 20 anos lendo sobre matemáticas.

[Clelixedda · Rating 5 out of 5]

Was für ein schönes Buch! Ian Stewart stellt hier 17 mathematische Formeln, ihren jeweiligen historischen Hintergrund, das Teilgebiet der Mathematik, aus dem sie entstanden oder das sie begründeten, ihre (mathematische) Bedeutung und die naturwissenschaftlichen, technologischen, gesellschaftlichen oder politischen Implikationen vor. Das macht dieses Buch thematisch sehr umfangreich: man bekommt einen Einblick in Analysis, Topologie, Stochastik und mathematische Physik, während die gesellschaftlichen Implikationen von DNA-Entschlüsselung und digitaler Bildbearbeitung zum Klimawandel und der Finanzkrise von 2008 reichen. Dabei schafft Stewart es jedoch wunderbar, sowohl kleinere Details zu erklären, die für das Verständnis der Formel wichtig sind, als auch sie in das größere Bild einzubetten.

Die behandelte Mathematik ist absolut nicht einfach (manches in den ersten Kapiteln schon, aber es wird recht schnell happig). Ich würde es daher eher Leser*innen empfehlen, die zumindest sehr interessiert an Mathematik und verwandten Themen sind, da es sonst durchaus demotivierend sein könnte, die eher mathematischen Passagen im Buch nachzuvollziehen. Stewart erklärt zwar wunderschön, aber auch seine einleuchtenden Erklärungen setzen zum Verständnis Interesse voraus. Auch Mathematiker*innen (so wie ich es eine bin) können beim Lesen des Buches noch etwas lernen - mir waren ca drei Viertel der Formeln bekannt, aber ihr historischer Kontext und ihre gesellschaftlichen Implikationen nicht unbedingt. Und es ist so schön geschrieben, dass ich mir von Stewart gerne auch Dinge erklären lasse, die ich schon kenne.

[Jose Gaona · Rating 4 out of 5]

http://conclusionirrelevante.blogspot...

(...) 17 ecuaciones que cambiaron el mundo no es un libro fácil en la medida en que su público potencial seremos lectores sin formación matemática profunda. Algunas partes requieren una lectura atenta y disciplinada y otras requerirán echar una mirada a capítulos precedentes para refrescar las nociones, ya que muchas ecuaciones se construyen a partir de ideas y conceptos ya presentados a los que el autor no vuelve. No es un manual o un libro de texto, ni mucho menos, sino un libro divulgativo. Pero uno que atiza al lector y que le espolea a no dormirse ni conformarse. Una obra divulgativa que respeta al lector, en la que se logra un equilibrio bastante justo entre claridad, rigor y sencillez, y que presenta el fascinante mundo de la matemática pura y de la matemática aplicada en todo su esplendor, a través de muchas de sus posibilidades, pero también con muchas de sus sombras. No es el libro perfecto ni tampoco el más completo, pero es una lectura que elucida satisfactoriamente los puntos que presenta y que, trazando una línea a través de ellos, logra dibujar la silueta de la disciplina que, por pureza y claridad, quizá sea la más apasionante y seductora de todo el conocimiento humano.

[Drew · Rating 3 out of 5]

A mostly fun read, hence the 3 stars. It is a neat idea but I wish there had been some coherence to why these equations were chosen, over other ones or why it has to be 17 instead of the top 10 or the top 20? There was no overarching theme other than each one is important, nor did I feel was there any attempt to flow from equation to equation. It was like a collection of individual papers stapled together and sent out to the printers.

As for the complexity of this book, it definitely is not an entry-level or casual book. I'm glad, since I was hoping that it wouldn't be watered down. Some of the chapters were pretty basic, some were quite complicated, especially the quantum mathematical ones. The author made it somewhat accessible but at times, the descriptions needed more words to flesh it out.

Overall, I'm glad to have read it and it taught me some new things and reminded me of some things I learned in the past.

[Efimia Snitari · Rating 5 out of 5]

Mi ha appassionata dall'inizio alla fine. Nonostante a tratti sia stato un libro di non facile lettura, ogni capitolo ha offerto qualcosa di coinvolgente; i temi trattati variano dal mondo microscopico a quello macro, dal punto di vista della matematica e spiegando i fenomeni con la stessa.
Come dicevo, non è di facile lettura per chi non ha avuto a che fare, almeno minimamente, con equazioni e concetti matematici e fisici; alcune volte era necessario rileggere una volta in più per riuscire a cogliere le nozioni e i concetti proposti. Sono però lieta di essere arrivata fino in fondo a questa lettura.

[David · Rating 3 out of 5]

While I enjoyed the description of many of the key equations covered, I did not find them well laid out. Either too great an understanding was assumed or too little. My major concern with the book arose in the final equation chapter where the author covers the black scholes equation and blames the financial crisis on the use of derivatives in a blanket manner. The arguments suggest a lack of understanding of fundamental economic theory particularly with regard to the need for derivatives in providing optimal allocations in an economy. He confuses securitised asset structures with futures and options. He even suggests at one point that hedge fund managers might somehow "influence market conditions to make [mortgage] defaults more likely." The populist banker bashing this chapter represented made me seriously question the accuracy of the detail in the other chapters. I am afraid one must approach this book with deep skepticism.

[Liquidlasagna · Rating 4 out of 5]

one interesting thing from wikipedia

British mathematician Ian Stewart, author of the 2012 book entitled In Pursuit of the Unknown: 17 Equations That Changed the World, said that Black–Scholes had "underpinned massive economic growth" and the "international financial system was trading derivatives valued at one quadrillion dollars per year" by 2007.

He said that the Black–Scholes equation was the "mathematical justification for the trading"—and therefore—"one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation" that contributed to the financial crisis of 2007–08.

He clarified that "the equation itself wasn't the real problem", but its abuse in the financial industry.

[Stephen · Rating 2 out of 5]

An interesting idea, but I found the book to be so badly written that it didn't really hold my attention. Some of the equations are really important, and we ought to have a working knowledge of them, but this isn't the vehicle to impart that knowledge.

[Philippe Guglielmetti · Rating 4 out of 5]

Ce livre de Ian Stewart présente 17 équations célèbres, leur histoire, leur importance, leurs applications. Bien fait, intéressant, ce livre ne soignera cependant pas les allergiques aux maths.

http://www.drgoulu.com/2014/03/16/17-...

[Riju Ganguly]

NO review. Just that I can't manage to bring myself back to this book again without putting myself to sleep. Maybe later.

[Pongsak Sarapukdee · Rating 3 out of 5]

I used some of those equations in my work that made me enjoyed the story behind it.

[Nick · Rating 4 out of 5]

A neat idea this, to sum up the history of human attempts to explain the physical world in 17 equations. Ian Stewart takes us on a journey from Pythagoras to Einstein and beyond which I found at times fascinating, at times frustrating. GSCE Maths doesn't get you all that far when you are trying to comprehend calculus.

Yet Stewart appears to be writing for the general reader. He references C.P. Snow's much-quoted complaint that educated people felt (perhaps still feel) quite comfortable not being able to explain the concepts of mass, or acceleration - the scientific equivalent of being able to read - and indeed have little more understanding of these concepts than their Neolithic ancestors.

I think there is failure on both sides. I would very much like to understand science and maths better, which is one reason I read this book, but I appreciate that I haven't always given them the attention they deserve. And I should have concentrated harder in those Physics lessons.

Yet the scientific community could try harder too. This book is a perfect example. Here is Ian Stewart very worthily setting out to explain 17 equations, some of them pretty complicated, to the general reader. And mostly, he does a good job. Yet in some chapters, I was reading and rereading paragraphs and still not getting it. I was struck by just how hard it is for experts - even excellent communicators like Stewart - to bring their explanations down to the level of their audience.

I still enjoyed the book. Stewart adopts an interesting approach of explaining the circumstances around the discovery of each equation, zooming into the maths a little, zooming out to explain the wider relevance of the equation, and finishing by talking about its applications in the modern world. Some of these are quite unexpected. For example, I didn't realise Einstein's classic "E=mc2" was vital to the accuracy of GPS systems. I certainly hadn't appreciated the importance of Newton's development of calculus, which Stewart breezily points out led to "most of mathematical physics". (I had read a description of calculus in another book recently, and this time I think I almost got it.)

While most of these equations seems to have an eternal quality of being "always true", Stewart also shows how they have limitations. Sometimes this is because they only work in certain circumstances. Pythagoras, for example, works very well on a two-dimensional plane - not so well on a curved surface. Newtonian physics is ideal for most practical applications (including planning space missions) but Einstein showed that if you work to a high enough degree of accuracy, it doesn't actually get you the right answers.

Other chapters in the book include: logarithms (invented by a Scottish laird in the 17th century), imaginary numbers (the square root of minus one), normal distributions, Schrodinger's equation (and a good discussion of the famous cat), information theory (used to show how much data can be compressed and detect errors in data), and the Black-Scholes equation used for option pricing (which had a starring role in the 2008 financial crisis).

Perhaps it is unfair to expect the author to give a general reader more than a glimpse of the significance of some of these very complex ideas. Stewart, on the whole, does a good job, even if 17 Equations is better suited to those with some basic grounding in mathematical and scientific theory than to readers whose existing knowledge is more, shall we say, Neolithic.

[Sven Kronshage · Rating 5 out of 5]

Ich schreibe üblicherweise keine Rezension zu Büchern mehr, weil diese subjektiv sind und es zu viele Bücher gibt die lesenswert sind.

Hier habe ich mich hinreißen lassen.
Es gibt Bücher die ich wirklich ungern aus der Hand lege weil diese zu Ende sind.
Dies ist eines von denen.
Im Herzen bin ich ein Nerd.
Dieses Buch führt ein zu anfänglichen Regeln die uns allen bewusst sind.
Es erinnert Dinge, die mir z.B. gar nicht mehr klar waren.
Im weiteren Verlauf liest es sich, wie Fantasie bzw. Fiktion, all die Dinge, die beschreiben werden, sind. Es erinnert mich an Descartes, ich weiß das ich bin.
Die Dinge in unser Welt sind nicht klar.
Wir können froh sein, dass es neben uns Individuen, andere Individuen gibt, die uns diesen Glauben durch Bestätigung erhalten. Die Dinge der Wirklichkeit sind unklar. Es gibt viel mehr als was wir uns vorstellen können und darum ist Fantasie eine gute Quelle.
Tolles Buch das ich ungern aus der Hand lege.

[Drew L · Rating 5 out of 5]

A fantastic read regarding both mathematics and the history of math/science

Each chapter of the book details a specific equation and follows a similar narrative: the history that led to the equation, the (informal) derivation of the equation, and how it impacted the future of science

For example in the chapter for imaginary numbers (i*i=-1), the chapter begins with how negative square roots started appearing when solving quadratic/cubic equations, then mathematicians finally put this concept on firm mathematical ground, and how i led to revolutions in physics such as quantum mechanics

Very well written. Highly recommend for those interested in this history of math/science 👍

[Diego Arquieta · Rating 4 out of 5]

El libro nos lleva por un recorrido entre las 17 ecuaciones qué a su consideración cambiaron el mundo. Indudablemente son ecuaciones qué lo han hecho también desde mi perspectiva y es un buen resumen de los logros que la ciencia y el razonamiento nos ha logrado dar. Sin embargo en ciertos capítulos se adentra mucho en el aspecto "técnico y duro" y se puede volver un poco difícil de seguirle el ritmo.
Por ello le doy un 3.8 en realidad, redondeado a 4 estrellas.
Si lo recomiendo

[Devero · Rating 3 out of 5]

Un tomo abbastanza pesante e certamente intenso. Alcuni capitoli sono più discorsivi, altri più matematici. In alcuni passaggi ho avuto la chiara sensazione che la traduzione italiana fosse inadeguata, se non errata. Anche dopo tre o quattro lettura non era chiaro il senso.
Comunque è un testo che i ragazzi di quinta superiore dovrebbero leggere.

[Duncan McKinnon · Rating 5 out of 5]

Surprisingly engaging! Each chapter is a focused look at a specific equation, the circumstances of its discovery, and the wider ramifications of its existence. Since the book is broken up into these chunks it's very easy to read, and the concepts are made quite accessible while still being explained in great depth.

[Enrico Allegretta · Rating 3 out of 5]

"La trattazione completa è sempre troppo complicata per tutti, con l'eccezione degli esperti, che la conoscono così bene da non credere ciecamente alla maggior parte di essa"

[Hafiz Hussain · Rating 5 out of 5]

I did not understand much mathematical stuff but I enjoyed the whole book and still understand most of the theory and real-life examples.

[Johan Vik · Rating 4 out of 5]

This was my first peek into the world of mathematics. One could argue that it changed me.

[Lucia Bolivar · Rating 5 out of 5]

Awesome, so fun to read.

[Ogi Ogas · Rating 4 out of 5]

My ratings of books on Goodreads are solely a crude ranking of their utility to me, and not an evaluation of literary merit, entertainment value, social importance, humor, insightfulness, scientific accuracy, creative vigor, suspensefulness of plot, depth of characters, vitality of theme, excitement of climax, satisfaction of ending, or any other combination of dimensions of value which we are expected to boil down through some fabulous alchemy into a single digit.

[Bence · Rating 5 out of 5]

Very easy to understand for the general audience. Interesting, relevant material; a healthy mix of history of science and cutting-edge research.