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The Secret Life of Equations: The 50 Greatest Equations and How They Work
Albert Einstein's general theory of relativity (E=mc2), is a central theory in modern physics with implications on our insight into everything from black holes to the expansion of the universe. But how did Einstein come up with it? And what has happened to it since then?
The Secret Life of Equations is not a mathematics book but a map by which readers can discover equations from a different perspective. Selected from geometry, technology, science, chance and mathematics, the 50 equations are explored by way of their history. Why were they needed? How were they developed? What is their value today?
The equations are presented as follows:
Concise, understandable text highlighted with clever illustrations. Visual and textual descriptions of the equations' components, for ultimate clarity. "What's It About" fictional scenarios to explain the original problems or theories in want of a solution or proof. "What's It Good For?" descriptions tell how the equations proved theories and how they are used today. In uncomplicated text, the book follows the evolution of each equation, bringing to life the brilliant minds and unique characters that starred in the story, and how their achievements advanced modern theory. It points out the faults and problems that arose and explains how the equations are fundamental to our understanding of the world, not to mention the unfathomable universe.
The Secret Life of Equations will enlighten and entertain in equal measure. It is excellent for readers interested in mathematics history and for students that would benefit from the allegorical explanations.
The Secret Life of Equations is not a mathematics book but a map by which readers can discover equations from a different perspective. Selected from geometry, technology, science, chance and mathematics, the 50 equations are explored by way of their history. Why were they needed? How were they developed? What is their value today?
The equations are presented as follows:
Concise, understandable text highlighted with clever illustrations. Visual and textual descriptions of the equations' components, for ultimate clarity. "What's It About" fictional scenarios to explain the original problems or theories in want of a solution or proof. "What's It Good For?" descriptions tell how the equations proved theories and how they are used today. In uncomplicated text, the book follows the evolution of each equation, bringing to life the brilliant minds and unique characters that starred in the story, and how their achievements advanced modern theory. It points out the faults and problems that arose and explains how the equations are fundamental to our understanding of the world, not to mention the unfathomable universe.
The Secret Life of Equations will enlighten and entertain in equal measure. It is excellent for readers interested in mathematics history and for students that would benefit from the allegorical explanations.
192 pages, Paperback
Published September 27, 2016
30 people are currently reading
803 people want to read
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Displaying 1 - 7 of 7 reviews
August 31, 2018
I finished this book a few days ago and I'm still finding it really hard to come up with a star rating.
I love the overall concept, and the book does a lot of things very well - especially explaining how each equation is actually used, either in practical applications like navigation and computing or to facilitate more complex mathematics.
However, I found it a little patchy; some of the equations are explained much more clearly than others, perhaps corresponding with the author's level of interest in each field. For example, I wasn't super happy that one of the few equations in the book that I've actually used - the ideal gas law - was described as
Erm, a little field snobbery there, I think.
I also found that for someone at my level (I loved and was very good at maths in high school, including getting an A at A level, and did OK at undergraduate level statistics, but haven't used "real maths" very much since) there were some logical gaps in some of the explanations. For example, the first equation in the book is Pythagoras's Theorem. Easy, right? Learned it when I was 11 or 12. The section starts really well, but then towards the end states that Pythagorean Triples are rare and difficult to find, then suddenly invites me to pick "any two different whole numbers" and plug them into a whole set of other equations (Euclid's), without really explaining why I would want to do that, how Euclid came up with the equations, or how they're used when you're not just putting random numbers into them. I found myself completely confused at the very first hurdle. I thought that maybe I just wasn't in the groove yet, so I came back to this page after finishing the rest of the book and was still just as baffled.
There are other examples of incorrect inferences about what a non-expert would be able to follow and understand, too, e.g.:
(I got this one eventually, but I had to read and re-read it. An illustration would have helped - the other illustrations in this section weren't particularly helpful and could have been switched out for something that actually helped to explain the equation, rather than having two different examples of the general concept of perspective).
There were also several punctuation, grammar, and copy editing errors that annoyed me, e.g.:
Overall though this is a good effort with some very informative content, and definitely worth reading if you don't mind the frustrations I listed above. I guess 3.5/5, but rounded down because I did get a bit annoyed with this book!
I love the overall concept, and the book does a lot of things very well - especially explaining how each equation is actually used, either in practical applications like navigation and computing or to facilitate more complex mathematics.
However, I found it a little patchy; some of the equations are explained much more clearly than others, perhaps corresponding with the author's level of interest in each field. For example, I wasn't super happy that one of the few equations in the book that I've actually used - the ideal gas law - was described as
isn't as amazing or impressive as many of its peers in this book. Perhaps, in comparison to them, it even looks a bit drab and shabby.
Erm, a little field snobbery there, I think.
I also found that for someone at my level (I loved and was very good at maths in high school, including getting an A at A level, and did OK at undergraduate level statistics, but haven't used "real maths" very much since) there were some logical gaps in some of the explanations. For example, the first equation in the book is Pythagoras's Theorem. Easy, right? Learned it when I was 11 or 12. The section starts really well, but then towards the end states that Pythagorean Triples are rare and difficult to find, then suddenly invites me to pick "any two different whole numbers" and plug them into a whole set of other equations (Euclid's), without really explaining why I would want to do that, how Euclid came up with the equations, or how they're used when you're not just putting random numbers into them. I found myself completely confused at the very first hurdle. I thought that maybe I just wasn't in the groove yet, so I came back to this page after finishing the rest of the book and was still just as baffled.
There are other examples of incorrect inferences about what a non-expert would be able to follow and understand, too, e.g.:
Think of something like a pencil, hanging in space, put the plane between the pencil and the viewpoint and think of some of those rays of light going between the two and making the picture on the plane
(I got this one eventually, but I had to read and re-read it. An illustration would have helped - the other illustrations in this section weren't particularly helpful and could have been switched out for something that actually helped to explain the equation, rather than having two different examples of the general concept of perspective).
There were also several punctuation, grammar, and copy editing errors that annoyed me, e.g.:
Here's a less fancy example, right now, the air in the room you're in [something about molecules that's too long to copy out]
First of all, we should say first of all that [something about Google that's too long to type out]
Overall though this is a good effort with some very informative content, and definitely worth reading if you don't mind the frustrations I listed above. I guess 3.5/5, but rounded down because I did get a bit annoyed with this book!
August 8, 2017
A good idea for introducing a wide range of mathematical concepts in a single book. A good book for beginners but readers who want more depth will be disappointed.
September 9, 2020
Richard Cochrane's The Secret Life of Equations: The 50 Greatest Equations and How They Work is an introductory math book. Using measured words, cartoons, and a dash of history, this book describes 50 equations developed in fields such as geometry and number theory, science, technology, and probability and statistics. What may sound abstract and dry turns into delightful explanations and everyday use.
+++ The idea is excellent and challenging. Presenting for a broad audience gems such as Einstein's equation on mass-energy equivalence (E=MC^2), Maxwell's equations on electromagnetism, and Shannon's fundamental equation on information theory, let alone Schröedinger's monstrous wave equation, poses exceptional difficulties. (Ever tried to explain Laplacians to a layperson audience?)
What I liked:
+++ The format fits well and the book is well executed. Each equation is given its own chapter, explaining what the equation is about, why it matters in today's world (the book is written in the 2010s), how to read it and what each part of the equation does, and a conclusion. These are supported by neat bits from the history of intellectual pursuit that led to creating the equation, and nice visuals that often are humorous cartoons. The structure considers carefully how to order and present the concepts, so that the hardest concepts to grasp are introduced in the context of the simplest equation using them.
+++ Overall, the writing is approachable, but also precise and in particular clever. Delightful!
+ Overall, good selection. I am sure everyone can recommend their own equations, but the selection presented here is solid.
What I didn't like:
-- I felt the examples in technology were treated a bit more vaguely than necessary. This could be the expert's bias.
-- The later two chapters, and especially the last on probability and statistics, allowed the what and the why sections of the same equation become too similar. This made for repetitive text and could be redone for a later edition.
- I would have liked to see a conclusion.
Minor issues:
- The figure on oage 159 includes a geometrical transformation (shear) that does not seem to match the chapter (on Google PageRank and eigenvectors).
- The formulas at the start of each chapter look very good, but within the main text of the chapter the other formulas look somewhat unequal and their mathematical structure suffers. For example, on page 140 the "e..." formulas are very small and one is even too small to read (right-hand column, for some reason the formula is inline). Similarly, on page 185 the position of the letter s is aligned with the equal sign (good) but not with the limit term "lim" to which it is the target (bad). Also, the main formula on page 174 includes a typo (a ")" without a matching open-parenthesis).
+++ The idea is excellent and challenging. Presenting for a broad audience gems such as Einstein's equation on mass-energy equivalence (E=MC^2), Maxwell's equations on electromagnetism, and Shannon's fundamental equation on information theory, let alone Schröedinger's monstrous wave equation, poses exceptional difficulties. (Ever tried to explain Laplacians to a layperson audience?)
What I liked:
+++ The format fits well and the book is well executed. Each equation is given its own chapter, explaining what the equation is about, why it matters in today's world (the book is written in the 2010s), how to read it and what each part of the equation does, and a conclusion. These are supported by neat bits from the history of intellectual pursuit that led to creating the equation, and nice visuals that often are humorous cartoons. The structure considers carefully how to order and present the concepts, so that the hardest concepts to grasp are introduced in the context of the simplest equation using them.
+++ Overall, the writing is approachable, but also precise and in particular clever. Delightful!
+ Overall, good selection. I am sure everyone can recommend their own equations, but the selection presented here is solid.
What I didn't like:
-- I felt the examples in technology were treated a bit more vaguely than necessary. This could be the expert's bias.
-- The later two chapters, and especially the last on probability and statistics, allowed the what and the why sections of the same equation become too similar. This made for repetitive text and could be redone for a later edition.
- I would have liked to see a conclusion.
Minor issues:
- The figure on oage 159 includes a geometrical transformation (shear) that does not seem to match the chapter (on Google PageRank and eigenvectors).
- The formulas at the start of each chapter look very good, but within the main text of the chapter the other formulas look somewhat unequal and their mathematical structure suffers. For example, on page 140 the "e..." formulas are very small and one is even too small to read (right-hand column, for some reason the formula is inline). Similarly, on page 185 the position of the letter s is aligned with the equal sign (good) but not with the limit term "lim" to which it is the target (bad). Also, the main formula on page 174 includes a typo (a ")" without a matching open-parenthesis).
December 1, 2025
A (surprisingly) wide range of equations which have particular relevance to a wide range of Physical and Social Sciences. They included traditional school equations such as Pythagoras and Newton, but also more specialist equations used to calculate populations or share prices.
The presentation of the book made it seem informal, with a good selection of pictures and diagrams which were usually pertinent to the point at issue. However, sometimes the text moved a little quick, and there were several points where the author re-arranged equations and instructed readers to ‘trust me’ that its right.
Ideally, those re-arrangements needed more detail and more explanation. Part of what makes the book useful to teachers and students alike is being able to engage with an equation for themselves, without having to ‘trust’ the book at a crucial step which is simply not explained.
Overall, this is an interesting read, well worth dipping into whether you have a background in mathematics or not, as even though the mathematics is sometimes stretching, its relevance is usually made clear with some appropriate analogies and comparisons to real world problems.
July 2, 2019
I applaud books like this that attempt to promote mathematics to a wider audience. The author picked equations from a variety of areas of mathematics and its applications, and explained them in a very down-to-earth way. Of course, this meant that some explanations were necessarily superficial. Harder to accept is the handful of glaring errors in the mathematical notation which marred an otherwise very enjoyable volume. Perhaps the next edition will get properly proofread.
November 1, 2019
Layman Friendly!
Neat, interactive, fun presentation.
Very intriguing, you might not find further detail of each equations (because this is supposed to be a entertaining and educational book, not a student textbook lol), but hey! That is the best part of the book!
Neat, interactive, fun presentation.
Very intriguing, you might not find further detail of each equations (because this is supposed to be a entertaining and educational book, not a student textbook lol), but hey! That is the best part of the book!
April 5, 2021
This was a really interesting book. I read 2 or 3 equations a day - each took 2 or 4 pages with some good illustrations throughout.
Some of the equations you would definitely need at least A-level maths or university level maths to understand the notation though the author did a pretty good job of explaining it. (It has things like Div and Curl in it).
Some of the equations you would definitely need at least A-level maths or university level maths to understand the notation though the author did a pretty good job of explaining it. (It has things like Div and Curl in it).
Displaying 1 - 7 of 7 reviews