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e: The Story of a Number
The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.
221 pages, Kindle Edition
First published January 1, 1993
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October 5, 2018
Eli Maor wrote quite a few books about the history of Mathematics. They are wonderful in combining interesting historical insights with the maths per se, but on the level of a school program. I loved his "Infinity" book. This is as well extremely erudite and fascinating.
e - is irrational number which is the basis of the natural logarithm. Sounds daunting, but one can think of this number as a basis for measuring rate of change in many processes involving so called exponential growth (the rate of growth is proportional to the current state of the system). It is very relevant nowadays while almost everything what matters grows exponentially including information, population, pollution etc.
The book is not very technical at all. It explains underlying maths. But also talks about fascinating historical characters and anecdotes. To illustrate, I will just mention here one episode:
As the story goes, the Calculus were "discovered" in the 17th simultaneously by Newton in England and Leibniz on the continent. Apparently, it was huge unresolved argument who hold the priority over this discovery. The majority of academy in England claimed it was Newton and that Leibniz has stollen his ideas after seeing some of the Newton's papers. This was severely rejected by the Leibniz's defenders on the continent. Nevertheless, Leibnitz's system of notation was more intuitive and easier to understand and apply.
"Knowledge of the calculus has become the dominating mathematical topic of the 18th century and quickly spread throughout the Continent. In England, where it originated, the calculus fared less well. Newton's towering figure discouraged British mathematicians from pursuing the subject with vigor. Worse, by siding completely with Newton in the priority dispute, they cut themselves off from developments on the Continent. The stubbornly stuck to Newton's dot notation, failing to see the advantages of Leibniz's differential notation. As a result, over the next hundred years, while mathematics flourished in Europe as never before, England did not produce a single first-rate mathematician. "
It is so true that history does not teach people any lessons; does it?
e - is irrational number which is the basis of the natural logarithm. Sounds daunting, but one can think of this number as a basis for measuring rate of change in many processes involving so called exponential growth (the rate of growth is proportional to the current state of the system). It is very relevant nowadays while almost everything what matters grows exponentially including information, population, pollution etc.
The book is not very technical at all. It explains underlying maths. But also talks about fascinating historical characters and anecdotes. To illustrate, I will just mention here one episode:
As the story goes, the Calculus were "discovered" in the 17th simultaneously by Newton in England and Leibniz on the continent. Apparently, it was huge unresolved argument who hold the priority over this discovery. The majority of academy in England claimed it was Newton and that Leibniz has stollen his ideas after seeing some of the Newton's papers. This was severely rejected by the Leibniz's defenders on the continent. Nevertheless, Leibnitz's system of notation was more intuitive and easier to understand and apply.
"Knowledge of the calculus has become the dominating mathematical topic of the 18th century and quickly spread throughout the Continent. In England, where it originated, the calculus fared less well. Newton's towering figure discouraged British mathematicians from pursuing the subject with vigor. Worse, by siding completely with Newton in the priority dispute, they cut themselves off from developments on the Continent. The stubbornly stuck to Newton's dot notation, failing to see the advantages of Leibniz's differential notation. As a result, over the next hundred years, while mathematics flourished in Europe as never before, England did not produce a single first-rate mathematician. "
It is so true that history does not teach people any lessons; does it?
October 30, 2009
One hundred and thirty pages into Eli Maor’s history of Euler’s number (e), Maor experiences what can only be described as a "John Nash moment". Here he departs from his straight-laced account to describe, at length, an imagined conversation between J. S. Bach and Johann Bernoulli.
Bernoulli: That perfectly fits my love for orderly sequences of numbers.
Bach: But there is a problem. A scale constructed from these ratios consists of three basic intervals: 9:8, 10:9, and 16:15. The first two are nearly identical, and each is called a whole tone, or a second… But the same ratios should hold regardless of which note we start from. Every major scale consists of the same sequence of intervals.
Bernoulli: I can see the confusion…
This bizarre interlude aside, Maor has a difficult time keeping to the project he outlines in his introduction. Maor says he hope his book will live up to Beckmann’s A History of ∏, which he describes as model of clarity and accessibility. Unfortunately, e doesn’t lend itself easily to non-mathematical description. After a brief and entertaining history of logarithms, as Maor begins his approach to the subject at hand, his text quickly becomes mired in equations—limits, infinite series, and calculus notation.
Readers equipped with some basic grounding in calculus will certainly be able to trudge through Maor’s book, and along with the history, Maor touches on many interesting applications of e—to such diverse fields as finance, number theory, physics, and architecture. All in all, though, Maor’s book is a rather whimsical attempt at a history of e, certainly nothing that will satisfy either armchair or academically-minded mathematicians.
Bernoulli: That perfectly fits my love for orderly sequences of numbers.
Bach: But there is a problem. A scale constructed from these ratios consists of three basic intervals: 9:8, 10:9, and 16:15. The first two are nearly identical, and each is called a whole tone, or a second… But the same ratios should hold regardless of which note we start from. Every major scale consists of the same sequence of intervals.
Bernoulli: I can see the confusion…
This bizarre interlude aside, Maor has a difficult time keeping to the project he outlines in his introduction. Maor says he hope his book will live up to Beckmann’s A History of ∏, which he describes as model of clarity and accessibility. Unfortunately, e doesn’t lend itself easily to non-mathematical description. After a brief and entertaining history of logarithms, as Maor begins his approach to the subject at hand, his text quickly becomes mired in equations—limits, infinite series, and calculus notation.
Readers equipped with some basic grounding in calculus will certainly be able to trudge through Maor’s book, and along with the history, Maor touches on many interesting applications of e—to such diverse fields as finance, number theory, physics, and architecture. All in all, though, Maor’s book is a rather whimsical attempt at a history of e, certainly nothing that will satisfy either armchair or academically-minded mathematicians.
July 13, 2012
Everyone knows about π, the ratio 3.14159... the universal constant governing circles. The constant e is just as important if not more so, but never managed to break its way into popular culture because it's a little hard to understand just what makes it so special. This book makes a valiant effort to redress that shortcoming, by explaining the history of logarithms and calculus and how the last 400 years of mathematics developed, empowered largely by this mysterious number which, before the invention of computers and calculators, was critical in doing any kind of serious arithmetic. Nowadays they don't even teach how logarithms are used to do multiplication - I'm 40 years old, and it was not taught when I was a kid either - but for hundreds of years the only realistic way to do it was to look up the numbers in a log table, add them up, look the sum up in another table, and get your result.
This book talks about the lives of mathematicians and their discoveries, and how those built on each other to produce the knowledge we now have about the amazing world of numbers. But books like this tend to have a fatal flaw, either dumbing down the math so much that it becomes basically just biography and handwaving, or having so much math that you need an advanced math degree to understand it. This one strikes a very careful balance between those extremes. There were definitely parts where I had to stretch my brain back 20 years to high school and college calculus classes, but each of the formulas was pretty well explained, and I'd like to think you could come away from this book with some understanding even if you'd never taken any advanced math.
This book talks about the lives of mathematicians and their discoveries, and how those built on each other to produce the knowledge we now have about the amazing world of numbers. But books like this tend to have a fatal flaw, either dumbing down the math so much that it becomes basically just biography and handwaving, or having so much math that you need an advanced math degree to understand it. This one strikes a very careful balance between those extremes. There were definitely parts where I had to stretch my brain back 20 years to high school and college calculus classes, but each of the formulas was pretty well explained, and I'd like to think you could come away from this book with some understanding even if you'd never taken any advanced math.
December 22, 2018
I love this concise history of one of Mathematics' most interesting numbers. e is usually dominated by pi in mathematical history, but e also has an interesting story behind it. Calculus was required to explain and understand it, which brought the Bernoullis, Leibnitz, Newton, Euler and a lot of other scientific geniuses to tackle it.
Unlike pi, which has been known for thousands of years, and which was foundational to geometry, one of Mathematics' oldest branches, e has been around for a shorter period of time (about 400 years), and deals with a bunch of things like irrationality, infinity and stuff that ancient mathematicians never liked to think much about.
I always find interesting the story of Hippasus, a Pythagorean who is famous for getting drowned by other Pythagoreans for his threat to expose irrationality.
Although a lot of stuff in the book was over my head and I steadily refused the urge to read the Appendices, I still think this book is a good work of mathematical history.
Unlike pi, which has been known for thousands of years, and which was foundational to geometry, one of Mathematics' oldest branches, e has been around for a shorter period of time (about 400 years), and deals with a bunch of things like irrationality, infinity and stuff that ancient mathematicians never liked to think much about.
I always find interesting the story of Hippasus, a Pythagorean who is famous for getting drowned by other Pythagoreans for his threat to expose irrationality.
Although a lot of stuff in the book was over my head and I steadily refused the urge to read the Appendices, I still think this book is a good work of mathematical history.
June 13, 2012
OK, so books on math, not going to become national best sellers by any stretch of the imagination. But any story in the field of math be it zero, 'e,' Phi, PI tells us more about that mystical, insightful language that can tell us so much about the why's and what's of our surroundings, as well as provide the more practical to suit our human needs. Math is interesting in the sense that it dictates to the mathematician not the mathematician to it to determine outcome. ie: in string theory, the math tells the mathematician that not only is a fourth dimension needed but up to a seventh. So, to the book. Maor has done a great job giving us some background on 'e' and its beginnings in logarithmic use. And even though 'e's use can be found in diverse places--"the interest earned in a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis"--its significance, only second to PI in importance, as a number is greatly and clearly expressed by Maor. It's written for the non-mathematician, no great depth of understanding needed to get the points here. Some anecdotes and diversions to bring home points made. Good effort.
December 2, 2018
Too. Much. Calculus. I was hoping this would be more like The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, but it wasn't. For one thing, this book has differential equations. A lot of them. As a STEM major, I did study calculus at the university level (but not Dif Eq), but this was still hard going. What really helped get me through the book were the historical anecdotes, and the parts of the book I was able to follow well were also well-done.
December 14, 2013
Enjoyable skim through the basics of logarithms, conic sections, calculus, and various other areas of mathematics relating to e. Not a textbook, so don't read this to learn those subjects, only to glance at them. The historical aspects add a narrative element, and of course the writing is far more pleasant than a textbook too. The background given, and also the original explanations, helped me to understand some of the concepts better, so I am glad that I read it. I will only be giving it a cursory glance though.
(Subject to edit on completion)
(Subject to edit on completion)
June 10, 2015
I found this basically unreadable. It oscillated too quickly between "history" and "refresher of AP calculus" and lacked any real unifying themes. It felt very rambly. The author has a lot of facts more or less related to logarithms, or exponentials, or infinite series, and wants to share them all.
January 18, 2019
Great book to explore mathematics from a different perspective (recreational rather than traditional mathematics education). Even suitable if you haven't touched and been learning more maths for a while. Many of the explanations were built from first principles.
Although there was a lot of overlap initially with mathematics covered in high school cirricula (e.g. logarithms, compound interest formula, limits & Zeno's paradox, differentiation from first principles, binomial theorem/Pascal's triangle, differentiation and integration). Similarly to An Imaginary Tale, this subject matter was approached in a chronological manner, with stories about the characters and mathematicians involved in the story of e. This improved the ease of the read and helped maintan my interest in combination with other general trivial facts and case studies e.g. the story of the Bernoulli family, the tables of logarithms.
There was ample new subject matter especially in the latter half of the book for me (stuff that wasn't covered in high school, wasn't proven and accepted as fact, or just forgotten by me): spira mirabillis, squaring of the hyperbola (proof for area under hyperbola without use of calculus), hyperbolic functions, mapping of complex functions etc.
It was especially satisfying to read about the relationship between e and pi (e.g. Euler's formula); as well as e appearing in the Prime Number Theorem; AND THAT YOU CAN EVALUATE LOGARITHMS OF NEGATIVE NUMBERS (explanation also in An Imaginary Tale (below)).
Would recommend reading in conjunction with An Imaginary Tale (a book about the imaginary number: i) - although the material of the latter seems to be more advanced. Having only read that book a month ago, I seem to have forgotten some of the theorems and proofs within. As such, this book was great to remind me of those theorems and the beauty of their proofs. (NB: some overlap in the content of the book e.g. Euler's thoerem, Laplace's equations, hyperbolic functions).
Maybe I wish that there was more maths in this book. Some proofs seem to be glossed over and "outside the scope of this book". Some of the explanations seem less clear than those within An Imaginary Tale. Maybe this is why I rate this book 4 starts instead of 5. (As well since the novelty of a book (that is not a textbook) fiddling with a lot of maths has been attenuated for me). I do wish there were more math equations/proofs rather than maths mixed in with wordy explanations. Although I'm not sure which one I retain better since it seems that a lot of the proofs and examples in An Imaginary Tale have already been lost on me.
Although there was a lot of overlap initially with mathematics covered in high school cirricula (e.g. logarithms, compound interest formula, limits & Zeno's paradox, differentiation from first principles, binomial theorem/Pascal's triangle, differentiation and integration). Similarly to An Imaginary Tale, this subject matter was approached in a chronological manner, with stories about the characters and mathematicians involved in the story of e. This improved the ease of the read and helped maintan my interest in combination with other general trivial facts and case studies e.g. the story of the Bernoulli family, the tables of logarithms.
There was ample new subject matter especially in the latter half of the book for me (stuff that wasn't covered in high school, wasn't proven and accepted as fact, or just forgotten by me): spira mirabillis, squaring of the hyperbola (proof for area under hyperbola without use of calculus), hyperbolic functions, mapping of complex functions etc.
It was especially satisfying to read about the relationship between e and pi (e.g. Euler's formula); as well as e appearing in the Prime Number Theorem; AND THAT YOU CAN EVALUATE LOGARITHMS OF NEGATIVE NUMBERS (explanation also in An Imaginary Tale (below)).
Would recommend reading in conjunction with An Imaginary Tale (a book about the imaginary number: i) - although the material of the latter seems to be more advanced. Having only read that book a month ago, I seem to have forgotten some of the theorems and proofs within. As such, this book was great to remind me of those theorems and the beauty of their proofs. (NB: some overlap in the content of the book e.g. Euler's thoerem, Laplace's equations, hyperbolic functions).
Maybe I wish that there was more maths in this book. Some proofs seem to be glossed over and "outside the scope of this book". Some of the explanations seem less clear than those within An Imaginary Tale. Maybe this is why I rate this book 4 starts instead of 5. (As well since the novelty of a book (that is not a textbook) fiddling with a lot of maths has been attenuated for me). I do wish there were more math equations/proofs rather than maths mixed in with wordy explanations. Although I'm not sure which one I retain better since it seems that a lot of the proofs and examples in An Imaginary Tale have already been lost on me.
May 24, 2018
As said by others - picked this up wanting to understand a complex mathematical topic, got this and also an awesome historical overview of the development of the calculus and more over hundreds of years. Awesome!
December 27, 2021
I may not be a mathematician, but I always loved math in school, and I like reading about math and science (I loved Infinite Powers, for example), so I was excited to read this book. Maor states in the prologue that his goal is "to tell the story of e on a level accessible to readers with only a modest background in mathematics" and promises to minimize the use of mathematical formulas in the text. Given that, I anticipated this book would be similar to Strogatz's in approach, and would be a fascinating look at the history of a number.
I think, however, that Maor and I have a different definition of "modest background." I found the book to be highly technical, and while the longer derivations might have been confined to the appendices, the text was still full of mathematical formulae. If I went verrrrry slowly and tried to pull out all of my old memories from my high school and college calculus classes, I could sort of follow him, but I certainly wouldn't call it accessible.
I'm guessing that math majors and others in fields that use complex math on a daily basis would find the book interesting. I just wasn't his target audience, no matter how he framed his intentions in the prologue.
I think, however, that Maor and I have a different definition of "modest background." I found the book to be highly technical, and while the longer derivations might have been confined to the appendices, the text was still full of mathematical formulae. If I went verrrrry slowly and tried to pull out all of my old memories from my high school and college calculus classes, I could sort of follow him, but I certainly wouldn't call it accessible.
I'm guessing that math majors and others in fields that use complex math on a daily basis would find the book interesting. I just wasn't his target audience, no matter how he framed his intentions in the prologue.
September 7, 2022
2.718281828 Maor’s writing is clear and easy to follow. Looking forward to reading more of his work.
February 27, 2009
Maor's account of the place of e, the base of the natural logarithms, in the history of mathematics provides a peek inside a mathematician's brain. More connected by mathematical ideas than by chronology or the usual social, cultural, economic, or political themes taken up by historians, Maor's book opened vistas in the calculus I did not see when I first ploddingly confronted derivatives and integrals some decades ago. He thoroughly covers the differing views of Newton and Leibniz as they developed the calculus. He discusses some of the special characteristics of e revealed in the fact that the exponential function is its own derivative. He shows how e appeared in nature and the arts - musical scales, the spiral mirablis, a hanging chain, the parabolic arc of a projectile, the Gateway Arch. More than other of recent books focused on a particular number, Maor explores the mathematics of e with a mathematician's interest. But metaphysics creeps in as it seems to in discursive accounts of mathematical developments and achievements. Numbers - in particular special numbers like e - have been imbued with mystical connections to larger or hidden things. This account of e raises the questions again, "What is this language of numbers that humans have developed and how is this language linked to the world 'out there'?" In one sense, the number e, like its more famous companion pi, turns out to be not only an irrational number but also non-algebraic - not a solution (root) of a polynomial equation. Such numbers are called transcendental, meaning merely 'beyond algebraic'. In the end, Maor's story of e is an account of human activity in a world of patterns. And it is an excellent companion to a course in calculus.
July 7, 2024
Il pi greco lo conoscono tutti o quasi; ma non è il solo numero "molto interessante" per i matematici. Secondo a ben poca distanza c'è infatti il numero e, che vale circa 2,718 e appare anch'esso nei punti più diversi della matematica; dal calcolo dell'area sotto un'iperbole a quello degli interessi composti, dai logaritmi alle funzioni trigonometriche. Nella sua bella collana a basso prezzo che recupera varie opere di storia della matematica, la Princeton University Press ha recuperato questo testo dedicato per l'appunto a e. Il libro è scritto molto bene; richiede qualche competenza matematica ma risulta facilmente leggibile e interessante. La parte storica è molto completa che parte dalla nascita dei logaritmi, con divagazioni all'indietro verso Archimede e i problemi della quadratura, per arrivare alla scoperta della trascendenza del numero. I concetti vengono spiegati in maniera molto chiara, oserei dire meglio che quanto viene fatto a scuola da noi. Naturalmente ci sono anche divagazioni su altri numeri famosi, π e i prima di tutti; d'altra parte tutti questi numeri sono (stranamente?) correlati tra loro...
February 28, 2012
Like its more famous cousin pi, e is an irrational number that shows up in unexpected places all over mathematics. It also has a much more recent history, not appearing on the scene until the 16th century. My favorite parts of this book were the historical anecdotes such as the competitive Bernoullis and the Nerwton-Leibniz cross-Channel calculus feud. Unfortunately, this math history text is much heavier on the math than the history, including detailed descriptions of limits, derivatives, integrals, and imaginary numbers. The trouble with this large number of equationsis that if you’re already familiar with the concepts you’ll be doing a lot of skimming, but if the subject is confusing then reading this book will probably not give you any new insights. In short, as much as I normally enjoy books about math and science, this particular one felt too much like a textbook. Recommended only for those folks with a very strong love for the calculus and related topics.
November 28, 2021
e rocks
The number e is shown to be just as fundamental and just as fascinating as it’s much more famous brother pi. And also has geometric interpretations/applications. For e in the properties of hyperbolae and logarithmic spirals. Just as pi does with circles . The author doesn’t quite manage to say that pi too could have been defined analytically and then discovered to have geometric applications. But he should have for the sake of completeness.
Well written, easy to understand but also comprehensive and engaging. The author does have a tendency to digress a little too much into biography and general history of science and math but this is not uncommon in this type of book and in this one it is not too excessive.
The level of math varies a little unsteadily. He tries to keep it very simple but occasionally cuts loose a bit. For example the sections on complex analysis are surely useless to anyone who doesn’t already understand it.
The number e is shown to be just as fundamental and just as fascinating as it’s much more famous brother pi. And also has geometric interpretations/applications. For e in the properties of hyperbolae and logarithmic spirals. Just as pi does with circles . The author doesn’t quite manage to say that pi too could have been defined analytically and then discovered to have geometric applications. But he should have for the sake of completeness.
Well written, easy to understand but also comprehensive and engaging. The author does have a tendency to digress a little too much into biography and general history of science and math but this is not uncommon in this type of book and in this one it is not too excessive.
The level of math varies a little unsteadily. He tries to keep it very simple but occasionally cuts loose a bit. For example the sections on complex analysis are surely useless to anyone who doesn’t already understand it.
October 26, 2013
The book takes you through an amazing journey of time in which you will be fascinated and humbled by the efforts which mathematician have put in to develop mathematics as it is today. The book is perfect to arouse interest in mathematics in your children, and to make them realize that more than its regular textbook form, mathematics is fun, inspiring and beautiful.
August 6, 2020
This is a fairly straightforward book, doing essentially what it set out to do. It gives you a history of how *e* came to be and shows you how it became increasingly important in mathematics. The one interesting wrinkle is the author's view of the Newton & Leibniz, where the author clearly takes a pro Leibniz stand. Having read other books by other authors with a distinctly different tone, I found the author's opinions troubling. For one, the author seemed to be somewhat dismissive of physics and other applied aspects of math. For example, the author says, in so many words, that Newton's syntax and approach were polluted by the real world applications to which it was applied, while Leibniz approached calculus with the eye of a true mathematician. And the one thing the book really has trouble explaining is why Leibniz died somewhat in obscurity while Newton was given great honors. Both had equal numbers of defenders and detractors. Why were Germany and France not honoring Leibniz and giving him accolades? The answer is that the author left out critical pieces of information and let his bias for mathematics against applied sciences warp his view of the players.
One accusation the author makes is that England essentially went into a temporary dark period for the development of mathematics until the 1830s because of their unwillingness to adopt the superior notation and reasoning made by Leibniz. But did that slow the advancement of physics, chemistry, engineering, mechanics in England? Leibniz was a giant of mathematics and probably better at the theoretical aspects of Calculus, but Newton had F = ma and history rightfully judges Newton the giant and Leibniz a far behind runner up. Also, though Leibniz wrote the superior Calculus textbook with superior insight and syntax, Newton was far better at actually solving challenging math problems with real world implications. And finally, though I believe Leibniz should get equal claim for developing Calculus and I disagree with those who wish to give majority credit to Newton, Leibniz and his supporters used dishonest methods, such as back dating documents, to make their case. They also wrote anonymous scurilious attacks which they denied they wrote and then were later found out to have actually written. Or to put it another way, Leibniz and his defenders behaved in ways that were perceived by others to be dishonorable.
There is one interesting subtext that the author does not really go into as well. In later years, Leibniz and Newton did make up to a certain extent and acknowledged each others roles as being vital. The real controversies started when Leibniz and Newton had gotten quite old and the dispute was taken up by other players. Then the controversy had more to do with politics than any real interest to determining who was responsible for what.
One accusation the author makes is that England essentially went into a temporary dark period for the development of mathematics until the 1830s because of their unwillingness to adopt the superior notation and reasoning made by Leibniz. But did that slow the advancement of physics, chemistry, engineering, mechanics in England? Leibniz was a giant of mathematics and probably better at the theoretical aspects of Calculus, but Newton had F = ma and history rightfully judges Newton the giant and Leibniz a far behind runner up. Also, though Leibniz wrote the superior Calculus textbook with superior insight and syntax, Newton was far better at actually solving challenging math problems with real world implications. And finally, though I believe Leibniz should get equal claim for developing Calculus and I disagree with those who wish to give majority credit to Newton, Leibniz and his supporters used dishonest methods, such as back dating documents, to make their case. They also wrote anonymous scurilious attacks which they denied they wrote and then were later found out to have actually written. Or to put it another way, Leibniz and his defenders behaved in ways that were perceived by others to be dishonorable.
There is one interesting subtext that the author does not really go into as well. In later years, Leibniz and Newton did make up to a certain extent and acknowledged each others roles as being vital. The real controversies started when Leibniz and Newton had gotten quite old and the dispute was taken up by other players. Then the controversy had more to do with politics than any real interest to determining who was responsible for what.
November 9, 2021
Eli Maor gives a great history of e, full of personalities and math concepts that I found very enjoyable. I was reminded of the difference between historical development and modern understanding, which led me to revisit Where Mathematics Comes From, which has in its part VI perhaps a better presentation of the latter way of knowing about e.
The historical perspective reminds me that math didn't start as formal as it is now. Like Bourbaki leading to New Math, modern formalism may not be the best way to teach concepts. Being able to prove something and understanding it are not the same thing. I'm not sure I agree completely with the idea of what math is in WMCF, but I do agree that humans do better when they understand things as something more than just a game of symbol manipulation. In a similar spirit to the tau movement, I think mathematical notation, proof, and especially education should focus on communicating meaning.
More broadly, I think there ought to be Feynman explanations for more topics.
The historical perspective reminds me that math didn't start as formal as it is now. Like Bourbaki leading to New Math, modern formalism may not be the best way to teach concepts. Being able to prove something and understanding it are not the same thing. I'm not sure I agree completely with the idea of what math is in WMCF, but I do agree that humans do better when they understand things as something more than just a game of symbol manipulation. In a similar spirit to the tau movement, I think mathematical notation, proof, and especially education should focus on communicating meaning.
More broadly, I think there ought to be Feynman explanations for more topics.
August 24, 2021
I had occasionally seen number e in many branches of mathematics from analytics to statistics but despite π, Its origin was kinda vague to me, hence when I saw the title of the book somewhere I was intrigued to read it. It's a book generally about the history of mathematic with an emphasis on e, It depicted the line of mathematical thoughts from greeks to Euler who defined the concurrent notation for the number albeit mathematicians knew about it for a few centuries before him. In many parts, It goes a little offtopic since it may be an impossible mission to write more than 200 pages merely about a number.
I assume that it's essential to have studied elementary calculus to make a grasp out of this book, even though If you want to fully understand it you need to know about more advanced calculus topics since the author tried to not make the book math-heavy, he escaped the full demonstration of many topics and you only understand them if you had studied the topic before.
I assume that it's essential to have studied elementary calculus to make a grasp out of this book, even though If you want to fully understand it you need to know about more advanced calculus topics since the author tried to not make the book math-heavy, he escaped the full demonstration of many topics and you only understand them if you had studied the topic before.
August 6, 2023
Eli Maor's e: The Story of a Number is a history of the irrational and transcendental number e. An irrational number defies representation as a fraction of two whole numbers. A transcendental number eludes expression as the solution to any polynomial with whole-number coefficients.
Maor is a mathematician and historian. He wrote several books about mathematical concepts for a broad audience. The book e: The Story of a Number is no different. Maor chronicles the development of e through logarithms, finance, and calculus. Along the way, we meet a cast of colorful characters. Furthermore, Maor teaches how to use logarithm tables for those who never had to use them.
At the end of each chapter is a section focused on the notes and sources Maor used in the book. He uses plenty of graphs and practical examples to engage the reader. The book is older but still practical. The uses of e haven't dried up yet.
Thanks for reading my review, and see you next time.
Maor is a mathematician and historian. He wrote several books about mathematical concepts for a broad audience. The book e: The Story of a Number is no different. Maor chronicles the development of e through logarithms, finance, and calculus. Along the way, we meet a cast of colorful characters. Furthermore, Maor teaches how to use logarithm tables for those who never had to use them.
At the end of each chapter is a section focused on the notes and sources Maor used in the book. He uses plenty of graphs and practical examples to engage the reader. The book is older but still practical. The uses of e haven't dried up yet.
Thanks for reading my review, and see you next time.
May 29, 2024
If you were looking for a 248 page book on the story of e, then this conflated volume reads like a storied text of how mathematicians dodged exponentiation for centuries and went with logarithms.
An interesting exploration of hyperbolic trig functions aside, and borrowing from Princeton Press' review, "The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics - from the law of compound interest to the shape of a hanging chain, from the area under a hyperbola to Euler's famous formula e(superscript i(pi)) = -1, from the inner structure of a nautilus shell to Bach's equal-tempered scale and to the art of M. C. Escher.
The book ends with an account of the discovery of transcendental numbers, an event that paved the way for Cantor's revolutionary ideas about infinity.
No knowledge of calculus is assumed, and the few places where calculus is used are fully explained:" Still, not for the faint of heart.
An interesting exploration of hyperbolic trig functions aside, and borrowing from Princeton Press' review, "The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics - from the law of compound interest to the shape of a hanging chain, from the area under a hyperbola to Euler's famous formula e(superscript i(pi)) = -1, from the inner structure of a nautilus shell to Bach's equal-tempered scale and to the art of M. C. Escher.
The book ends with an account of the discovery of transcendental numbers, an event that paved the way for Cantor's revolutionary ideas about infinity.
No knowledge of calculus is assumed, and the few places where calculus is used are fully explained:" Still, not for the faint of heart.
April 19, 2019
I can trace all of my interest, and success, in mathematics back to this book. I read it at a far too young age, and harassed my friends with my otherworldly knowledge of numbers and mathematics for years.
Eli Maor is extremely capable at distilling complex concepts into simple and intuitive explanations, and weaving the human nature of discovery into the story of this number.
e, the number, is visible so much in the world around us, and this book does an excellent job at explaining the significance and peculiarity of this relation.
I cannot stress enough that this book should not be passed up, especially by curious children.
Eli Maor is extremely capable at distilling complex concepts into simple and intuitive explanations, and weaving the human nature of discovery into the story of this number.
e, the number, is visible so much in the world around us, and this book does an excellent job at explaining the significance and peculiarity of this relation.
I cannot stress enough that this book should not be passed up, especially by curious children.
May 22, 2022
e is my favorite number. It feels like it shouldn't exist, and yet it appears everywhere and to lend a helping hand. This book cemented my love for the number. It's standard popular mathematics fare: accessible explanations of mathematical mixed in fun anecdotes about the mathematicians that discovered/invented them. First year me would have been consoled to learn that the great mathematicians of old also thought it was weird that the integral of 1/x is ln(x). As I often find, my favorite chapters are near the end. I'm particularly fond of the chapter on the logarithmic spiral, a shape so perfect that it drove Jacob Bernoulli to obsession.
November 8, 2023
Highly interesting survey of the history of the number e. Maybe a bit too much computational content for a history book as such, but that's probably my own laziness. Maor makes mathematical discovery an exciting thing, which is something most teachers and professors of mathematics continuously fail to do. My mind was blown when I read that the arc length of a logarithmic spiral from the origin to a point on the x-axis is EQUAL to the length of the tangent line to the spiral from that point on the y-axis!!
January 7, 2018
Absolutely brilliant. Among my favorite books. It has everything---from the infamous Newton/Leibniz controversy and the first derivation of Euler's constant from compound-interest calculations to the rectification of the logarithmic spiral and the Cauchy-Riemann equations for (complex) analytic functions. The appendix alone is nearly worth the price of the book. A true gem. Riveting and well written. Essential reading.
June 28, 2019
This book is, I think, as good as it could be given its dry subject matter. The histotical portion of the book was well written and well researched, but it's not a page-turner. The math was well explained, although, I think you had better understand calculus to get much out of it. In his preface, Maor's stated goal is for the book to be "accessible to readers with only a modest background in mathematics". In that, I think he falls well short.
October 15, 2020
Well that was quick. Skimmed thru to cherry pick what was accessible to me as a non math background person. My main interest was the imaginary number represented by "e" or Euler's number 2.718281828... that has to do with a compound interest problem. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest.
Now I have a feeling and basic understanding of "e" which was my goal.
Now I have a feeling and basic understanding of "e" which was my goal.
May 13, 2023
If you have any interest in the history of mathematics, this is one of the best books ever written (fortunately by a mathematician from Princeton University) on that subject. Starting with numbers of different bases, logarithms, interest rate and interest payments, the development of calculus by Leibitz and Newton, this book has it all and more. I thoroughly enjoyed this book, and it is short enough that I just might read it again.
September 30, 2018
Interesting enough. Best thing about the book IMO is the appendix that offers proofs for the existence of the number in its earliest form (i.e., limit of (1+1/n)^n). I always find the typical discussions of e or of that limit to be circular, so it's nice to have a from-scratch defense of the number!
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