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Men of Mathematics
Here is the classic, much-read introduction to the craft and history of mathematics by E.T. Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton's calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians -- an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work's clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.
590 pages, Paperback
First published January 1, 1937
About the author
Eric Temple Bell
58 books41 followersEric Temple Bell (February 7, 1883 – December 21, 1960) was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life. He published his non-fiction under his given name and his fiction as John Taine.
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December 26, 2012
I came across this outstanding book in my schooldays, and read it then, not understanding much, but enough to know that I had got hold of something awesome. It made the subject of maths and the mathematicians come to life. Maths class at school was not as boring as it used to be, after realizing that Archimedes and Newton were real, flesh-and-blood men.
Then I read the book again, while at engineering college. This time around, I was familiar with at least the names of the important mathematicians, and knew a little about their work. After this second reading, I felt more than a little love for the subject of maths, when I learned about the interesting lives that the mathematicians had led, and the often curious ways in which they had created the mathematics that we now took so much for granted. I realized that in the world of the intellect, Cauchy, Riemann, Newton, Liebnitz, Gauss, Abel and all the rest of them were true heroes. Not only that, many of them did their magnificent work in the face of desperate odds against them, like Abel and Galois. Knowing all this made the subject of mathematics come alive to me, and to this day, mathematics remains a thing of beauty to me. For this wonderful gift, I am forever indebted to E. T. Bell's Men of Mathematics.
Then I read the book again, while at engineering college. This time around, I was familiar with at least the names of the important mathematicians, and knew a little about their work. After this second reading, I felt more than a little love for the subject of maths, when I learned about the interesting lives that the mathematicians had led, and the often curious ways in which they had created the mathematics that we now took so much for granted. I realized that in the world of the intellect, Cauchy, Riemann, Newton, Liebnitz, Gauss, Abel and all the rest of them were true heroes. Not only that, many of them did their magnificent work in the face of desperate odds against them, like Abel and Galois. Knowing all this made the subject of mathematics come alive to me, and to this day, mathematics remains a thing of beauty to me. For this wonderful gift, I am forever indebted to E. T. Bell's Men of Mathematics.
September 1, 2016
Са овом књигом сам се први пут срео на четвртој години факултета, кад сам спремао семинарски из историје српске културе (!!?!?!?!?!??!), када сам је прочитао у српском преводу под називом Велики математичари. Сада сам је репризирао у оригиналу и могу да кажем да је ово једно ђаволски вриједно штиво, при чему бих ипак препоручио српски превод јер је овај енглески из тридесетих година прошлог вијека прилично тежак за читање.
Елем, шта је заправо ово? У питању је нека врста "популарне математике", да је тако назовемо. Заправо, већ летимичан поглед на садржај књиге даје нам до знања да су у питању биографије разних великих математичара, почевши од старих Грка, па све до модерног доба, при чему се то "модерно" доба завршава са Кантором, који је умро 1918. Међутим, кроз те биографије илустроване су све математичке дисциплине и велики број најбитнијих открића и теорија. У сваком поглављу обрађена је по једна личност, (евентуалне) пикантерије из његовог (кажем "његовог", јер у књизи нема жена) приватног живота и најпознатија његова открића, тамо гдје је било простора да се тако нешто опише.
Ово посљедње је гдје се књига разилази са највећим бројем научнопопуларних књига којих сам имао прилику да се прихватим - наиме, иако је скоро све објашњено тако да и нематематичари могу да разумију (под условом да имају барем солидно средњошколско знање математике и да нису баш тотални дудуци за логику), Бел се уопште не устручава да вам у лице саспе разноразне формуле и цртеже, па ћете се тако овде нагледати бесконачних низова, редова, полинома, алгебарских структура, комплексних бројева и сличних звијери од којих (ако се не бавите математиком) неке можда нисте ни срели, а већину сте упознали у средњој школи и онда са одушевљењем заборавили при изласку из исте. Међутим, као што рекох, овде су скоро сви (не баш СВИ) ти концепти објашњени тако да их је уз мало труда могуће разумјети.
Дакле, иако ово није класичан уџбеник, неко ко се не бави математиком откриће рапидан скок у свом разумијевању математичких појмова и њихових односа. За нас који смо имали несрећу да немамо на студију историју математике као посебан предмет књига ће добро да послужи да се барем неке рупе попуне.
Неко је стил писања упоредио са Раселовом Историјом западне филозофије и то поређење није сасвим бесмислено - ово је, што би се рекло, књига "са ставом", у којој се аутор не устручава да буде духовит и да повремено поткачи неку од личности које су му предмет анализе. Видио сам да аутору замјерају што је на неким (многим?) мјестима анегдоте сумњиве аутентичности навео као чињенице, у чему ја лично не видим никакав проблем, али ето ако баш имате некакав опсесивно-компулсивни поремећај, можете да отрчите на нет и провјерите догађај који вам изгледа превише невјероватно.
Елем, шта је заправо ово? У питању је нека врста "популарне математике", да је тако назовемо. Заправо, већ летимичан поглед на садржај књиге даје нам до знања да су у питању биографије разних великих математичара, почевши од старих Грка, па све до модерног доба, при чему се то "модерно" доба завршава са Кантором, који је умро 1918. Међутим, кроз те биографије илустроване су све математичке дисциплине и велики број најбитнијих открића и теорија. У сваком поглављу обрађена је по једна личност, (евентуалне) пикантерије из његовог (кажем "његовог", јер у књизи нема жена) приватног живота и најпознатија његова открића, тамо гдје је било простора да се тако нешто опише.
Ово посљедње је гдје се књига разилази са највећим бројем научнопопуларних књига којих сам имао прилику да се прихватим - наиме, иако је скоро све објашњено тако да и нематематичари могу да разумију (под условом да имају барем солидно средњошколско знање математике и да нису баш тотални дудуци за логику), Бел се уопште не устручава да вам у лице саспе разноразне формуле и цртеже, па ћете се тако овде нагледати бесконачних низова, редова, полинома, алгебарских структура, комплексних бројева и сличних звијери од којих (ако се не бавите математиком) неке можда нисте ни срели, а већину сте упознали у средњој школи и онда са одушевљењем заборавили при изласку из исте. Међутим, као што рекох, овде су скоро сви (не баш СВИ) ти концепти објашњени тако да их је уз мало труда могуће разумјети.
Дакле, иако ово није класичан уџбеник, неко ко се не бави математиком откриће рапидан скок у свом разумијевању математичких појмова и њихових односа. За нас који смо имали несрећу да немамо на студију историју математике као посебан предмет књига ће добро да послужи да се барем неке рупе попуне.
Неко је стил писања упоредио са Раселовом Историјом западне филозофије и то поређење није сасвим бесмислено - ово је, што би се рекло, књига "са ставом", у којој се аутор не устручава да буде духовит и да повремено поткачи неку од личности које су му предмет анализе. Видио сам да аутору замјерају што је на неким (многим?) мјестима анегдоте сумњиве аутентичности навео као чињенице, у чему ја лично не видим никакав проблем, али ето ако баш имате некакав опсесивно-компулсивни поремећај, можете да отрчите на нет и провјерите догађај који вам изгледа превише невјероватно.
July 10, 2014
A must read for anybody interested in the life of Mathematicians, the history of Math, or Math itself. The author has managed to make a seemingly dull subject lively and fun to read. Highly recommended.
January 28, 2023
This quirky tome and mini biography of the world's great mathematicians was written some eighty years ago. It is quite dated and the prose is purple.
3.5 stars
3.5 stars
March 3, 2015
A history of mathematics up to Georg Cantor, who died in 1918, the book itself was published in 1937. Each chapter summarises the life of a mathematician (sometimes two, if their lives are intertwined), with about a quarter of each chapter being reserved for details on one or two discoveries.
In tone it reminded be a lot of Russell's History of Western Philosophy - there's the British humor and the strong opinions, some people may be put off by this. It's definitely no unbiased retelling of the history of mathematics (furthermore, about 80 years have passed. Many of these stories may turned out to have been falsehoods by now [and in looking up this book, many of them are, but that doesn't detract from their fun]).
Some quotes to show the humor:
or
or
Some things I learned:
- many famous mathematicians were ridiculous child prodigies in their youngest ages, Gauss being the most famous example, discovering formulas at the age of 9, finishing Disquisitiones Arithmeticae at the age of 21 (!!!) in Latin (!!!); William Rowan Hamilton spoke 13 languages by the time he was 13 years old (E. T. Bell gets very angry about this "waste of time", he could have been doing mathematics!). It may make you look at your own life with a hint of having already wasted it.
- others did terrible in traditional systems - like Poincaré, who nearly failed the mathematical parts of his Bachelor's degree and was only admitted because of his previous mathematical importance
- funding of science changed a lot with the French revolution - before that, good mathematicians got their money from benevolent rulers, after that, they either had to give lessons or were (sometimes poorly) employed by universities
- transfinite numbers are weird
- and much more, it's a long book
The biggest drawback, and here the book shows its age, is the very dry style of the mathematical parts, maybe I'm too spoiled by pop-science writing, maybe it's the age. Sometimes, the mathematics is rather simple and you wonder why the author takes so much time to expand on these points (the age?), sometimes it's so short that you have to go look it up on Wikipedia. These definitely take their time if you want to read them properly.
But then again, to quote the author (on a different occasion):
Recommended for: People into mathematics; people who think a book about mathematics is boring (you may want to skip or skim the mathematical parts, but it's your loss); fans of British humor
Not recommended for: People without patience, as it took me a few weeks to read this; People who need the truth and nothing but the boring truth
In tone it reminded be a lot of Russell's History of Western Philosophy - there's the British humor and the strong opinions, some people may be put off by this. It's definitely no unbiased retelling of the history of mathematics (furthermore, about 80 years have passed. Many of these stories may turned out to have been falsehoods by now [and in looking up this book, many of them are, but that doesn't detract from their fun]).
Some quotes to show the humor:
As a matter of temperament some find the Laplacian conception of an eternally stable solar system repeating the complicated cycle of its motions time after time for ever and ever as depressing as an endless nightmare. For these there is the recent comfort that the Sun will probably explode some day as a nova. Then stability will cease to trouble us, for we shall all quite suddenly become perfect gases.
or
Cauchy's life and character affect us like poor Don Quixote's — we sometimes do not know whether to laugh or to cry, and compromise by swearing.
or
But on the utterly imbecilic advice of his physician he began meddling in politics "to benefit his nervous system." If ever a more idiotic prescription was handed out by a doctor to a patient whose complaint he could not diagnose it has yet to be exhumed.
Some things I learned:
- many famous mathematicians were ridiculous child prodigies in their youngest ages, Gauss being the most famous example, discovering formulas at the age of 9, finishing Disquisitiones Arithmeticae at the age of 21 (!!!) in Latin (!!!); William Rowan Hamilton spoke 13 languages by the time he was 13 years old (E. T. Bell gets very angry about this "waste of time", he could have been doing mathematics!). It may make you look at your own life with a hint of having already wasted it.
- others did terrible in traditional systems - like Poincaré, who nearly failed the mathematical parts of his Bachelor's degree and was only admitted because of his previous mathematical importance
- funding of science changed a lot with the French revolution - before that, good mathematicians got their money from benevolent rulers, after that, they either had to give lessons or were (sometimes poorly) employed by universities
- transfinite numbers are weird
- and much more, it's a long book
The biggest drawback, and here the book shows its age, is the very dry style of the mathematical parts, maybe I'm too spoiled by pop-science writing, maybe it's the age. Sometimes, the mathematics is rather simple and you wonder why the author takes so much time to expand on these points (the age?), sometimes it's so short that you have to go look it up on Wikipedia. These definitely take their time if you want to read them properly.
But then again, to quote the author (on a different occasion):
The choice of such phraseology is not merely stereotyped pedantry. There is a reason for its use, and careful writers mean exactly what they say when they assert that “we can find, etc” They mean that they can do what they say.
Recommended for: People into mathematics; people who think a book about mathematics is boring (you may want to skip or skim the mathematical parts, but it's your loss); fans of British humor
Not recommended for: People without patience, as it took me a few weeks to read this; People who need the truth and nothing but the boring truth
January 1, 2015
The main intent here is biographical rather than mathematical. But this isn't a very good account. He doesn't distinguish between facts and anecdotes and the author always lets his prejudices get in the way of narrative. I guess it just reflects the times in which it was written. The parts i liked the most of this book were the mathematical parts.
July 21, 2022
Men of Mathematics, by E.T. Bell is a collection of (brief) biographies of the more well known mathematicians through history and the lasting marks they have made. Included in each chapter is a description of their major works and an attempt to bring them down to the average readers' comprehension.
Where oh where to begin. It should have been straightforward; a short bio into some remarks on major published works. But Bell cannot make it that simple. He needs to write with excessively florid prose that often loses the reader in its self indulgence. He must throw names around as if everyone is familiar with the world of mathematics. Idioms and other turns of phrase are violently inserted by Bell, who must think highly of himself indeed, and is unable to leave himself out of his writing.
Next, the descriptions of major works. Complexity upon complexity is thrown upon the reader, followed by condescending remarks about how simple it should be to anyone who has completed their basic courses...blah blah blah…
I hated this book, and I suffered. And yet, despite all of this, I was drawn into the lives of these men, and I find myself wanting to know more. In the long run, this book served its purpose; it sparked an interest within me.
This is a terribly subjective attempt at a non fiction survey of mathematicians. I beg any prospective reader to look elsewhere, it will not be too hard to find a higher quality substitution for this nonsense.
Rating: 3/10
Where oh where to begin. It should have been straightforward; a short bio into some remarks on major published works. But Bell cannot make it that simple. He needs to write with excessively florid prose that often loses the reader in its self indulgence. He must throw names around as if everyone is familiar with the world of mathematics. Idioms and other turns of phrase are violently inserted by Bell, who must think highly of himself indeed, and is unable to leave himself out of his writing.
Next, the descriptions of major works. Complexity upon complexity is thrown upon the reader, followed by condescending remarks about how simple it should be to anyone who has completed their basic courses...blah blah blah…
I hated this book, and I suffered. And yet, despite all of this, I was drawn into the lives of these men, and I find myself wanting to know more. In the long run, this book served its purpose; it sparked an interest within me.
This is a terribly subjective attempt at a non fiction survey of mathematicians. I beg any prospective reader to look elsewhere, it will not be too hard to find a higher quality substitution for this nonsense.
Rating: 3/10
October 5, 2016
First 1/3: 4 starts
Later 2/3: 2 stars
I guess that averages out to a 2 & 2/3 star rating, although it feels like I slugged through the boring parts for so long that I'm rounding down.
The biggest point against Men of Mathematics is that is truly the Men of Mathematics. And it really should have been White European Men of Mathematics. While it is true that most of modern mathematics was discovered by European men *cough* imperialism *cough*, there were some people of color and women who some important work. Like Ada Lovelace, the first computer scientist. Or Emmy Noether, a landmark abstract algebraist whose theories underpin all of modern physics. Or, you know, the Arabs who invented Algebra. Or the Indians who invented zero. It’s not as if there was a time period to focus on, the book opens on ancient Greece and then skips straight to Descartes.
I guess this book is a product of its times. It was written in 1937. Ideas like including women on the merit of their accomplishments weren’t invented yet.
Aside from the imperialist and sexist attitude of the author, it was quite enjoyable! For some of it at least. The book is structured as a series of mini biographies of famous mathematicians. There are 23 chapters (intro + 22 mathematicians) from Zeno to Descartes to Gauss to Eisenstein to…if you’re bored already this book is not for you. My main issue is that if you are not already familiar with the characters and their accomplishments, the writing will not make you interested. I know this because I was already familiar with the characters in the 1/3 of the chapters I liked and unfamiliar with the 2/3 of the characters in the chapters I didn’t.
I learned some neat tidbits, and some pretty cool math, but mostly I get to say I read the damn thing and have it look impressive on my shelf. Men of Mathematics, where you have to be white, male, and french or german, and a genius as 22 to get a few pages jotted down about you. Oh and you’ll probably die poor and sick and young anyway.
Later 2/3: 2 stars
I guess that averages out to a 2 & 2/3 star rating, although it feels like I slugged through the boring parts for so long that I'm rounding down.
The biggest point against Men of Mathematics is that is truly the Men of Mathematics. And it really should have been White European Men of Mathematics. While it is true that most of modern mathematics was discovered by European men *cough* imperialism *cough*, there were some people of color and women who some important work. Like Ada Lovelace, the first computer scientist. Or Emmy Noether, a landmark abstract algebraist whose theories underpin all of modern physics. Or, you know, the Arabs who invented Algebra. Or the Indians who invented zero. It’s not as if there was a time period to focus on, the book opens on ancient Greece and then skips straight to Descartes.
I guess this book is a product of its times. It was written in 1937. Ideas like including women on the merit of their accomplishments weren’t invented yet.
Aside from the imperialist and sexist attitude of the author, it was quite enjoyable! For some of it at least. The book is structured as a series of mini biographies of famous mathematicians. There are 23 chapters (intro + 22 mathematicians) from Zeno to Descartes to Gauss to Eisenstein to…if you’re bored already this book is not for you. My main issue is that if you are not already familiar with the characters and their accomplishments, the writing will not make you interested. I know this because I was already familiar with the characters in the 1/3 of the chapters I liked and unfamiliar with the 2/3 of the characters in the chapters I didn’t.
I learned some neat tidbits, and some pretty cool math, but mostly I get to say I read the damn thing and have it look impressive on my shelf. Men of Mathematics, where you have to be white, male, and french or german, and a genius as 22 to get a few pages jotted down about you. Oh and you’ll probably die poor and sick and young anyway.
March 26, 2015
3/5 for historical accuracy, 4/5 for culture. Ultimately, 3/5, but still highly recommendable.
The only problem I have with Bell is that the characterisation of mathematics may put off some impressionable young mathematician-to-bes. Bell, most likely inadvertently, gives a sense that, if one is not going to be a first-rate, world-class mathematician, then they should not bother taking up the art.
On the other hand, Bell's enthusiasm for mathematics is infectious. Many have criticised his tendency to embellish and from a historian's point of view Bell does more harm than good. But as a piece of mathematical culture it remains very important -- think Romance of the Three Kingdoms in Chinese literature, except not as fictionalised. So long as you take some of the historical accounts with a grain of salt, Men of Mathematics will be a pleasure to read, even for the non-mathematician. In fact, I would say that the gravitas Bell attributes to certain eras, ideas and theorems of mathematics is only an approximation, for their universal significance is truly ineffable. So in that sense, Bell is actually being modest.
My final qualm with it is that it doesn't really capture the collaborative spirit that is even more pronounced in modern mathematics. In this sense Men of Mathematics is outdated, and perhaps a tad too romantic for my taste. Nonetheless, it is a classic, to inspire at least one more generation of mathematicians (mine!).
The only problem I have with Bell is that the characterisation of mathematics may put off some impressionable young mathematician-to-bes. Bell, most likely inadvertently, gives a sense that, if one is not going to be a first-rate, world-class mathematician, then they should not bother taking up the art.
On the other hand, Bell's enthusiasm for mathematics is infectious. Many have criticised his tendency to embellish and from a historian's point of view Bell does more harm than good. But as a piece of mathematical culture it remains very important -- think Romance of the Three Kingdoms in Chinese literature, except not as fictionalised. So long as you take some of the historical accounts with a grain of salt, Men of Mathematics will be a pleasure to read, even for the non-mathematician. In fact, I would say that the gravitas Bell attributes to certain eras, ideas and theorems of mathematics is only an approximation, for their universal significance is truly ineffable. So in that sense, Bell is actually being modest.
My final qualm with it is that it doesn't really capture the collaborative spirit that is even more pronounced in modern mathematics. In this sense Men of Mathematics is outdated, and perhaps a tad too romantic for my taste. Nonetheless, it is a classic, to inspire at least one more generation of mathematicians (mine!).
October 10, 2011
When I was younger, I liked this book a lot. Later, however, it is easy to notice that there are several great mathematicians who are curiously omitted simply because they were female, and that some of the biographies have a few liberties taken with them to be more dramatic. As another reviewer said, this is a product of the times in which it was written. Still, a readable overview of the sometimes overly dramatic lives of the greatest male contributors to mathematics, but by now there are many more accurate and complete texts on the history of mathematics.
June 19, 2010
A book about the lives and contributions of the greatest mathematicians up to early 19th century; the book starts with some . There are many threads running through the book. It shows how mathematics the subject itself evolved from its infancy. But mostly the book is about the mathematician and his work. Before I started the book, I wanted to know the common denominator across these great minds. The only common characteristic that all of them had was a true love for subject. And most of them started learning mathematics from their childhood.
To prove the greatness of a mathematician, his works have to be explained. And the author has done a fabulously job of conveying the greatness of each mathematician without too much mathematical details. Mind you there is still plenty of mathematics in each chapter, I would guess about 40%. I didn't understood many mathematical proofs, but still was able to appreciate the contribution of the mathematician.
I have been reading this book on and off for more than a year. It is not the lightest book I have read, but definitely one of the best non-fictions I have picked.
To prove the greatness of a mathematician, his works have to be explained. And the author has done a fabulously job of conveying the greatness of each mathematician without too much mathematical details. Mind you there is still plenty of mathematics in each chapter, I would guess about 40%. I didn't understood many mathematical proofs, but still was able to appreciate the contribution of the mathematician.
I have been reading this book on and off for more than a year. It is not the lightest book I have read, but definitely one of the best non-fictions I have picked.
December 17, 2012
E.T. Bell is by no means unbiased, but he doesn't ever claim to be. His writing reflects his captivating wit and seemingly endless knowledge; it is anyone's pleasure to read.
February 16, 2018
I've always been interested in the life of Physicists and Mathematicians, so this was a entertaining read for me. What strikes out for me is that Bell tries to portray these men as gods; outworldly people capable of doing inhuman tasks. No doubt these men are legends in their own right but this praise is not justified. But I loved reading about the little stories behind these men's lives. Since it was written in the 1930s, the author has been very reserved about lot of things. A similar book written contemporarily would have been much spicier. Because let's face it, people reading this book have a vested interest in Mathematics and know most of the men discussed in the book. We were looking for stories about these men and not an explanation of the math they did, an explanation, which in my opinion. I should rate it 3.5 but since the author did the arduous task of combining so many eras of Mathematics, I'll be generous in the rounding-off.
July 17, 2019
We generally think of mathematicians as some old, senile professors who think that common people don't understand them that they are just good for teaching. But the mathematicians have been politicians, administrators, churchmen, soldiers and whatnot. This book is not about mathematics but rather than the life of mathematicians in general.
Mathematicians: more humane than humans of any craft ever be - the ones who believed in logic deduced from fundamentals and stood for them even if the world stood against!
#MenOfMathematics #ETBell #Completed #Book_No_12 #Obsessed #Emotional #Humans
Mathematicians: more humane than humans of any craft ever be - the ones who believed in logic deduced from fundamentals and stood for them even if the world stood against!
#MenOfMathematics #ETBell #Completed #Book_No_12 #Obsessed #Emotional #Humans
July 28, 2019
An impressive body of work on the life of famous (and less famous) mathematicians from antiquity to the early 20th century. We discover a melting pot of lives, poor and rich, happy and sad, uneventful and rich of adventures. It is a pleasure to discover all those mathematicians from that personal-life angle and how mathematical discoveries are made within the socio-political sphere of the Time. It feels, however, that more than simple knowledge in mathematics is needed to truly enjoy this book and the importance of each mathematician's contribution. A brief overview of the evolution of Mathematics would have been welcome to help follow the flow.
May 22, 2019
Whenever I feel down or I am distracted, whenever I loose interest in Studies (Math and Computer Science), I read this book, sure shot way to get re-motivated.
September 19, 2009
slow going, but fascinating, because he describes how mathematics has evolved over time, and you get some idea of how remarkable these discoveries were. Starts with Pythagoras. I I'm as far as Newton now. Some math, but not a lot. Very opinionated writer, which really comes through when he is discussing mathematicians who also were theologians, like pascal and Newton. He has no time whatever for those endeavors.
September 27, 2017
I can see why this book inspired Freeman Dyson. The book contains bio-sketches of more than 27 mathematicians, arranged chronologically in 29 chapters. The book starts with Zeno of Elea (ca. 490 - 430 BC) and ends with George Cantor (1845 - 1918). It successfully compiles the lives of the 27 great mathematicians, depicting interesting aspects of their lives. An outstanding book by a great mathematician. Highly recommended!!
December 10, 2007
As history, this book should be taken with some salt. As a book about mathematical characters and the character of mathematics, though, I think Men of Mathematics is hard to beat. I first read this when I was in middle school or high school, and while it wasn't the only thing that got me into mathematics, it was certainly an influence.
June 16, 2012
This is one of the ones I keep on my shelf for easy access rather than in a box in the closet. Each chapter is a self-contained bio with personal info, the mathematician's place in history, and life in the context of his/her times. Laid back, not like other scientific bios that can be annoyingly stuffy. One of my favs. Just now finding out there's a part 2. Hot damn!
November 25, 2012
Mathematics has evolved over centuries. It is unlike any other branch of science where someone proposes a theory and years later it is proved wrong. When something is accepted in mathematics, it is forever in there. This book provides an insight into the lives of those great mathematicians who have shown the world new ways and opened new dimensions in various fields of mathematics.
August 21, 2013
it very good
December 2, 2015
Extremely biased against protestants. Author seems to be an angry Catholic.
May 5, 2016
A wonderful biography, however a little bit old, it is not with Ramanujan, Von Neumann, Hilbert, Godel...
I can get some new ideas.
I can get some new ideas.
September 26, 2017
Just as good as I remembered it. I like that when in doubt he tells us the anecdote even if there are no proofs. I want Evariste Galois to have led exactly the life that Bell gives us.
September 3, 2019
Es una obra de arte, aún sin logrará entender todo su contenido, apasiona la forma en cómo se describen y muestran las obras de estos genios de la humanidad.
Recomendado.
Recomendado.
November 1, 2016
I recently finished reading Eric Temple Bell’s Men of Mathematics, which looked at the history of mathematics from the days of the Babylonians through to the dawn of the twentieth century. As the subtitle of his quasi-historical work states, Bell looks at “the lives and achievements of the great mathematicians from Zeno to Poincare.” He wrote the book in 1937 and it was posthumously reprinted in 1965, the version I enjoyed reading. Although Bell’s book of biographical sketches inspired many people to study mathematics, historians of mathematics do not consider it as completely accurate. Bell in his preface said he was not writing history, but a summary of the mathematicians’ humanity and their seminal achievements. It is an excellent read and I heartily recommend it.
The world’s great mathematicians have played a major part in the evolution of scientific and philosophic thought. Many believe the three greatest mathematicians of all time include Archimedes, Newton, and Gauss. In fact, some historians postulate that if the Greeks took their cue from Archimedes instead of Euclid, Plato, and Aristotle, they might have advanced the era of modern mathematics of Newton and physical science of Galileo during the 17th century by 2,000 years.
Modern mathematics began with two great advances - analytic geometry in 1637 with Rene Descartes (1596-1650) and calculus with Sir Isaac Newton (1642-1727) and Gottfried Leibniz (1646-1716) around 1666. Descartes took that final step with his Cartesian coordinate system in building out analytic geometry “with its structure of geometrical proof, discovery, and invention.” Descartes can be said to have invented geometry and he documented his mathematical findings in an appendix to his great work Method (1637). Newton and Leibniz independently developed calculus in order to explain the physics of nature. Both built upon the incredible insight of Archimedes regarding the idea of limiting sums from which the integral calculus emerges.
The entire development of mathematics owes its progress to the ongoing battle between the notion of the discrete and the idea of the continuous. The use of the discrete, captured by the numbers 1,2,3,..., attempts to define the natural world atomistically, as individual elements put together to describe the whole. The world of the discrete belongs to algebra, symbolic logic, and the theory of numbers.
The continuous, on he other hand, tries to describe nature as undulating, coursing, and flowing phenomena, such as the rise and fall of the tides, the orbits of the planets, and the movement of electricity. Such continuity takes us into the mathematical world of the calculus and to a huge array of applications common to the fields of science and technology - the world of mathematical analysis. Engineers make much use of the tools of mathematics to solve practical problems.
The appearance of continuous mathematics can be attributed to Pythagoras’s failed attempt to describe the world solely with discrete mathematics. What we call the Pythagorean Theorem proves the point. If two sides of a triangle have a length of one unit, the diagonal produced with geometry yields an answer of the square root of 2. This number cannot be derived with a finite number of measurements simply because the square root of 2 is an irrational number, a series of never-ending numbers needed to describe the length. Some of the Greeks must have been less tolerant, as the young mathematician who raised the issue of irrational numbers was thrown overboard and killed. The followers of the discrete did not want to be derailed by the ideas of the continuous.
Other biographical sketches Bell shares with his readers include:
- Fermat, who founded the theory of numbers, shared in the creation of the theory of probability, and developed both Fermat’s Theorem and Fermat’s Last Theorem,
- Pascal, who cofounded the theory of probability, invented the first calculating machine, carried on Toricelli’s work on atmospheric pressure, and solved many aspects of the cycloid,
- The Bernoulli family, which produced eight mathematicians over three generations, the greatest of which was Daniel who developed principles leading to the conservation of energy postulate and is best known for his work in pure and applied fluid motion,
- Euler, who was brilliant in both discrete and continuous mathematics, has never been surpassed as an algorist. He developed a solution to the three-body problem useful for navigation and made mechanics and analytical science,
- Lagrange, who was close friends with the great chemist Lavoisier, used methods of approximation to develop six-body solutions in celestial mathematics,
- Laplace, who was a mathematical astronomer, proved the stability of the Solar System in his era and developed the theory of the potential, key to understanding the basics of electromagnetism,
- Monge, the inventor of descriptive geometry used for all mechanical drawings and graphical methods that helped make mechanical engineering a reality,
- Fourier developed the theory of heat conduction, which led to useful ideas on boundary-value problems, concepts critical to the development of electrical engineering and acoustical engineering,
- Poncelet developed projective geometry and introduced the principles of continuity and duality,
- Gauss, considered the Prince of Mathematicians, applied rigor to mathematical analysis, inventing the law of reciprocity, the method of “least squares” - the Gaussian law of normal distribution of errors in statistics and the associated bell-shaped curve that is familiar to many, developed the laws of biquadratic and cubic reciprocity, discovered the double periodicity of certain elliptical functions, unified cartesian and polar coordinates by noting that multiplication by i has the effect of rotation through a right angle, laid a mathematical theory of electromagnetism and coinvented an electric telegraph, developed differential geometry, and built up conformal mapping,
- Cauchy introduced rigor into mathematical analysis and the combinatorial, which led to the theory of groups
- Abel and Jacobi jointly developed the theory of elliptic functions and the Hamilton-Jacobi equations contributed to quantum mechanics,
- Cayley developed the theory of invariants of great importance to the theory of relativity, the notion of geometry of “higher space” (or of n dimensions), and the theory of matrices, which proved most useful for Heisenberg when he used matrix multiplcation for his work in quantum theory 67 years later,
- Weierstrass created a theory of irrational numbers to address the concepts of limits, continuity, and covergence,
- Boole’s original work added mathematical logic to the domain of algebra,
- Hermite solved the general equation of the fifth degree using elliptical functions instead of radicals, which proved to be impossible as a solution set, and developed the concept of transcendance of the number e (2.71828...),
- Kronecker combined the the theory of numbers, the theory of equations, and elliptic functions into one pattern, and
- Reimann, one of the most original mathematicians of modern times, defined curvature and recognized its invariance, and devised processes for the investigation of quadratic differential forms, both which found their physical interpretation in Einstein’s theory of relativity.
Read Bell’s summary of these great mathematicians and learn about their humanity, appreciate their strengths and frailties, and admire their seminal achievements.
Good reading!
The world’s great mathematicians have played a major part in the evolution of scientific and philosophic thought. Many believe the three greatest mathematicians of all time include Archimedes, Newton, and Gauss. In fact, some historians postulate that if the Greeks took their cue from Archimedes instead of Euclid, Plato, and Aristotle, they might have advanced the era of modern mathematics of Newton and physical science of Galileo during the 17th century by 2,000 years.
Modern mathematics began with two great advances - analytic geometry in 1637 with Rene Descartes (1596-1650) and calculus with Sir Isaac Newton (1642-1727) and Gottfried Leibniz (1646-1716) around 1666. Descartes took that final step with his Cartesian coordinate system in building out analytic geometry “with its structure of geometrical proof, discovery, and invention.” Descartes can be said to have invented geometry and he documented his mathematical findings in an appendix to his great work Method (1637). Newton and Leibniz independently developed calculus in order to explain the physics of nature. Both built upon the incredible insight of Archimedes regarding the idea of limiting sums from which the integral calculus emerges.
The entire development of mathematics owes its progress to the ongoing battle between the notion of the discrete and the idea of the continuous. The use of the discrete, captured by the numbers 1,2,3,..., attempts to define the natural world atomistically, as individual elements put together to describe the whole. The world of the discrete belongs to algebra, symbolic logic, and the theory of numbers.
The continuous, on he other hand, tries to describe nature as undulating, coursing, and flowing phenomena, such as the rise and fall of the tides, the orbits of the planets, and the movement of electricity. Such continuity takes us into the mathematical world of the calculus and to a huge array of applications common to the fields of science and technology - the world of mathematical analysis. Engineers make much use of the tools of mathematics to solve practical problems.
The appearance of continuous mathematics can be attributed to Pythagoras’s failed attempt to describe the world solely with discrete mathematics. What we call the Pythagorean Theorem proves the point. If two sides of a triangle have a length of one unit, the diagonal produced with geometry yields an answer of the square root of 2. This number cannot be derived with a finite number of measurements simply because the square root of 2 is an irrational number, a series of never-ending numbers needed to describe the length. Some of the Greeks must have been less tolerant, as the young mathematician who raised the issue of irrational numbers was thrown overboard and killed. The followers of the discrete did not want to be derailed by the ideas of the continuous.
Other biographical sketches Bell shares with his readers include:
- Fermat, who founded the theory of numbers, shared in the creation of the theory of probability, and developed both Fermat’s Theorem and Fermat’s Last Theorem,
- Pascal, who cofounded the theory of probability, invented the first calculating machine, carried on Toricelli’s work on atmospheric pressure, and solved many aspects of the cycloid,
- The Bernoulli family, which produced eight mathematicians over three generations, the greatest of which was Daniel who developed principles leading to the conservation of energy postulate and is best known for his work in pure and applied fluid motion,
- Euler, who was brilliant in both discrete and continuous mathematics, has never been surpassed as an algorist. He developed a solution to the three-body problem useful for navigation and made mechanics and analytical science,
- Lagrange, who was close friends with the great chemist Lavoisier, used methods of approximation to develop six-body solutions in celestial mathematics,
- Laplace, who was a mathematical astronomer, proved the stability of the Solar System in his era and developed the theory of the potential, key to understanding the basics of electromagnetism,
- Monge, the inventor of descriptive geometry used for all mechanical drawings and graphical methods that helped make mechanical engineering a reality,
- Fourier developed the theory of heat conduction, which led to useful ideas on boundary-value problems, concepts critical to the development of electrical engineering and acoustical engineering,
- Poncelet developed projective geometry and introduced the principles of continuity and duality,
- Gauss, considered the Prince of Mathematicians, applied rigor to mathematical analysis, inventing the law of reciprocity, the method of “least squares” - the Gaussian law of normal distribution of errors in statistics and the associated bell-shaped curve that is familiar to many, developed the laws of biquadratic and cubic reciprocity, discovered the double periodicity of certain elliptical functions, unified cartesian and polar coordinates by noting that multiplication by i has the effect of rotation through a right angle, laid a mathematical theory of electromagnetism and coinvented an electric telegraph, developed differential geometry, and built up conformal mapping,
- Cauchy introduced rigor into mathematical analysis and the combinatorial, which led to the theory of groups
- Abel and Jacobi jointly developed the theory of elliptic functions and the Hamilton-Jacobi equations contributed to quantum mechanics,
- Cayley developed the theory of invariants of great importance to the theory of relativity, the notion of geometry of “higher space” (or of n dimensions), and the theory of matrices, which proved most useful for Heisenberg when he used matrix multiplcation for his work in quantum theory 67 years later,
- Weierstrass created a theory of irrational numbers to address the concepts of limits, continuity, and covergence,
- Boole’s original work added mathematical logic to the domain of algebra,
- Hermite solved the general equation of the fifth degree using elliptical functions instead of radicals, which proved to be impossible as a solution set, and developed the concept of transcendance of the number e (2.71828...),
- Kronecker combined the the theory of numbers, the theory of equations, and elliptic functions into one pattern, and
- Reimann, one of the most original mathematicians of modern times, defined curvature and recognized its invariance, and devised processes for the investigation of quadratic differential forms, both which found their physical interpretation in Einstein’s theory of relativity.
Read Bell’s summary of these great mathematicians and learn about their humanity, appreciate their strengths and frailties, and admire their seminal achievements.
Good reading!
September 28, 2022
580 pages! And nearly 450 pages dedicated to beautiful mathematical ideas in the 4 areas of maths- arithmetic, analysis, algebra and geometry. In an ordinary school system, it's the immense lingering hatred of maths that gives the possibility of converting hatred into a love for maths.. it's a flawed subject.. and it's very apparent because we see most children struggle in maths.. but we see only the flaw.. books like this heal our mind. They give a great mental pleasure.. a great fortitude of thoughts that guide our thinking.. without mathematics nothing is possible. That most people know only the difficult side of this.. is the subject's flaw.
Getting back to the book, the lives of 29 mathematicians are covered. The author very wisely saves the analysis and the arithmetic to the later half of the book because they seem to be more daunting to a novice reader. He presents geometrical and algebraic ideas as singular descriptive contributions and pens the other two as collaborative efforts. So, there is a subtle shift in the tone of the book in the later sections. It makes for a very creative narration of the lives of these mathematical men ☺️ getting back to the ideas, you do come to understand
1. The importance of method
2. The symbolism of logic and how it is used in discrete maths
3. The importance of group theory
4. Projection and invariance
5. Algebraic number field and it's proof that makes it possible to be included in maths.
6. The imaginings of infinity and infinite series ☺️
7. Irrational number, rational number, cardinal number, ideal number, prime number.. all the imaginings and equations explaining the behaviour of these numbers.
And finally.. the abstractions that help the enthralled reader to experience the pleasure of imagining these ideas themselves.
This book is a keeper ☺️ it even gives you deep emotional truths without trying to.. obviously the author wants the readers to be sympathetic and yet at the same time be at awe at the wonderful world of mathematics. And his enthusiasm in visiting the lives of these men and their works has a sly undertone of instilling in us the same enthusiasm.. everything we need to learn about the mathematician.. why he invented his concept.. why that particular concept.. what were the social conditions that lead up to that discovery.. what effect did the discovery have upon his mental and physical health.. the responsibilities, accolades and opposition that the discoveries lead to.. everything is discussed and it is all whole hearted and meant to inspire the reader.
Getting back to the book, the lives of 29 mathematicians are covered. The author very wisely saves the analysis and the arithmetic to the later half of the book because they seem to be more daunting to a novice reader. He presents geometrical and algebraic ideas as singular descriptive contributions and pens the other two as collaborative efforts. So, there is a subtle shift in the tone of the book in the later sections. It makes for a very creative narration of the lives of these mathematical men ☺️ getting back to the ideas, you do come to understand
1. The importance of method
2. The symbolism of logic and how it is used in discrete maths
3. The importance of group theory
4. Projection and invariance
5. Algebraic number field and it's proof that makes it possible to be included in maths.
6. The imaginings of infinity and infinite series ☺️
7. Irrational number, rational number, cardinal number, ideal number, prime number.. all the imaginings and equations explaining the behaviour of these numbers.
And finally.. the abstractions that help the enthralled reader to experience the pleasure of imagining these ideas themselves.
This book is a keeper ☺️ it even gives you deep emotional truths without trying to.. obviously the author wants the readers to be sympathetic and yet at the same time be at awe at the wonderful world of mathematics. And his enthusiasm in visiting the lives of these men and their works has a sly undertone of instilling in us the same enthusiasm.. everything we need to learn about the mathematician.. why he invented his concept.. why that particular concept.. what were the social conditions that lead up to that discovery.. what effect did the discovery have upon his mental and physical health.. the responsibilities, accolades and opposition that the discoveries lead to.. everything is discussed and it is all whole hearted and meant to inspire the reader.
This entire review has been hidden because of spoilers.
September 17, 2017
It must be difficult to write biographies of mathematicians. Their excellence in math does not mean they are interesting subjects otherwise. However, Bell has a done a very good job. My favorite passages:
“Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional.” – Charles Proteus Steinmetz
“Of all the ancients Archimedes is the only one who habitually thought with the unfettered freedom that the greater mathematicians permit themselves today with all the hard-won gains of twenty five centuries to smoother their way, for he alone of all the Greeks had sufficient stature and strength to stride clear of the obstacles thrown in the path of mathematical progress by frightened geometers who had listened to the philosophers.” (20)
“Give me a place to stand on and I will move the earth.” – Archimedes (on levers)
Descartes spent his mornings lying in bed thinking, remembering is schoolboy days when the rector told him to do just that, and understanding that the quiet meditation the habit produced was responsible for his philosophy and mathematics. (37)
On Newton, “In all the history of mathematicsc Newton has had no superior (and perhaps no equal) in the ability to concentrate all the forces of his intellect on a difficulty at an instant’s notice.” (116)
Funny story at the court of Catherine the Great. Denis Diderot was trying to convert to atheism, and Catherine commissioned Euler to silence him, knowing how uncomfortable Diderot was with math. “Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: ‘Sir, (a+b to the nth) / n = x, hence God exists; reply!’ It sounded like sense to Diderot. Humiliated by the unrestrained laughter which greeted his embarrassed silence, the poor man asked Catherine’s permission to return at once to France.” (147)
Euler calculated the complex mathematics of lunar motion entirely in his head. (150)
If you love mathematics, and want to learn the context and lives of the people who contributed to its development, this is a great source.
See my other reviews here!
“Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional.” – Charles Proteus Steinmetz
“Of all the ancients Archimedes is the only one who habitually thought with the unfettered freedom that the greater mathematicians permit themselves today with all the hard-won gains of twenty five centuries to smoother their way, for he alone of all the Greeks had sufficient stature and strength to stride clear of the obstacles thrown in the path of mathematical progress by frightened geometers who had listened to the philosophers.” (20)
“Give me a place to stand on and I will move the earth.” – Archimedes (on levers)
Descartes spent his mornings lying in bed thinking, remembering is schoolboy days when the rector told him to do just that, and understanding that the quiet meditation the habit produced was responsible for his philosophy and mathematics. (37)
On Newton, “In all the history of mathematicsc Newton has had no superior (and perhaps no equal) in the ability to concentrate all the forces of his intellect on a difficulty at an instant’s notice.” (116)
Funny story at the court of Catherine the Great. Denis Diderot was trying to convert to atheism, and Catherine commissioned Euler to silence him, knowing how uncomfortable Diderot was with math. “Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: ‘Sir, (a+b to the nth) / n = x, hence God exists; reply!’ It sounded like sense to Diderot. Humiliated by the unrestrained laughter which greeted his embarrassed silence, the poor man asked Catherine’s permission to return at once to France.” (147)
Euler calculated the complex mathematics of lunar motion entirely in his head. (150)
If you love mathematics, and want to learn the context and lives of the people who contributed to its development, this is a great source.
See my other reviews here!
Read
August 8, 2022Fun survey of many of the great math dudes with lots of interesting factoids. E.T. Bell is very saucy and frequently sexist in this mild, old-fashioned way. He is very opinionated about Napoleon and the inheritance of mental traits. The secret bonus biography is E.T. Bell, who is himself a real character from a bygone age.
I've never read a non-fiction book with so much math in it, but I largely skimmed over the math, which will be reductive if you have learned it before and gibberish if you haven't. Can anyone combine good prose with good math? It certainly seems like many of the enlightenment mathematicians could.
Like Bell, I also wish we still used Latin as the language of science, but I guess it's for the best that we don't any more.
Can you learn how to be a great mathematician from this book? Not really. If you were a genius, you'd probably know by now. I've often had a hard time reading biographies of the great and famous because I usually vacillate between poles of self-pity ('How come I can't do math in my head like Euler?') and smug superiority ('Ha! at least I have a better ear for music than old Kronecker!'). This is a bad attitude, but I'm starting to get over it.
No matter how fortunate you are in money, prestige, talents, the basic human condition doesn't change. There are men in this book who live blissfully and beautifully; men who die young and brutal; men who die old and wretched. We all must play the hand we are dealt.
The lesson for me is just this: do the work. It's cliche, but it really is the journey that matters, not the destination.
I've never read a non-fiction book with so much math in it, but I largely skimmed over the math, which will be reductive if you have learned it before and gibberish if you haven't. Can anyone combine good prose with good math? It certainly seems like many of the enlightenment mathematicians could.
Like Bell, I also wish we still used Latin as the language of science, but I guess it's for the best that we don't any more.
Can you learn how to be a great mathematician from this book? Not really. If you were a genius, you'd probably know by now. I've often had a hard time reading biographies of the great and famous because I usually vacillate between poles of self-pity ('How come I can't do math in my head like Euler?') and smug superiority ('Ha! at least I have a better ear for music than old Kronecker!'). This is a bad attitude, but I'm starting to get over it.
No matter how fortunate you are in money, prestige, talents, the basic human condition doesn't change. There are men in this book who live blissfully and beautifully; men who die young and brutal; men who die old and wretched. We all must play the hand we are dealt.
The lesson for me is just this: do the work. It's cliche, but it really is the journey that matters, not the destination.
Displaying 1 - 30 of 99 reviews