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A Concise History of Mathematics
This compact, well-written history — first published in 1948, and now in its fourth revised edition — describes the main trends in the development of all fields of mathematics from the first available records to the middle of the 20th century. Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating.
Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others.
For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others.
"The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.
Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others.
For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others.
"The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.
256 pages, Paperback
First published January 1, 1948
82 people are currently reading
611 people want to read
About the author
Dirk Jan Struik
30 books11 followersDirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician and Marxian theoretician who spent most of his life in the United States.
Dirk Jan Struik was born in 1894 in Rotterdam, Netherlands, as a teacher's son, Struik attended the Hogere Burgerschool (HBS) in The Hague. It was in this school that he was first introduced to left-wing politics by some of his teachers. In 1912 Struik entered University of Leiden, where he showed great interest in mathematics and physics, influenced by the eminent professors Paul Ehrenfest and Hendrik Lorentz. In 1917 he worked as a high school mathematics teacher for a while, after which he worked as a research assistant for J.A. Schouten. It was during this period that he developed his doctoral dissertation, "The Application of Tensor Methods to Riemannian Manifolds." In 1922 Struik obtained his doctorate in mathematics from University of Leiden. He was appointed to a teaching position at University of Utrecht in 1923. The same year he married Ruth Ramler, a Czech mathematician with a doctorate from the Charles University of Prague. In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time. In 1926 Struik was offered positions both at the Moscow State University and the Massachusetts Institute of Technology. He decided to accept the latter, where he spent the rest of his academic career. He collaborated with Norbert Wiener on differential geometry, while continuing his research on the history of mathematics. He was made full professor at MIT in 1940.
Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994), Mathematics, and Marxism. It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics. Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.
In 1950 Stuik published his Lectures on Classical Differential Geometry, which gained praise from Ian R. Porteous:
Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.
Struik died October 21, 2000, 21 days after celebrating his 106th birthday.
Source: http://en.wikipedia.org/wiki/Dirk_Jan...
Dirk Jan Struik was born in 1894 in Rotterdam, Netherlands, as a teacher's son, Struik attended the Hogere Burgerschool (HBS) in The Hague. It was in this school that he was first introduced to left-wing politics by some of his teachers. In 1912 Struik entered University of Leiden, where he showed great interest in mathematics and physics, influenced by the eminent professors Paul Ehrenfest and Hendrik Lorentz. In 1917 he worked as a high school mathematics teacher for a while, after which he worked as a research assistant for J.A. Schouten. It was during this period that he developed his doctoral dissertation, "The Application of Tensor Methods to Riemannian Manifolds." In 1922 Struik obtained his doctorate in mathematics from University of Leiden. He was appointed to a teaching position at University of Utrecht in 1923. The same year he married Ruth Ramler, a Czech mathematician with a doctorate from the Charles University of Prague. In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time. In 1926 Struik was offered positions both at the Moscow State University and the Massachusetts Institute of Technology. He decided to accept the latter, where he spent the rest of his academic career. He collaborated with Norbert Wiener on differential geometry, while continuing his research on the history of mathematics. He was made full professor at MIT in 1940.
Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994), Mathematics, and Marxism. It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics. Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.
In 1950 Stuik published his Lectures on Classical Differential Geometry, which gained praise from Ian R. Porteous:
"Of all the textbooks on elementary differential geometry published in the last fifty years the most readable is one of the earliest, namely that by D.J. Stuik (1950). He is the only one to mention Allvar Gullstrand."
Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.
Struik died October 21, 2000, 21 days after celebrating his 106th birthday.
Source: http://en.wikipedia.org/wiki/Dirk_Jan...
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Displaying 1 - 27 of 27 reviews
February 9, 2018
This book crams a lot of history into just 200 pages. It is very reasonably priced! My copy cost only 8 pounds.
This is about the development of mathematical ideas over a long period of many centuries. Researching and writing such a book must have been an onerous task.
It goes from the ancient world of Babylonia to about 1945 AD. Maths is now a vast subject, and one book cannot cover everything. The early centuries are covered in detail. By the time we get to the 19th century AD, it is not at all possible to record every milestone and theorem! Instead, it mentions the more significant breakthroughs.
There is a brilliant section on the geometry of the Ancient Greeks, and another great section on Leonhard Euler who achieved so much for the development of mathematics. Towards the end, it mentions Alan Turing briefly.
On the whole, this is worth reading. It would suit people who do not have the time or money to read the longer histories, such as Boyer, although I don't doubt that Boyer's history is excellent.
By the way, some reviews mention that the author, Dirk Struik, was a Marxist/communist. If so, this does not find its way into the text, which remains objective throughout.
This is about the development of mathematical ideas over a long period of many centuries. Researching and writing such a book must have been an onerous task.
It goes from the ancient world of Babylonia to about 1945 AD. Maths is now a vast subject, and one book cannot cover everything. The early centuries are covered in detail. By the time we get to the 19th century AD, it is not at all possible to record every milestone and theorem! Instead, it mentions the more significant breakthroughs.
There is a brilliant section on the geometry of the Ancient Greeks, and another great section on Leonhard Euler who achieved so much for the development of mathematics. Towards the end, it mentions Alan Turing briefly.
On the whole, this is worth reading. It would suit people who do not have the time or money to read the longer histories, such as Boyer, although I don't doubt that Boyer's history is excellent.
By the way, some reviews mention that the author, Dirk Struik, was a Marxist/communist. If so, this does not find its way into the text, which remains objective throughout.
October 28, 2018
I don't usually write reviews, but regarding this book, I think a reader needs some preparation.
As a university student who has taken and is going to take quite a few pure math courses, I started reading from Chapter 6, the seventeenth century. It was so exhilarating to read such that I didn't stop until I reached the end of Chapter 9. the nineteenth century. However, most of my enjoyment came from discovering the origins and contexts of a lot of the theorems that I have studied in my courses. When content regarding analysis came up, I was full of delight because I remember studying the theorems in class, but any content on geometry showed little appeal to me because I had never studied any sort of geometry in a classroom.
I would image then, that for those who have little exposure to pure math, the content on the development of calculus, analysis, and later on geometry and algebra, would hold little to no appeal. To get the most enjoyment out of this book, one would need to have some technical understanding of undergraduate-level mathematics up to measure theory (Lebesgue integral) in terms of analysis, group theory in term of algebra, and quite advanced as well in terms of geometry.
I still have the final chapter and the earlier chapters to finish, but the seventeenth to the nineteenth century to me really are the golden ages of mathematics. I say this most likely because I am studying the mathematics from that period at school. I would definitely recommend this book to any math students who would like to know the context behind what they are learning in class.
As a university student who has taken and is going to take quite a few pure math courses, I started reading from Chapter 6, the seventeenth century. It was so exhilarating to read such that I didn't stop until I reached the end of Chapter 9. the nineteenth century. However, most of my enjoyment came from discovering the origins and contexts of a lot of the theorems that I have studied in my courses. When content regarding analysis came up, I was full of delight because I remember studying the theorems in class, but any content on geometry showed little appeal to me because I had never studied any sort of geometry in a classroom.
I would image then, that for those who have little exposure to pure math, the content on the development of calculus, analysis, and later on geometry and algebra, would hold little to no appeal. To get the most enjoyment out of this book, one would need to have some technical understanding of undergraduate-level mathematics up to measure theory (Lebesgue integral) in terms of analysis, group theory in term of algebra, and quite advanced as well in terms of geometry.
I still have the final chapter and the earlier chapters to finish, but the seventeenth to the nineteenth century to me really are the golden ages of mathematics. I say this most likely because I am studying the mathematics from that period at school. I would definitely recommend this book to any math students who would like to know the context behind what they are learning in class.
December 5, 2016
This is a mandatory book for those who love math.
For those who doesn't understand math, you can still read this with no difficulty. There is very little math on the book. Although, there many references on math work which might be uninteresting if the read doesn't understand math.
It is a resume of math through human history. In a nutshell, who discover what and who publish what.
For those who doesn't understand math, you can still read this with no difficulty. There is very little math on the book. Although, there many references on math work which might be uninteresting if the read doesn't understand math.
It is a resume of math through human history. In a nutshell, who discover what and who publish what.
September 28, 2023
This is the kind of book to be prescribed in colleges as starting point, before they go depth in mathematics. These helps to understand why there are lot of equations and what's the inspiration towards it. Great book. Advice to read.
February 7, 2025
Makes me wanna read more about this
May 3, 2023
The book felt more like a world history* book with mathematical concepts serving as supplementary information, rather than a book that delves solely on how mathematical concepts were developed. In other words, I think this book could actually be more suited for a general history class as well, rather than solely just a specialized history of mathematics class.
I did enjoy having a little refresher on the world's history with mathematical concepts as additional context. The text, true to its title of being 'concise', does not provide any supporting information on the mathematical concepts presented, and simply discusses them assuming that you already know the concepts. So if you're not familiar with some of the concepts, then you'd have to research on your own. I don't really think that's a large caveat though, because the book is 'concise', but again, if you're looking for insights on how mathematical concepts were historically formed, rather than the role of mathematics in shaping history, then this book is probably not for you.
* 'world history' might be too generous, as the text is quite Euro-centric. However, the author did provide a disclaimer on the larger availability of recorded history in the West (or 'the Occident' as referred to in the book) versus the East (or 'the Orient'), so I guess it's understandable.
I did enjoy having a little refresher on the world's history with mathematical concepts as additional context. The text, true to its title of being 'concise', does not provide any supporting information on the mathematical concepts presented, and simply discusses them assuming that you already know the concepts. So if you're not familiar with some of the concepts, then you'd have to research on your own. I don't really think that's a large caveat though, because the book is 'concise', but again, if you're looking for insights on how mathematical concepts were historically formed, rather than the role of mathematics in shaping history, then this book is probably not for you.
* 'world history' might be too generous, as the text is quite Euro-centric. However, the author did provide a disclaimer on the larger availability of recorded history in the West (or 'the Occident' as referred to in the book) versus the East (or 'the Orient'), so I guess it's understandable.
February 7, 2025
Extremely what it says on the tin -- concise almost to the point of terseness. The early parts on math of antiquity have more of a historical/sociological view: the aridity of Platonic idealism deriving from the conservativism and inertia of a slaveholding aristocracy, lots of stuff about static "Oriental" ways of life (🤷🏻) versus dynamism of the Med, etc. This is the place where any of the author's Marxist bona fides are I guess best on display. Everything after the middle ages becomes much more personalized and closer to ET Bell type history. There are a few scattered references to how industrialization affected the academic landscape in the 19th century, but it doesn't have much incisive bite.
He really does persuade you what a genius Archimedes was, as well as Leibniz, Euler, Riemann, Poincare, but unless you already know what e.g. a doubly-periodic function is, the litany of accomplishments will sound like medaling in a unknown sport.
Nice description of the gradual development of calculus. Gets lots of funny digs in at the backwardness of English academia's Newton-fetish retarding their science well into the 19th century. Had to ding him for describing the publication of Russell and Whitehead's book as the crescendo of mathematical logic -- Struik's book was published in 1948 so he should have known better!
He really does persuade you what a genius Archimedes was, as well as Leibniz, Euler, Riemann, Poincare, but unless you already know what e.g. a doubly-periodic function is, the litany of accomplishments will sound like medaling in a unknown sport.
Nice description of the gradual development of calculus. Gets lots of funny digs in at the backwardness of English academia's Newton-fetish retarding their science well into the 19th century. Had to ding him for describing the publication of Russell and Whitehead's book as the crescendo of mathematical logic -- Struik's book was published in 1948 so he should have known better!
November 5, 2023
A great bird's-eye view of the development of mathematics from the very beginnings of civilisation to the (at time of writing) modern day.
Though the book is, as the title clearly demarcates, concise in its treatment of the subject matter, it invites further study to almost each and every paragraph. The limited number of pages spent on such an overwhelmingly large topic is more than compensated for by the rightfully efficient construction of each paragraph. As such, it provides a great starting point for exploring the history of mathematics. Of course, the terse use of language means some parts of the book could do with some more exposition to properly drive home the point. However, it should rightfully be noted that the details are best left to deep dives into the topics at hand, whereas this book is meant more as the kiddy-pool in which to discover which topics to even consider diving into.
Though the book is, as the title clearly demarcates, concise in its treatment of the subject matter, it invites further study to almost each and every paragraph. The limited number of pages spent on such an overwhelmingly large topic is more than compensated for by the rightfully efficient construction of each paragraph. As such, it provides a great starting point for exploring the history of mathematics. Of course, the terse use of language means some parts of the book could do with some more exposition to properly drive home the point. However, it should rightfully be noted that the details are best left to deep dives into the topics at hand, whereas this book is meant more as the kiddy-pool in which to discover which topics to even consider diving into.
March 26, 2024
TL; DR: When Struik said "concise", he really meant it.
A Concise History of Mathematics is certainly that. There is zero fluff here; every sentence is purely factual, and there are no narrative characteristics whatsoever. This makes it brutal to read, because there is no rhythm to the writing and no time to absorb any of the information; as soon as one sentence is done, here comes more info. It's also unfriendly to a casual reader, containing tons of unexplained mathematical jargon that made it even more difficult to slug through. To be fair, it’s probably an impossible task to cover thousands of years of mathematics in just 200 pages, but the attempt could have been done in a more reader-friendly way. To those interested in the history of math, I would suggest looking elsewhere.
Grade: D+
A Concise History of Mathematics is certainly that. There is zero fluff here; every sentence is purely factual, and there are no narrative characteristics whatsoever. This makes it brutal to read, because there is no rhythm to the writing and no time to absorb any of the information; as soon as one sentence is done, here comes more info. It's also unfriendly to a casual reader, containing tons of unexplained mathematical jargon that made it even more difficult to slug through. To be fair, it’s probably an impossible task to cover thousands of years of mathematics in just 200 pages, but the attempt could have been done in a more reader-friendly way. To those interested in the history of math, I would suggest looking elsewhere.
Grade: D+
January 8, 2026
A pretty good intro to the history of math. Super short, but covers a lot of ground. Unlike most books on math history which are unimaginably boring and have hundreds of unexplained deprecated math terms on each page, this book is just pretty boring and has almost no unexplained deprecated math terms on a given page. The bad thing is that, because of its length, someone like Euler will only be written about for like two pages, and someone like Fourier is lucky to get a paragraph. But a pretty perfect way to whet your appetite and get a sense of which people/places/time periods you want to know more about.
March 2, 2024
Adoro como o Struik introduz a matemática junto aos aspectos sociais e nos faz ter uma visão ampla acerca da relação dialética que uma tem com a outra. Para os que já tem algum background filosófico eventualmente vão se encontrar discordando de algumas opiniões dele, entretanto, me parece uma leitura essencial na área de história da matemática, junto ao Boyer. Espero reler num futuro onde possa ler calmamente e apreciar, sentir, a história e a matemática passando diante de meus olhos, rápido o suficiente para assimilar porém devagar o suficiente para entender que algo de especial ocorreu.
September 27, 2020
The title of this book is just what it is. If you throw out all of the highly advanced mathematical references and just pay attention to the actual history of the people, you would be better served. Unless you're a mathematician, you'll be lost. But it was the author's intention to keep it concise, and that is what he did.
March 16, 2021
This book lives up to its title: it is very concise. I enjoyed reading the sections on 18th to 20th century mathematics, mostly because I had enough background on the developments and the principal researchers to fill in gaps for those sections. The remaining sections felt too much like a listing of events.
March 9, 2025
Thoroughly enjoyed the start of the book and how it explains the origins of mathematics and it’s simultaneous development in societies across the world before globalisation but later on I found it become too much of a list of mathematicians and their papers rather than a history on the development of maths and its impacts.
May 10, 2017
Not as good as I hoped
It started out ok, but the last few chapters are just a barrage of names and subjects with no real look at the underlying ideas. The Kindle edition also has problems with some of the formatting, turning exponents into footnotes.
It started out ok, but the last few chapters are just a barrage of names and subjects with no real look at the underlying ideas. The Kindle edition also has problems with some of the formatting, turning exponents into footnotes.
March 12, 2018
I found this dull and, though crammed with data, pretty uninformative. Read Morris Kline's "Mathematics and (or in) Western Culture" instead.
February 15, 2021
bit dry, bit male and euro-centric, and a bit out-dated
March 23, 2021
This book is excellent if you are having trouble sleeping. If you are masochistic this may also be a book you would like.
May 2, 2021
A humbling book. Do not expect hand-holding, especially in the final chapters. I feel like I spent more time reading Wikipedia than the book, but the was an intellectually rewarding experience.
July 20, 2022
Dense, really dense. But thorough. More of a reference book.
August 22, 2025
ربما تاريخ الرياضيات هو موجز تاريخ الكون والحضارة
February 15, 2016
I gave this book two stars for several reasons. First off, after getting past chapter seven, this got boring really fast. For that reason, there was really not anything new to be exposed to except the same mathematicians who discovered the same things that you would see today in Calculus and Differential Equations
October 16, 2016
This started quite well but turned into a way of beating myself up with my own ignorance. If the later chapters had been as detailed as the earlier ones I'd have felt a little bit less dim. Then George Boole popped up and for almost half a page I knew what he was talking about and then - oh no, he's gone, I'm thick again...
October 21, 2025
¡Y tan conciso que es! Es un libro que solo tiene sentido leer si cuentas con un enorme bagaje matemático. Si no, no te enteras de nada, es como si te contaran la historia de un país del que nunca has oído hablar, usando muchos nombres propios y tecnicismos...
January 30, 2013
I'm disappointed because the book is just a list of people and the texts they've written essentially. What I'm really looking for is context around mathematical discoveries.
January 7, 2014
so far so good
i'll finish this book some other time
stopped at: somewhere around ancient orient or greece
i'll finish this book some other time
stopped at: somewhere around ancient orient or greece
September 5, 2016
The 30000 foot view.....dense math terms and topics, but does give a good overview.
Displaying 1 - 27 of 27 reviews