What do you think?
Rate this book
Une brève histoire des maths
In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure.
Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt.
The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.
Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt.
The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.
192 pages, Paperback
First published January 1, 2004
44 people are currently reading
515 people want to read
About the author
David Berlinski
31 books265 followersDavid Berlinski is a senior fellow in the Discovery Institute’s Center for Science and Culture.
Recent articles by Berlinski have been prominently featured in Commentary, Forbes ASAP, and the Boston Review. Two of his articles, “On the Origins of the Mind” (November 2004) and “What Brings a World into Being” (March 2001), have been anthologized in The Best American Science Writing 2005, edited by Alan Lightman (Harper Perennial), and The Best American Science Writing 2002, edited by Jesse Cohen, respectively.
Berlinski received his Ph.D. in philosophy from Princeton University and was later a postdoctoral fellow in mathematics and molecular biology at Columbia University. He has authored works on systems analysis, differential topology, theoretical biology, analytic philosophy, and the philosophy of mathematics, as well as three novels. He has also taught philosophy, mathematics and English at Stanford, Rutgers, the City University of New York and the Université de Paris. In addition, he has held research fellowships at the International Institute for Applied Systems Analysis in Austria and the Institut des Hautes Études Scientifiques. He lives in Paris.
Recent articles by Berlinski have been prominently featured in Commentary, Forbes ASAP, and the Boston Review. Two of his articles, “On the Origins of the Mind” (November 2004) and “What Brings a World into Being” (March 2001), have been anthologized in The Best American Science Writing 2005, edited by Alan Lightman (Harper Perennial), and The Best American Science Writing 2002, edited by Jesse Cohen, respectively.
Berlinski received his Ph.D. in philosophy from Princeton University and was later a postdoctoral fellow in mathematics and molecular biology at Columbia University. He has authored works on systems analysis, differential topology, theoretical biology, analytic philosophy, and the philosophy of mathematics, as well as three novels. He has also taught philosophy, mathematics and English at Stanford, Rutgers, the City University of New York and the Université de Paris. In addition, he has held research fellowships at the International Institute for Applied Systems Analysis in Austria and the Institut des Hautes Études Scientifiques. He lives in Paris.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 43 reviews
November 23, 2016
For geeks that at one time knew what a partial differential equation was or for non-geeks interested in what math geeks get orgasms over, this book is an easy to read but fascinating voyage into math geekdom. Several number theories are explained and some biographies (I was most fascinated with Cantor!) are given and the reader (unless s/he is already a PhD in mathematics for which this is all oh-so-boring) is drawn into the debates and challenges of modern mathematics. I would gladly read a second volume should one ever exist. An excellent layman's introduction!
October 8, 2023
I hate math, but I thought I'd go ahead and dip my toe in it.
Although I was often lost in the detailed explanations of the abstract theories that were the most innovative in the history of mathematics, David Berlinski's writing style is ultimately what made this history bearable.
Because when he seemed to be truly lost in describing these mathematical concepts, he was quick to relate to the common reader who was lost (as I was) with a clever wink and a "...yeah I know. Blah blah blah."
It probably would've been much better if my math knowledge was.
Although I was often lost in the detailed explanations of the abstract theories that were the most innovative in the history of mathematics, David Berlinski's writing style is ultimately what made this history bearable.
Because when he seemed to be truly lost in describing these mathematical concepts, he was quick to relate to the common reader who was lost (as I was) with a clever wink and a "...yeah I know. Blah blah blah."
It probably would've been much better if my math knowledge was.
April 4, 2008
Though at first I was reluctant to read a book about math, this one actually turned out to be quite interesting. Upon strong urging from a teacher, I was persuaded into reading this book. The book details the history of math in a surprisingly engaging, enlightening way. It is not so much about the math itself as it is about the people behind it; the text is more of a detailed biography of the sociological aspects of the development of mathematical thought over time than anything else. Though Berlinski addresses some intimidating topics and theories I have never heard of, he does so in a way that is easy to understand and rarelyoverwhelming. A dual math and english connoisseur, Berlinski marries his two great talents exquisitely through this text. His superb command of language is pervasive throughout the book, and sometimes his use and plays on words are more impressive than what he is actually using them to say. This book was certainly the first of its kind that I have ever read, but I must say I was very pleased with it in the end. It turned out to be the product of great intellect, and the union of the fields of math, english, and history, in such a way that is rarely explored, and even more rarely done so finely.
October 6, 2014
Hrvatski prijevod je tragičan, na svako drugoj stranici je neka pogreška- posebno u formulama.
Unatoč tome, knjiga je zanimljiva ali dosta slična drugim knjigama na istu temu.
Unatoč tome, knjiga je zanimljiva ali dosta slična drugim knjigama na istu temu.
December 8, 2015
I'm not really quite sure for whom this book was written, but it was assuredly not meant for me.
Though I appreciate his attempt (and more so the publisher's fortitude) to include some very simple equations and even the occasional proof, I have a feeling they're likely lost on much of his readership due to general presentational style and didactic modality. Those who are seeing this material for the first time may enjoy some of the flowery language and impassioned approach to mathematics, but are likely completely lost from a mathematical standpoint. Most generally serious mathematical students who have likely seen two or more of his general subjects would otherwise appreciate this type of exposition are likely put off by the poor writing style and lack of what could have been a tad more math and a far better historical presentation. In trying to reach too many audiences, I have a feeling he's lost them all.
The text is an all-too-quick survey of some of the larger concepts in mathematical history with only brief excursions into the mathematicians' personalities and backgrounds. While trying to cover the history, the personalities, the philosophies, and even some of the math simultaneously he gives short shrift to all four.
Many concepts, particularly early on are all too quickly glossed over and often not even in complete or coherent thoughts. Berlinski often uses the ellipses (the grammatical ones, not the mathematical ones) not only to poor effect, but he actually goes so far as to pat himself on the back for it.
His overall coverage of the history and characters involved is scant at best in comparison to various other books in this category. Most egregiously I get the feeling that in general he's parroting back much of what is already written in the generic mathematical literature without providing any particularly interesting perspective of his own. Worse yet, there are no discernible references to other works for those wishing to delve deeper. If there were at least a clear thread tying all of the generally disparate chapters together into a more cogent whole representing the current state of mathematics, I would have felt more fulfilled and felt that the author had made an interesting and original contribution to the broad general literature, but alas, even this was wholly missing.
Many of his historical sketches aren't as well put together, thorough or well-referenced as an average Wikipedia article on any of these subjects. In some cases, particularly relating to early mathematicians as Pythagoras and Euclid, despite saying explicitly that very little exists about their actual lives, he proceeds swiftly to wax far more poetic about them than the historical record could possibly allow.
In sum, I'd recommend the interested reader to spend some time reading Euclid's elements, or delving into Galois' back story directly instead of reading this treatise. At best, I had hoped that Berlinski might do for mathematics what Simon Singh did for physics in Big Bang, but he seems to have fallen far too short; perhaps in his second draft he'll do better.
Though I appreciate his attempt (and more so the publisher's fortitude) to include some very simple equations and even the occasional proof, I have a feeling they're likely lost on much of his readership due to general presentational style and didactic modality. Those who are seeing this material for the first time may enjoy some of the flowery language and impassioned approach to mathematics, but are likely completely lost from a mathematical standpoint. Most generally serious mathematical students who have likely seen two or more of his general subjects would otherwise appreciate this type of exposition are likely put off by the poor writing style and lack of what could have been a tad more math and a far better historical presentation. In trying to reach too many audiences, I have a feeling he's lost them all.
The text is an all-too-quick survey of some of the larger concepts in mathematical history with only brief excursions into the mathematicians' personalities and backgrounds. While trying to cover the history, the personalities, the philosophies, and even some of the math simultaneously he gives short shrift to all four.
Many concepts, particularly early on are all too quickly glossed over and often not even in complete or coherent thoughts. Berlinski often uses the ellipses (the grammatical ones, not the mathematical ones) not only to poor effect, but he actually goes so far as to pat himself on the back for it.
His overall coverage of the history and characters involved is scant at best in comparison to various other books in this category. Most egregiously I get the feeling that in general he's parroting back much of what is already written in the generic mathematical literature without providing any particularly interesting perspective of his own. Worse yet, there are no discernible references to other works for those wishing to delve deeper. If there were at least a clear thread tying all of the generally disparate chapters together into a more cogent whole representing the current state of mathematics, I would have felt more fulfilled and felt that the author had made an interesting and original contribution to the broad general literature, but alas, even this was wholly missing.
Many of his historical sketches aren't as well put together, thorough or well-referenced as an average Wikipedia article on any of these subjects. In some cases, particularly relating to early mathematicians as Pythagoras and Euclid, despite saying explicitly that very little exists about their actual lives, he proceeds swiftly to wax far more poetic about them than the historical record could possibly allow.
In sum, I'd recommend the interested reader to spend some time reading Euclid's elements, or delving into Galois' back story directly instead of reading this treatise. At best, I had hoped that Berlinski might do for mathematics what Simon Singh did for physics in Big Bang, but he seems to have fallen far too short; perhaps in his second draft he'll do better.
July 29, 2020
The author is an arrogant ass. If you can get past that, it's an entertaining and unique retelling of the history of mathematics.
February 10, 2010
I am about three quarters through this book. I took algebra I in high school (hated it), then geometry (loved it), then quit. In college I took matrix algebra (did not understand either the subject or how I squeeked by with a C-), and then elementary functions (I followed it better and got a B-). Curiously, I scored better on aptitude tests for math than language. 20 years later I taught a 6/7/8 grade class, all subjects including math, and I began to learn what they tried to teach me in school, and even began to enjoy some of it (I had a teaching certificate that said I was licensed to teach all subjects in grades 7&8, including those I had not actually studied myself...). With this background, 18 years later, I approached Berlinski's book. It looked like the right size for me, not too long. But it presumes a little more background knowledge than I possess. The elegantly written prose, with a touch of condescension toward readers like myself (well-deserved might I add), is enjoyable, but I got the impression that I wasn't catching all of the jokes. Never-the-less, I am finding it well-worth the read, and like many a book, the more I get into it, the better I follow. It provides an interesting glimpse into the world of the few who understand what's gowing on (mathematically speaking), and it is bracing.
July 29, 2015
Berlinksi gets tingles up and down his spine when an elegant proof reaches a surprising conclusion, but what really turns him on is smart men losing intellectual pissing contests to even smarter men. It is possible that his own excitement and passion might inspire readers to study math, but that his not his intention. In addition to crowing about his own ability to follow others' mental gymnastics, he manages to fire off a great deal of misanthropy and to generally reinforce the wall of misogyny that has kept women out of this field and out of his history of it.
As someone else already said in another review, if you are already familiar with the math he is talking about you'll find the history a little thin and if you are not familiar with the math, you probably won't be able to follow his explanations of it. Berlinski takes mathematical proofs and concepts as starting off points for metaphors and brief but detailed images so that Gödel's theorem becomes a story about pony-tailed film editors and long-legged Bryn Mawr film studies graduates. Not amusing and not helpful, there are more spine-tingling moments in your average geometry textbook.
As someone else already said in another review, if you are already familiar with the math he is talking about you'll find the history a little thin and if you are not familiar with the math, you probably won't be able to follow his explanations of it. Berlinski takes mathematical proofs and concepts as starting off points for metaphors and brief but detailed images so that Gödel's theorem becomes a story about pony-tailed film editors and long-legged Bryn Mawr film studies graduates. Not amusing and not helpful, there are more spine-tingling moments in your average geometry textbook.
March 7, 2008
I'm glad I started reading this book after I discovered that the author is a 'senior fellow at the Discovery Institute' (ew!). Because this is a nice little (181 pages) introduction to the major innovations in mathematics throughout history. Because it's short the author makes little mention of the Babylonian or Islamic periods. He skips from ancient Greece to Descartes quickly. His writing at times can be almost poetic, it's clear he loves his subject and has unlimited respect for the geniuses of mathematics. Sometimes his lyrical writing gets a bit much in places where I would have preferred a straighter explanation of the concepts. And I do get a whiff of contempt here and there for us non-geniuses. But over all I recommend this primer to mathematics, the chapters titles tell you exactly what it covers: Number, Proof, Analytic Geometry, The Calculus, Complex Numbers, Groups, Non-Euclidean Geometry, Sets, Incompleteness and The Present.
November 10, 2009
Berlinski's Short History is a quirky rollercoaster ride through the big ideas of math from Pythagoras to Mandelbrot. He fills the story with interesting and odd anecdotes like the mathematician who quickly wrote out a proof of group theory on the night before he was destined to die in a duel. Overall, it is a good review of the major concepts of math as they developed. That said, I have to say that Berlinski lost me somewhere in the 19th century and about 2/3 of the way through the book when he started discussing non-Euclidean geometry and then the 20th century work in incompleteness. I felt like I really needed to have background experience in the more recent work in the field to make any sense of concepts that are outside of calculus and some discrete mathematics. Ultimately this a book for folks with at least a basic background in advanced mathematics.
June 15, 2014
# infinite ascent - a short history of mathematics
## by David Berlinski
ISBN 0-679-64234-X
I enjoyed reading this book. I love reading history, I love mathematics, I reserve time in my busy schedule to read as much philosophy as I can. This book has all three subjects; it’s well written, concise, and has many concrete examples of the significant contributors and discoveries made through the human curiosity of the only pure science - and my first love - mathematics. This is the first and only book I’ve read by Mr. Belinski- I hope to pick up another of his books again someday soon.
Shelves: Owned, Re-read
Read more at [Goodreads.com]
Filed under: Book Reviews, Mathematics
Posted to: [http://philchartrand.com]
## by David Berlinski
ISBN 0-679-64234-X
I enjoyed reading this book. I love reading history, I love mathematics, I reserve time in my busy schedule to read as much philosophy as I can. This book has all three subjects; it’s well written, concise, and has many concrete examples of the significant contributors and discoveries made through the human curiosity of the only pure science - and my first love - mathematics. This is the first and only book I’ve read by Mr. Belinski- I hope to pick up another of his books again someday soon.
Shelves: Owned, Re-read
Read more at [Goodreads.com]
Filed under: Book Reviews, Mathematics
Posted to: [http://philchartrand.com]
March 17, 2010
This book could have done with more graphics and less self-importance. Still, it is about Mathematics.
January 4, 2024
once again, David Berlinski has caused me to learn something
While I was in college, I wanted to take the course, ‘history of mathematics’, which was taught by the department of mathematics. I was disappointed to learn that this class was unavailable to me because I had not successfully completed calc II. I really wanted to study this subject. However, my career in mathematics was cut short by this very subject, my brain being unable to accept that the determining of an area under a curve could be achieved by using infinitely small rectangles. (Some of you know that this is the very beginning of calculus class and that if you don’t get it here, it’s over) My professor, Dr. Young, at the University of Akron, politely and kindly stated one day that he could not make Mozarts out of us. Maybe we should try history if we don’t understand calculus. I took his advice to heart and graduated with that degree in history. Nonetheless, I still attempt math, largely thanks to YouTube and books like this. Maybe one day I will retake that college course and ace it. Until then, David Berlinsky produced this wonderful book. I understood it completely up until halfway through the chapter on Descartes, or “Dess Carties” as it is pronounced by most college students. It is not replete, but it is close and it has reawakened within me that desire to learn more, which is the usual for anything by David Berlinski. This book might be more interesting to those who have successfully completed a degree in mathematics, those smart people that I am still a little jealous of.
While I was in college, I wanted to take the course, ‘history of mathematics’, which was taught by the department of mathematics. I was disappointed to learn that this class was unavailable to me because I had not successfully completed calc II. I really wanted to study this subject. However, my career in mathematics was cut short by this very subject, my brain being unable to accept that the determining of an area under a curve could be achieved by using infinitely small rectangles. (Some of you know that this is the very beginning of calculus class and that if you don’t get it here, it’s over) My professor, Dr. Young, at the University of Akron, politely and kindly stated one day that he could not make Mozarts out of us. Maybe we should try history if we don’t understand calculus. I took his advice to heart and graduated with that degree in history. Nonetheless, I still attempt math, largely thanks to YouTube and books like this. Maybe one day I will retake that college course and ace it. Until then, David Berlinsky produced this wonderful book. I understood it completely up until halfway through the chapter on Descartes, or “Dess Carties” as it is pronounced by most college students. It is not replete, but it is close and it has reawakened within me that desire to learn more, which is the usual for anything by David Berlinski. This book might be more interesting to those who have successfully completed a degree in mathematics, those smart people that I am still a little jealous of.
August 23, 2019
Not my favorite book on math I have ever read. The first two chapters were almost a chore to read. It did get better though.
The things I liked. He tried to reference lots of other fields and areas of life (e.g. so-and-so occupies the same place in mathematics that this other guy occupies in music). I imagine this makes easier for a broader audience to make connections. I also like that he mentions a lot of people that get over looked but laid important groundwork for those that get credit for starting a new field. Lastly, I like the amount of material he covers (including, groups, set, and completeness). A lot of books I have read do not (or hardly touch) these fields unless they are they main topic.
I really did not like his writing style it was very informal and conversational. I am sure he would be wonderful at lecturing but for reading this is a bad way to write. For a book on mathematics his writing style was especially poor. Much of it felt ethereal which is jarring when reading about something so precise.
The things I liked. He tried to reference lots of other fields and areas of life (e.g. so-and-so occupies the same place in mathematics that this other guy occupies in music). I imagine this makes easier for a broader audience to make connections. I also like that he mentions a lot of people that get over looked but laid important groundwork for those that get credit for starting a new field. Lastly, I like the amount of material he covers (including, groups, set, and completeness). A lot of books I have read do not (or hardly touch) these fields unless they are they main topic.
I really did not like his writing style it was very informal and conversational. I am sure he would be wonderful at lecturing but for reading this is a bad way to write. For a book on mathematics his writing style was especially poor. Much of it felt ethereal which is jarring when reading about something so precise.
July 10, 2017
David Berlinski tackles the history of mathematics in his book Infinite Ascent. Within its pages he highlights the important discoveries from Pythagoras to present day. I have to admit, I honestly got lost many times while reading this piece. David has his PhD in mathematics and he would often try to explain the process of a specific, groundbreaking proof. Since I haven't taken math in nearly 10 years and only went up to calculus quite a bit was “Greek to me.” What's more, is if I did try to follow it I'd discover three pages later that the proof has been disproven and not applied modern mathematics. His writing style was also a bit confusing. He'd switch between storytelling and lecturing and back to storytelling without any narration to indicate that was what he was doing.
February 9, 2024
i cannot believe i finished this book. enormous effort. i really should not have. at first i was like aw it's poetic but very soon it became apparent that it's RIDICULOUSLY pretentious. the contempt throughout the narration is CRAZY. how are you gonna be like omg i can't Believe they didn't figure this out it's so obvious HUH??? the LAST attitude a math/science history writer should ever have wtf?? the math itself,, i mean if you didn't know the math before this certainly will not teach you. HUGE waste of time with this book the only thing i got out of it was 1) it was occasionally funny and 2) it's always great to learn anything about the personal lives of historical figures known only for their achievements. but overall: SO bad. do not recommend.
November 10, 2017
Infinite Ascent is an overview by an accomplished mathematician of the major advances in mathematics since the Greeks. It is clearly written and gives enough explanation of difficult subjects to help them make some sense. In one chapter, for instance, he gives an explanation of Goedel's proof that makes as much sense as the whole of Goedel, Escher, and Bach conveyed, without of course the beautiful pictures.
This is a book for exploring the territory, but it is unlikely to be used for references. It seems to me that it is a grownup version of the famous 1, 2, 3, Infinity when I was an adolescent.
This is a book for exploring the territory, but it is unlikely to be used for references. It seems to me that it is a grownup version of the famous 1, 2, 3, Infinity when I was an adolescent.
February 8, 2021
This book began very interestingly. I was enjoying it until just after halfway through. At that point it really started to drag. The last chapter was amusing to me though.
As a person with a B.A. in Eng & Am Lit, who did well in math growing up, I did enjoy the prose and approach to this book. I appreciated the in-depth discussions of some of the classic thinkers and their work. After chapters 7 (Non-Euclidean Geometry) & 8 (Sets), my enthusiasm was really starting to wane. At that point, reading felt more like work than enjoyment, and yes, I initially read this book for informative enjoyment. It's a good read, but definitely not one of my tops.
As a person with a B.A. in Eng & Am Lit, who did well in math growing up, I did enjoy the prose and approach to this book. I appreciated the in-depth discussions of some of the classic thinkers and their work. After chapters 7 (Non-Euclidean Geometry) & 8 (Sets), my enthusiasm was really starting to wane. At that point, reading felt more like work than enjoyment, and yes, I initially read this book for informative enjoyment. It's a good read, but definitely not one of my tops.
June 29, 2023
Not for Newbs
I could follow the first 2-3 chapters, but I did not comprehend much, if anything, after that. The writing style - particularly, asides other needless distractions, and some run on sentences - was annoying at times. However, overall, the writing was nicely fluid. I learned some new names and concepts to follow up on. The book would probably be best appreciated by individuals who have been exposed to mathematics subjects that are generally learned after calculus.
I could follow the first 2-3 chapters, but I did not comprehend much, if anything, after that. The writing style - particularly, asides other needless distractions, and some run on sentences - was annoying at times. However, overall, the writing was nicely fluid. I learned some new names and concepts to follow up on. The book would probably be best appreciated by individuals who have been exposed to mathematics subjects that are generally learned after calculus.
August 28, 2017
A good history of math for layman like myself.
October 11, 2018
Great content about selected topics in the history of mathematics, although I found some chapters barely readable
February 8, 2021
The author’s a bit full of himself
December 30, 2021
Very very cool argument at the end about pure math being the most important driver of progressions in science! Would love to hear more about that. Will check out more STEM history
March 27, 2012
It's short. Ten chapters, with about as many concepts explored. It may be a fun reminder if you're familiar with the history of mathematics; it may infuriate you because of its omissions or because of Berlinski's writing style, which sometimes illuminates and entertains, sometimes confuses, and sometimes even left me dazed. I suspect most readers will either love his style or hate it.
My extremely brief summary of Infinite Ascent, using Berlinski's chapter titles, is subtitled A Shorter History of Mathematics: Number - The Pythagoreans believed that numbers underlie reality; an influential idea from then to now. Proof - Arguments in mathematics use a structure basically unchanged since Euclid's Elements. Analytic Geometry - The Cartesian coordinate system united numbers and geometry. Geometric objects became identified with numbers and equations, sparking new investigations. The Calculus - Calculus, extremely useful because of its success modeling continuous change, caused mathematics to become fundamental in the study of the physical sciences. Integration and differentiation are 'inverse operations'. Complex Numbers - The square root of minus one plagued mathematicians. Euler used complex numbers, which incorporate the square root of minus one, to discover relationships and make connections between trigonometric and exponential functions. It didn't stop there either. Groups - I think Evariste Galois used groups to approach equations in new ways. Membership in various groups reveals a problem's solvability while also affirming the fundamental importance of numbers. Non-Euclidean Geometry - Doubts about Euclid's parallel postulate led to its replacement. Eventually Bernhard Riemann focused on coordinates only, the local area, eliminating any focus on the background, the plane. His analysis utilized calculus. Whatever the dimensions, however impossible to visualize, numbers determine points. Sets - Sets replaced numbers. Examining infinite sets resulted in wholes that are not greater than their parts. Georg Cantor's 'tools and techniques' permeate mathematics. Incompleteness - By assigning prime numbers to mathematical symbols, formulas, and series, Kurt Godel demonstrated that axiomatic systems can't be completely consistent. They will always produce some false statements and/or fail to produce some true statements. The Present - The algorithm is one of mathematics biggest contributions. Computers have not changed the practice of mathematics very much.
If I misunderstood something, let me know.
The best thing about this book: it made me want to try solving problems in a text book.
My extremely brief summary of Infinite Ascent, using Berlinski's chapter titles, is subtitled A Shorter History of Mathematics: Number - The Pythagoreans believed that numbers underlie reality; an influential idea from then to now. Proof - Arguments in mathematics use a structure basically unchanged since Euclid's Elements. Analytic Geometry - The Cartesian coordinate system united numbers and geometry. Geometric objects became identified with numbers and equations, sparking new investigations. The Calculus - Calculus, extremely useful because of its success modeling continuous change, caused mathematics to become fundamental in the study of the physical sciences. Integration and differentiation are 'inverse operations'. Complex Numbers - The square root of minus one plagued mathematicians. Euler used complex numbers, which incorporate the square root of minus one, to discover relationships and make connections between trigonometric and exponential functions. It didn't stop there either. Groups - I think Evariste Galois used groups to approach equations in new ways. Membership in various groups reveals a problem's solvability while also affirming the fundamental importance of numbers. Non-Euclidean Geometry - Doubts about Euclid's parallel postulate led to its replacement. Eventually Bernhard Riemann focused on coordinates only, the local area, eliminating any focus on the background, the plane. His analysis utilized calculus. Whatever the dimensions, however impossible to visualize, numbers determine points. Sets - Sets replaced numbers. Examining infinite sets resulted in wholes that are not greater than their parts. Georg Cantor's 'tools and techniques' permeate mathematics. Incompleteness - By assigning prime numbers to mathematical symbols, formulas, and series, Kurt Godel demonstrated that axiomatic systems can't be completely consistent. They will always produce some false statements and/or fail to produce some true statements. The Present - The algorithm is one of mathematics biggest contributions. Computers have not changed the practice of mathematics very much.
If I misunderstood something, let me know.
The best thing about this book: it made me want to try solving problems in a text book.
March 11, 2017
I looked forward to reading this book and anticipated liking it; I have always liked math and numbers, and to learn the history of mathematical findings and the context in which discoveries were made seemed to me an engrossing prospect. In this book I was hoping to find a narrative that would reinvigorate my passion for numbers just as The Food Lab: Better Home Cooking Through Science inflamed my love of kitchen chemistry and A Dash of Style: The Art and Mastery of Punctuation reinforced and intensified my zeal for punctuation, but I would have settled for merely a straightforward history.
Unfortunately, Berlinski is a little too enamored of using abstruse phrasings and metaphors to describe or illustrate the historical anecdotes and mathematical concepts he surveys in this book. Chapter after chapter, I had the impression that he was infatuated with his own grandiloquent ways of saying things, and I was left reading over a sentence or a paragraph again, wondering if there wasn't a clearer and simpler way of conveying the same point.
Did I learn something, despite all that? Yes, I know more about the history of mathematics now, and that was my purpose for reading the book, so I do not regret spending my time on it. But did I like the book? Ehh... I desired to like it, but no matter how much I wanted to, I couldn't. Perhaps I would have appreciated Berlinski's rambles more if I were conversant in higher mathematics, because I had no trouble grasping the algebraic concepts (even though incompleteness and non-Euclidean geometry got crazy), but even so, his style vexed me and I kept feeling that he was bloviating on a hobbyhorse rather than lucidly laying out a history.
2.5 stars, rounded up to 3 because I did learn something.
Unfortunately, Berlinski is a little too enamored of using abstruse phrasings and metaphors to describe or illustrate the historical anecdotes and mathematical concepts he surveys in this book. Chapter after chapter, I had the impression that he was infatuated with his own grandiloquent ways of saying things, and I was left reading over a sentence or a paragraph again, wondering if there wasn't a clearer and simpler way of conveying the same point.
Did I learn something, despite all that? Yes, I know more about the history of mathematics now, and that was my purpose for reading the book, so I do not regret spending my time on it. But did I like the book? Ehh... I desired to like it, but no matter how much I wanted to, I couldn't. Perhaps I would have appreciated Berlinski's rambles more if I were conversant in higher mathematics, because I had no trouble grasping the algebraic concepts (even though incompleteness and non-Euclidean geometry got crazy), but even so, his style vexed me and I kept feeling that he was bloviating on a hobbyhorse rather than lucidly laying out a history.
2.5 stars, rounded up to 3 because I did learn something.
May 2, 2015
The author provides a rich historical understanding of the development of the various disciplines of mathematics: algebra, geometry, algebraic geometry,probability, the theory of finite simple groups, partial differential equations, algebraic topology . . . (the use of an "elipse" being a favorite device among mathematicians, so I learned). However, the author, most certainly an accomplished mathematician in his own right, writes in a manner that borders on 'losing' the lay reader such as myself. The material being covered kept me pushing forward in my reading despite the author's sometimes unclear presentation of the content. (But of course, that could have been due to my lay person's level of understanding of the subject matter.) Even so, I will read other works by Mr. Berlinski.
March 15, 2016
The first sentence, "The history of mathematics begins in 532 BC, the date marking the birth of the Greek mathematician Pythagoras," made me question the author's understanding of history. Hasn't he even heard of Babylonian mathematics? In fact, history is not the strength of this book, nor is the style intended to make the lay reader more comfortable. (I bridled at his admonition after a somewhat technical definition of Groups for the reader to relax and "have a cigarette." Barely appropriate in 1955, definitely not in 2005.) I did appreciate his willingness to provide more of the technical detail than most popular histories of math, especially in the chapters on Complex Numbers and Group Theory, although he lost me in the chapter on Incompleteness.
July 9, 2013
Even though most of the concepts were either nearly or completely incomprehensible to me, this short book has inspired me to give math another chance. The branch of mathematics I thought was explained very lucidly was meta- mathematics. Its association with the philosophy of language was most fascinating. This book is a testament to the fact that an imagination is just as essential to understanding math as much as a logical mind is. I envy the author, who can admire the complexity of such enigmas and describe the studying of them being like, "first love". Maybe one day I'll too have such an experience with math.
July 19, 2015
The Mathematical topics covered, and the depth to which they are covered make for enjoyable reading. The survey of several different areas and the history of those areas makes for a fantastic overview, almost looking onto different faces of a polyhedron, where each side is just glimpse of the whole. My major dislike of this book is that the author seems to be writing as much about himself in the subject as the subject itself, without actually saying as much, and even some of the liberties he takes with the narrative become more distracting than amusing.
December 17, 2009
Berlinski does a quick overview of many of the intellectual leaps in mathematics since Pythagoras. This isn't a book of every formula ever -- just the results that really shook the field. I thought he did a good job of giving sort of the flavor and drama surrounding each new topic, but (unsurprisingly) it wasn't super-rigorous, so it left me wanting a more convincing argument. It was also a little too self-consciously literary/artistic for my taste.
Displaying 1 - 30 of 43 reviews