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Very Short Introductions #066
Mathematics
Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.
180 pages, Hardcover
First published January 1, 2002
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November 26, 2020
من کلاً اهل کتاب علمی خوندن نیستم و این کتاب رو به پیشنهاد یکی از دوستان خوندم. نمیتونم بگم صددرصد دوسش داشتم ولی کتاب خوبی بود و تاکیدش روی تفکر مجرد واسم جالب بود چون با چنین تفکری در هنر هم مواجه هستیم و من این تفکر را در نقاشی یاد گرفتم. در این کتاب به ارتباط تفکر مجرد و ریاضیات برخوردم که واسم خیلی جالب بود
January 24, 2017
Absolutely great. Let me explain. Firstly about the level of the book. It is elementary but not basic. There are some concepts and especially some proofs that require some focus to grasp. The amount of equations is minimal, but still some maturity is required to fully appreciate the contents. I would say that the best audience of the book is a beginning undergrad in a stem program, a motivated and mature high school students with a keen interest on maths or a layman with some maturity of mathematical concepts. I was searching for books to recommend to my students and after finishing that i would highly recommend it.
What the book does, is to introduce us to the world of mathematics, what it isall about and how mathematicians approach different ideas and the way Timothy does that is by explaining an array of different ideas from model building, basic arithmetic, formal proofs, complex numbers, number theory, coordinate systems, infinity, higher dimensions, non Eucledian geometries, approximations etc. In the final chapter there are some comments on common misconceptions about mathematics.
There are so many gems in every chapter and the way they are connected makes you understand why mathematicians treat them in that way. From the geometric(!) proof of the irrationality of φ, to ''visualizing'' objects in higher dimensions and being able to grasp some of their properties, to how the curvature of different geometries affects the shortest path.
The reason of 5 stars is all of the above plus finally understanding why airplanes tend to move towards the poles (had to finish my bachelor in physics without ever anyone touching that concept...) plus the 2 most basic ideas of the book, that the meaning of a mathematical object is the rules it obeys and how it is related to other objects and how to extend familiar ideas to unfamiliar territory. These two concepts and how the are used in what Timothy calls the ''abstract method'' are the spine of the book and worth buying just for those two only.
True gem.
What the book does, is to introduce us to the world of mathematics, what it isall about and how mathematicians approach different ideas and the way Timothy does that is by explaining an array of different ideas from model building, basic arithmetic, formal proofs, complex numbers, number theory, coordinate systems, infinity, higher dimensions, non Eucledian geometries, approximations etc. In the final chapter there are some comments on common misconceptions about mathematics.
There are so many gems in every chapter and the way they are connected makes you understand why mathematicians treat them in that way. From the geometric(!) proof of the irrationality of φ, to ''visualizing'' objects in higher dimensions and being able to grasp some of their properties, to how the curvature of different geometries affects the shortest path.
The reason of 5 stars is all of the above plus finally understanding why airplanes tend to move towards the poles (had to finish my bachelor in physics without ever anyone touching that concept...) plus the 2 most basic ideas of the book, that the meaning of a mathematical object is the rules it obeys and how it is related to other objects and how to extend familiar ideas to unfamiliar territory. These two concepts and how the are used in what Timothy calls the ''abstract method'' are the spine of the book and worth buying just for those two only.
True gem.
January 30, 2020
بسم الله
اسم الكتاب الرياضيات مقدمة قصيرة جدا
اسم الكاتب تيموثي جاورز
فكرة الكتاب تتسم في توضيح سبب تجرد الرياضيات بكونها تتعامل مع اشياء غير ملموسة للاسف قرات ما ترجم منه فقط لأنه لم تترجم جميع فصول الكتاب تطرق الكاتب لاعطاء مفهوم عن التفكير المجرد و ذلك لتبرير التقارير الحسابية كما وضح مبادئ الحساب و اسباب توسيع نظام العد من اكتشاف الصفر بعد الاعداد الطبيعية الى الاعداد السالبة ثم الكسور بعدها الاعداد النسبية الى الاعداد المركبة
وضح كذلك منهج دراسة الرياضيات التركيبي بحيث انه لم تكن تفهم الاجزاء التي تعرف الكل سيبقى الكل غامضا لديك و انا اقول من اراد ان يفهم الرياضيات.عليه ان يكثر من التعرض لها لانه ليس هناك بديلا للمارسة حتى تكشف لك اسرارها و تفهمها المحتوى بسيط و جيد لمن اراد ان يتعرف على بعض مبادئ الرياضيات الحقيقية و سبب تجردها
اسم الكتاب الرياضيات مقدمة قصيرة جدا
اسم الكاتب تيموثي جاورز
فكرة الكتاب تتسم في توضيح سبب تجرد الرياضيات بكونها تتعامل مع اشياء غير ملموسة للاسف قرات ما ترجم منه فقط لأنه لم تترجم جميع فصول الكتاب تطرق الكاتب لاعطاء مفهوم عن التفكير المجرد و ذلك لتبرير التقارير الحسابية كما وضح مبادئ الحساب و اسباب توسيع نظام العد من اكتشاف الصفر بعد الاعداد الطبيعية الى الاعداد السالبة ثم الكسور بعدها الاعداد النسبية الى الاعداد المركبة
وضح كذلك منهج دراسة الرياضيات التركيبي بحيث انه لم تكن تفهم الاجزاء التي تعرف الكل سيبقى الكل غامضا لديك و انا اقول من اراد ان يفهم الرياضيات.عليه ان يكثر من التعرض لها لانه ليس هناك بديلا للمارسة حتى تكشف لك اسرارها و تفهمها المحتوى بسيط و جيد لمن اراد ان يتعرف على بعض مبادئ الرياضيات الحقيقية و سبب تجردها
February 8, 2017
As the name suggests the book tries to tell a non-mathematician but interested person, what is Math about, what is it's goals, how mathematicians think and some techniques and results of modern and classical Math.
But for someone who is not very familiar with mathematics, it won't make any sense, for such a person this book can be hard, confusing and boring. Math was never an easy thing to understand.
Actually I think the book can be very enlightening for math undergraduate students, especially for math teachers.
The book is short, warm, rigid and has good points about how to do Math.
But for someone who is not very familiar with mathematics, it won't make any sense, for such a person this book can be hard, confusing and boring. Math was never an easy thing to understand.
Actually I think the book can be very enlightening for math undergraduate students, especially for math teachers.
The book is short, warm, rigid and has good points about how to do Math.
March 24, 2007
I generally find the "A Very Short Introduction" series to actually be quite good, with most of the volumes accomplishing exactly what they intend to by giving a good overall sense of a field of inquiry and its methods, or of the important elements of a given topic. Unfortunately, this volume did none of this very well. Many of the examples used to introduce to the reader to mathematical thinking are explained more clearly (and in a more engaging fashion) in Fermat's Enigma by Simon Singh. In general, the latter is probably a better overall introduction to the world of mathematics (both the subject as well as the academic practice) than this Very Short Introduction managed to be.
Read
January 22, 2018جميع النسخ الموجوده (pdf)
غير مكتملة
غير مكتملة
Read
July 15, 2017عندي منذ الصغر متلازمة كره الرياضيات ، في أول سنة جامعية لي قررت أن أشتري كتب في مجال الرياضيات في محاولة عبثية لأحبه ، و اشتريت هذا الكتاب من معرض القاهرة الدولي للكتاب 2015 حاولت قراءته عدة مرات و فشلت .
October 12, 2014
الكتاب صغير جدًا وجيد، فهو بسيط في عرض معلومات
الكتاب يناقش الرياضيات من الناحية الفلسفية والتجريدية
جيدٌ كبداية في معرفة الرياضيات التي تعد لغة الكون !
الكتاب يناقش الرياضيات من الناحية الفلسفية والتجريدية
جيدٌ كبداية في معرفة الرياضيات التي تعد لغة الكون !
November 14, 2015
Jedna o knjiga o matematici koju svi mogu čitati i koja opravdava svoj naslov. Neki ce možda biti razočarani jer nije detaljna, a neki što je prenapredna, ali meni se svidjela prvenstveno jer je prepuna činjenica koje do sada nisam čula ili shvatila na način objašnjen u knjizi. Preporučam je posebno onima koji misle da je matematika računanje (da vide da nije :-))
December 13, 2009
Surprisingly disappointing. I can't imagine who this book is written for. Nothing new to people who knew anything about math, and not terribly interesting to people trying to learn something about math.
February 26, 2022
I started this book nearly four days ago, through weekend with dozen amount of coffee and panic attacks (which I usually get.) finally finished this one, and here is my review on it:
Mathematica, the language of nature. wether one thinks of it as a rigid and dry subject or have the other opinion about the subject, it doesn't really matter since it works. it is fascinating when, having thoughts of the debates of wether it was invented or discovered, and thinking about mathematics generally on very basic terms, how the phenomenas of the universe and nature (even in social and economic sciences) are translated from them to us through this language, how we preserve and receive that knowledge through mathematics. it is one of those dazzling and hair itching thoughts that are enchanting and captivating. all this being said, this book is great for someone who has had mathematics in high school and knows what's what. the book is more a descriptive approach for the technical side of mathematics and since it's written by a mathematician, you can sense their handprint on the subject matter, it may seem complex and dry on the surface but when you keep on going it introduces topics which might surprise you in lots of ways. especially in the 3rd part which is titled "Proofs", part 5 with dimensions and part 6 with Geometry. while reading the 6th part I remembered of the phrase that was engraved on the door of plato's academy which goes like this: "LET NO ONE IGNORANT OF GEOMETRY ENTER HERE", I wonder how many people were rejected.
this book is great if you want a guide through the mysterious and beautiful path of numbers but for me, it still didn't do justice to mathematics, the way that Roger Penrose does to mathematica.
Mathematica, the language of nature. wether one thinks of it as a rigid and dry subject or have the other opinion about the subject, it doesn't really matter since it works. it is fascinating when, having thoughts of the debates of wether it was invented or discovered, and thinking about mathematics generally on very basic terms, how the phenomenas of the universe and nature (even in social and economic sciences) are translated from them to us through this language, how we preserve and receive that knowledge through mathematics. it is one of those dazzling and hair itching thoughts that are enchanting and captivating. all this being said, this book is great for someone who has had mathematics in high school and knows what's what. the book is more a descriptive approach for the technical side of mathematics and since it's written by a mathematician, you can sense their handprint on the subject matter, it may seem complex and dry on the surface but when you keep on going it introduces topics which might surprise you in lots of ways. especially in the 3rd part which is titled "Proofs", part 5 with dimensions and part 6 with Geometry. while reading the 6th part I remembered of the phrase that was engraved on the door of plato's academy which goes like this: "LET NO ONE IGNORANT OF GEOMETRY ENTER HERE", I wonder how many people were rejected.
this book is great if you want a guide through the mysterious and beautiful path of numbers but for me, it still didn't do justice to mathematics, the way that Roger Penrose does to mathematica.
October 5, 2016
I enjoyed this book so much, and because of its length, I finished it in one "seating" :-) The most important idea that I learned is to think about what a mathematical object DOES rather what it IS. This is the way mathematicians learn math, do math, and teach math. I plan to do the same in my mathematical endeavors.
January 15, 2026
Mission 2026: Binge reviewing all previous Reads, I was too slothful to review back when I read them
Timothy Gowers’s ‘Mathematics: A Very Short Introduction’ is one of those rare books that manages to be both a doorway and a mirror. At first glance, it is a concise survey of a massive and intimidating subject, but as you read, it becomes much more than a summary—it is an invitation to ‘think like a mathematician’, to inhabit the reasoning, structure, and beauty that underpin mathematical thought.
This is not about memorizing formulas or performing computations; it is about exploring the logic and creativity that make mathematics one of humanity’s most profound intellectual achievements.
Gowers opens with a deceptively simple point: mathematics is not a collection of truths waiting to be discovered; it is a human endeavor, constructed, refined, and reasoned. From the beginning, he emphasizes the distinction between mathematical objects and our understanding of them.
Numbers, sets, functions, groups, spaces—these are not just abstract entities but tools of thought, frameworks that allow us to reason rigorously about patterns, structures, and possibilities.
Gowers’s insistence that mathematics is ‘about ideas’, not just results, frames the entire book and immediately challenges conventional assumptions. For anyone whose primary experience of mathematics is school exercises, this perspective is liberating.
One of the book’s great strengths is its accessibility without compromise. Gowers introduces topics that can feel forbidding—number theory, algebra, topology, logic, and more—yet he does so with clarity, humor, and concrete examples. For instance, he explains the nature of proof not through axioms and theorems alone, but through the lens of problem-solving, argumentation, and mathematical intuition.
The reader is invited to appreciate why proofs matter, not just as formal verification but as demonstrations of understanding, insight, and creativity. Mathematics, Gowers reminds us, is a way of seeing the world with precision and subtlety.
The book also explores the tension between abstraction and application. Gowers presents examples from pure mathematics—prime numbers, infinite sets, symmetry groups—alongside applied contexts such as physics, computation, and cryptography. This balance is instructive: mathematics is not merely a theoretical playground, nor is it only a practical tool.
It is a dynamic interplay between abstract reasoning and real-world application, a field in which intuition and rigor continually reinforce each other.
The examples are carefully chosen to illuminate patterns of thought, not just technical results, reinforcing the idea that mathematics is ultimately about clarity and structure of thought.
Another striking feature is the book’s treatment of mathematical creativity. Gowers challenges the stereotype of mathematics as dry, mechanical, or unimaginative. He emphasizes the role of conjecture, experimentation, and insight, showing how mathematicians navigate uncertainty, discover patterns, and refine understanding over time. In discussing famous problems—Fermat’s Last Theorem, the classification of finite simple groups, the Riemann Hypothesis—he demonstrates that mathematics is a living, human activity, full of surprise, elegance, and occasionally frustration.
The narrative reveals that the joy of mathematics lies not in answers alone but in the process of discovery, in the elegance of reasoning, and in the thrill of connecting disparate ideas.
Gowers also addresses the philosophical dimensions of mathematics.
1) What is mathematical truth?
2) How do abstraction, proof, and logic relate to reality?
3) How does certainty in mathematics compare to certainty in other fields?
These reflections elevate the book from a survey into a meditation on knowledge itself. Mathematics becomes not only a technical pursuit but a lens through which to consider the nature of reasoning, certainty, and human cognition. The discussion of infinity, paradoxes, and foundational questions is subtle yet intellectually exhilarating, providing glimpses into the philosophical depths that underlie even simple-seeming mathematical ideas.
The prose is elegant and precise. Gowers’s style is conversational but rigorous, blending clarity with subtle wit. He anticipates the reader’s questions, addresses common confusions, and structures arguments in a way that makes complex ideas approachable.
This is mathematics as dialogue rather than monologue, a process of engagement that respects both the reader’s intelligence and curiosity. Examples, analogies, and thought experiments abound, ensuring that the text is not merely informative but intellectually stimulating.
For readers like me, who approach mathematics from a literary or philosophical background, the book is transformative. It challenges assumptions about what mathematics is “for” and how it is experienced. Gowers makes clear that mathematics is not a solitary or mechanical activity but a deeply creative, collaborative, and conceptual pursuit.
By the conclusion, one is not just informed about the field; one begins to ‘think mathematically’, learning to structure arguments, recognize patterns, and embrace abstraction as a tool of insight.
Ultimately, ‘Mathematics: A Very Short Introduction’ succeeds because it does not condescend. It does not offer shortcuts or oversimplifications. Instead, it demonstrates that mathematics is accessible through careful thought, engagement, and reflection. The reader comes away not just with knowledge but with a sense of possibility—the realization that mathematics is not a closed system of rules, but a living intellectual landscape in which curiosity, creativity, and rigor coexist.
In short, Gowers’s book is a masterclass in intellectual generosity. It is an invitation to explore, to reason, and to appreciate the elegance of thought itself.
It transforms the intimidating edifice of mathematics into a space of wonder, insight, and human imagination—a reminder that the discipline is at once precise, creative, and profoundly human.
For anyone curious about the inner life of mathematics, this book is indispensable.
Most recommended.
Timothy Gowers’s ‘Mathematics: A Very Short Introduction’ is one of those rare books that manages to be both a doorway and a mirror. At first glance, it is a concise survey of a massive and intimidating subject, but as you read, it becomes much more than a summary—it is an invitation to ‘think like a mathematician’, to inhabit the reasoning, structure, and beauty that underpin mathematical thought.
This is not about memorizing formulas or performing computations; it is about exploring the logic and creativity that make mathematics one of humanity’s most profound intellectual achievements.
Gowers opens with a deceptively simple point: mathematics is not a collection of truths waiting to be discovered; it is a human endeavor, constructed, refined, and reasoned. From the beginning, he emphasizes the distinction between mathematical objects and our understanding of them.
Numbers, sets, functions, groups, spaces—these are not just abstract entities but tools of thought, frameworks that allow us to reason rigorously about patterns, structures, and possibilities.
Gowers’s insistence that mathematics is ‘about ideas’, not just results, frames the entire book and immediately challenges conventional assumptions. For anyone whose primary experience of mathematics is school exercises, this perspective is liberating.
One of the book’s great strengths is its accessibility without compromise. Gowers introduces topics that can feel forbidding—number theory, algebra, topology, logic, and more—yet he does so with clarity, humor, and concrete examples. For instance, he explains the nature of proof not through axioms and theorems alone, but through the lens of problem-solving, argumentation, and mathematical intuition.
The reader is invited to appreciate why proofs matter, not just as formal verification but as demonstrations of understanding, insight, and creativity. Mathematics, Gowers reminds us, is a way of seeing the world with precision and subtlety.
The book also explores the tension between abstraction and application. Gowers presents examples from pure mathematics—prime numbers, infinite sets, symmetry groups—alongside applied contexts such as physics, computation, and cryptography. This balance is instructive: mathematics is not merely a theoretical playground, nor is it only a practical tool.
It is a dynamic interplay between abstract reasoning and real-world application, a field in which intuition and rigor continually reinforce each other.
The examples are carefully chosen to illuminate patterns of thought, not just technical results, reinforcing the idea that mathematics is ultimately about clarity and structure of thought.
Another striking feature is the book’s treatment of mathematical creativity. Gowers challenges the stereotype of mathematics as dry, mechanical, or unimaginative. He emphasizes the role of conjecture, experimentation, and insight, showing how mathematicians navigate uncertainty, discover patterns, and refine understanding over time. In discussing famous problems—Fermat’s Last Theorem, the classification of finite simple groups, the Riemann Hypothesis—he demonstrates that mathematics is a living, human activity, full of surprise, elegance, and occasionally frustration.
The narrative reveals that the joy of mathematics lies not in answers alone but in the process of discovery, in the elegance of reasoning, and in the thrill of connecting disparate ideas.
Gowers also addresses the philosophical dimensions of mathematics.
1) What is mathematical truth?
2) How do abstraction, proof, and logic relate to reality?
3) How does certainty in mathematics compare to certainty in other fields?
These reflections elevate the book from a survey into a meditation on knowledge itself. Mathematics becomes not only a technical pursuit but a lens through which to consider the nature of reasoning, certainty, and human cognition. The discussion of infinity, paradoxes, and foundational questions is subtle yet intellectually exhilarating, providing glimpses into the philosophical depths that underlie even simple-seeming mathematical ideas.
The prose is elegant and precise. Gowers’s style is conversational but rigorous, blending clarity with subtle wit. He anticipates the reader’s questions, addresses common confusions, and structures arguments in a way that makes complex ideas approachable.
This is mathematics as dialogue rather than monologue, a process of engagement that respects both the reader’s intelligence and curiosity. Examples, analogies, and thought experiments abound, ensuring that the text is not merely informative but intellectually stimulating.
For readers like me, who approach mathematics from a literary or philosophical background, the book is transformative. It challenges assumptions about what mathematics is “for” and how it is experienced. Gowers makes clear that mathematics is not a solitary or mechanical activity but a deeply creative, collaborative, and conceptual pursuit.
By the conclusion, one is not just informed about the field; one begins to ‘think mathematically’, learning to structure arguments, recognize patterns, and embrace abstraction as a tool of insight.
Ultimately, ‘Mathematics: A Very Short Introduction’ succeeds because it does not condescend. It does not offer shortcuts or oversimplifications. Instead, it demonstrates that mathematics is accessible through careful thought, engagement, and reflection. The reader comes away not just with knowledge but with a sense of possibility—the realization that mathematics is not a closed system of rules, but a living intellectual landscape in which curiosity, creativity, and rigor coexist.
In short, Gowers’s book is a masterclass in intellectual generosity. It is an invitation to explore, to reason, and to appreciate the elegance of thought itself.
It transforms the intimidating edifice of mathematics into a space of wonder, insight, and human imagination—a reminder that the discipline is at once precise, creative, and profoundly human.
For anyone curious about the inner life of mathematics, this book is indispensable.
Most recommended.
February 21, 2020
این کتاب ریاضی رو جوری متفاوت با آنچه ما میشناسیم به طور معمول معرفی میکنه و باعث نگاه درستی به ریاضیات داشته باشیم. من به شخصه احساس میکردم که از یه زمانی توی مدرسه با ریاضی قهر کردیم یا شاید از همون اول اونجور که باید باهم آشنا نشدیم. خوندن این کتاب تلاشی برای درک و آشتی دوباره با ریاضی بود.
May 10, 2011
Long story short, I didn't really like this one. Gowers isn't a bad writer, but when all is said and done, this 'Introducution' is rather boring. It doesn't capture the imagination, and as far as math books are concerned, this quite simply isn't allowed. Don't bother with this one; if you want an engaging an accessible overview of mathematics, go pick up the far more interesting 'Language of Mathematics,' by Kieth Devlin.
May 24, 2019
O ovoj knjizi ne bih puno pisao. Kupio sam je i pročitao iz razloga što sam profesor matematike i uvek tragam za ovakvom literaturom u nadi da ću otkriti neke nove načine kako se matematika može učiniti zanimljivija učenicima. Onom ko matematiku ne voli, ili mu nije jasna, ovaj priručnik neće baš puno pomoći. Iako je autor sve to fino objašnjavao, opet mislim da treba da postoji neka podloga znanja za lakše razumevanje svih ovih stvari koje on spominje.
May 19, 2015
المقدمات القصيرة جداً ليست للقراءة حول الموضوع لأول مره، بل تكون مراجعة للمفاهيم الرئيسة للموضوع بعد الاطلاع عليه من الكتب الأساسية للموضوع.
January 15, 2023
Mathematics : A Very Short Introduction (2002) by Timothy Gowers is a good introduction to what Mathematicians actually do and what modern mathematics is really about. Gowers is a professor of Mathematics at Cambridge and College de France.
There are chapters on Models, Numbers and Abstraction, Proofs, Limits and Infinity, Dimension, Geometry, Estimates and Approximations and a list of Frequently Asked Questions.
The first few chapters are very strong, Gowers describes that mental models are, goes on to describing numbers, graphs and abstractions and then goes on to proofs. All are done really well and in a way that elucidates what higher level math is all about. The writing is also nicely clear and the examples are well chosen. Some of the later chapters are not as good but are still clear and give more idea of what math is rally about.
Mathematics : A Very Short Introduction is a really good book for anyone interested in what mathematicians actually do. It’s remarkably good for the length.
There are chapters on Models, Numbers and Abstraction, Proofs, Limits and Infinity, Dimension, Geometry, Estimates and Approximations and a list of Frequently Asked Questions.
The first few chapters are very strong, Gowers describes that mental models are, goes on to describing numbers, graphs and abstractions and then goes on to proofs. All are done really well and in a way that elucidates what higher level math is all about. The writing is also nicely clear and the examples are well chosen. Some of the later chapters are not as good but are still clear and give more idea of what math is rally about.
Mathematics : A Very Short Introduction is a really good book for anyone interested in what mathematicians actually do. It’s remarkably good for the length.
March 14, 2023
A really pleasant read for anyone who enjoys mathematics! (not necessary to have a math background to follow most of it).
Even if you are familiar with the majority of the presented concepts, this (very) short intro, will surely provide you with a fresh and interesting way of viewing them.
Recommendable for anyone who ever considered math beautiful.
Even if you are familiar with the majority of the presented concepts, this (very) short intro, will surely provide you with a fresh and interesting way of viewing them.
Recommendable for anyone who ever considered math beautiful.
August 17, 2023
Very unusual VSI.
The author views mathematics through a late-wittgensteinian lense, abstracting from semantics of mathematical terms while focusing on their use.
Tbh, it might be a pretty hard book for beginners, at least harder than other pop science math books, but it's food for thought.
Had to read some paragraphs like 5 times, lol.
The author views mathematics through a late-wittgensteinian lense, abstracting from semantics of mathematical terms while focusing on their use.
Tbh, it might be a pretty hard book for beginners, at least harder than other pop science math books, but it's food for thought.
Had to read some paragraphs like 5 times, lol.
December 28, 2021
The book was nice and all but it just got very boring and the way the topics were written (even topics I enjoy) seemed uninteresting.
August 10, 2019
هرچند مفاهیم مطرح شده در کتاب قابل فهم برای کسر بزرگی از افراد است و نیاز به دانش ریاضی پیشرفتهای ندارد اما دیدگاههای مطرح شده در کتاب و ایجاد پرسشهای مقدمانی که جواب سادهای برای آنها نمیتوان مطرح کرد از هنرمندیهای ظریف این کتاب است.
به نظرم خواندن این کتاب برای هرفرد غیر ریاضیدان علاقهمند به ریاضی و همینطور افرادی که به تدریس ریاضی به کودکان و دانشآموزان مشغول هستند میتواند مفید باشد.
به نظرم خواندن این کتاب برای هرفرد غیر ریاضیدان علاقهمند به ریاضی و همینطور افرادی که به تدریس ریاضی به کودکان و دانشآموزان مشغول هستند میتواند مفید باشد.
April 29, 2025
I usually find these ‘Introduction’ books to be good. But not this one. I wonder who the author thinks he was writing for? If you wanted to be genuinely introduced to the subject of mathematics then this book might as well have been written in Klingon.
June 14, 2024
A very lucid and quite fun book for those interested in mathematics. There's a good summary of loads and loads of different bits of maths, and I think the problem-solving and conceptual aspects really strike at the heart of what I and so many others love about it - perhaps the most fun I've had per page!
So exciting, in fact, that I'd finished it in one go over the last few hours...
So exciting, in fact, that I'd finished it in one go over the last few hours...
October 9, 2017
This book has vividly elaborated how the complex set of theorems or proofs arise from the basics axioms.
The writer starts from the evolution of number system and how the modelling and abstracting plays vital role in developing certain theorem.
Concepts of limits and infinity are great. The most impressive thing that the book tells you about is of the concept of infinity. Texts on these book would certainly clear up the concept of infinity in reader's mind. This approach is made by explaining the square root of two(2).
Moreover, the text of this evolves from the simple Euclidean geometry, leading up to spherical geometry and then hyperbolic. The author has beautifully explained why latter types are needed. Finally, the author talks about the importance of estimates and approximation and their importance in different fields like A Prime Number theory, Theoretical computer science and several others.
Thing I liked about this book was, superficially, the writers has vividly explained topics. But when he goes little deeper like the concepts of hyperbolic geometry, I found the explanation little hard to comprehend.
Nevertheless this OK read!
The writer starts from the evolution of number system and how the modelling and abstracting plays vital role in developing certain theorem.
Concepts of limits and infinity are great. The most impressive thing that the book tells you about is of the concept of infinity. Texts on these book would certainly clear up the concept of infinity in reader's mind. This approach is made by explaining the square root of two(2).
Moreover, the text of this evolves from the simple Euclidean geometry, leading up to spherical geometry and then hyperbolic. The author has beautifully explained why latter types are needed. Finally, the author talks about the importance of estimates and approximation and their importance in different fields like A Prime Number theory, Theoretical computer science and several others.
Thing I liked about this book was, superficially, the writers has vividly explained topics. But when he goes little deeper like the concepts of hyperbolic geometry, I found the explanation little hard to comprehend.
Nevertheless this OK read!
December 17, 2010
کتابی کوچک اما پربار که به شکلی زیرکانه و با بیانی کمیاب جلوههایی از ریاضیات را بدون پرداختن به جزییات پیچیده نمایان نموده است. شاید بهترین توصیف را نویسنده خود در پیشگفتار آورده باشد:
«اگر بتوان گفت این کتاب پیامی دارد، آن پیام این است که باید انتزاعی اندیشیدن را یادگرفت، چون با این کار بسیاری از مشکلات فلسفی خودبخخود از میان میروند.»
«اگر بتوان گفت این کتاب پیامی دارد، آن پیام این است که باید انتزاعی اندیشیدن را یادگرفت، چون با این کار بسیاری از مشکلات فلسفی خودبخخود از میان میروند.»
March 30, 2017
Has the potential to change how we look at Mathematics, or at least us non-mathematicians, especially in regard to the use of the abstract method and fundamental concepts such as: "A mathematical object is what it does."
Wish I had read it sooner.
Wish I had read it sooner.
November 6, 2021
A very good book - interesting argument against Platonism around chapter 3
April 17, 2023
This book was simply amazing. For my whole life, I have been HORRIBLE at math (or, at least since the 3rd grade, when fractions were introduced to my life). But this book revealed to me what I've secretly suspected for a long time: that I actually really, really like math, despite being terrible at it (it was actually my favorite subject until the 3rd grade...which was about the age I started bombing tests).
Timothy Gowers, who is himself an award-winning mathematician, has written a book that is easy to understand and is very, very sympathetic to those of us who can't calculate. But despite this, he doesn't shy away from discussing very complicated aspects of mathematics. It's obvious that he's a wonderful teacher. Gowers has written a beautiful book that dabbles in the 'very mathematical', but never actually becomes mathematical. It is always for the uninformed and uninitiated, as these little books always should be. This was a wonderful book and I feel more in touch with math now than I have in many, many years.
Timothy Gowers, who is himself an award-winning mathematician, has written a book that is easy to understand and is very, very sympathetic to those of us who can't calculate. But despite this, he doesn't shy away from discussing very complicated aspects of mathematics. It's obvious that he's a wonderful teacher. Gowers has written a beautiful book that dabbles in the 'very mathematical', but never actually becomes mathematical. It is always for the uninformed and uninitiated, as these little books always should be. This was a wonderful book and I feel more in touch with math now than I have in many, many years.
November 17, 2023
people tend to ignore the relationship between math and music (which leads to sound, which leads to the meter in poetry), math and language (linguistics, which structures our LLM and potentially AGI), and math and philosophy (multi-dimensional space - phenomenology, architecture, technology - , symbolic logic - public policy, and so on). i wonder how mathematics can play around with affect theory. few days ago i read this wonderful poetry collection that plays with Fibonacci's sequence by Ingot Christensen.
(these are just notes to myself)
(these are just notes to myself)
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