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Letters to a Young Mathematician

3.75 of 5 stars 3.75 · rating details · 329 ratings · 42 reviews

The first scientific entry in the acclaimed Art of Mentoring series from Basic Books, Letters to a Young Mathematician tells readers what Ian Stewart wishes he had known when he was a student and young faculty member. Subjects ranging from the philosophical to the practical--what mathematics is and why it's worth doing, the relationship between logic and proof, the role of...more

Hardcover, 224 pages

Published March 27th 2006 by Basic Books (first published 2006)

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Dec 12, 2009 Zoe rated it 3 of 5 stars

As the title suggests, this book is written in the form of letters to a "young mathematician", offering advice and generally discussing what mathematics is and what it means to be a mathematician. The back cover promises that it "tells readers what world renowned mathematician Ian Stewart wishes he had known when he was a student", and I was intrigued because I had a mixed experience with mathematics in university and always wondered what I could have done differently.

I have to say, my experienc...more As the title suggests, this book is written in the form of letters to a "young mathematician", offering advice and generally discussing what mathematics is and what it means to be a mathematician. The back cover promises that it "tells readers what world renowned mathematician Ian Stewart wishes he had known when he was a student", and I was intrigued because I had a mixed experience with mathematics in university and always wondered what I could have done differently.

I have to say, my experience with this book was also mixed. First of all, lest the title mislead, I think it's actually more suited for a general non-mathematical audience than for someone who's actually in the process of becoming a mathematician--which wasn't a problem for me, since I read it for general interest and not as an aspiring mathematician.

Stewart raises a lot of interesting points here, but he often doesn't discuss them in as much detail as I would have liked. I think this is part of a series, and it was probably a requirement that the book be barely 200 pages long, but there are times when a bit more depth would have been nice. It was good in a way that the book left me wanting more, and it did include references to other interesting reading throughout, but it wasn't quite satisfying enough in itself. Many people will probably appreciate the brevity, though.

A more serious concern for me was the fact that I just didn't agree with some of his more important points. I know, he's the mathematician and I'm not, but still. The book got off to a bad start, in my mind, with the initial chapter entitled "Why Do Math?". Stewart's reason, briefly, is that math is everywhere. There's a bit too much focus on the utility and not enough on the beauty of it. The same is true even in his chapter on proofs: "it would be silly to suggest that this agreement [with experiment to an accuracy of nine decimal places:] is an accident, and that no physical principle is involved.... [but:] it is equally silly not to try to find out the deep logic that justifies the calculation. Such understanding... will surely advance mathematics." So even proofs are presented not as necessary, but merely as useful (a view that he steps back from slightly in the following chapter, but to my mind, the damage was done).

Another point that left me wondering is his claim that not everyone can be a mathematician, because "originality is one of those things that you either have or you don't." I really appreciate the fact that he expressly disagrees with the politically-correct view that everyone can be good at everything, but I think he simplifies the issue a bit too much. In particular, I'm just not convinced that originality is the key. He compares it to the attempt of a tone-deaf person to become a great musician, but there's nothing in there to make me think that creativity is the problem rather than some more basic musical/mathematical aptitude. His explanations about how he excelled at math without effort from the time he was 10 didn't convince me either; the mathematics that one does at age 10 is so different from "real" mathematics that it can barely be called the same subject. Creativity certainly isn't the main factor there. I wonder whether Stewart's various unconvincing arguments are a direct result of the book's extreme brevity; maybe I would have been more convinced if he had elaborated his position further.

On the other hand, I think the fact that I have so much to say about this book speaks in its favour. Regardless of whether I agree with everything Stewart says, he makes plenty of interesting and provocative points in a short space. And there's a fair bit of humour, too, including a whole chapter on what not to do as a tenure-track professor that consists mainly of humorous anecdotes about various mishaps ("I was once abandoned inside a Dutch mathematics building when my hosts went off to the parking garage to go to a restaurant. I had to make my escape through a window, setting off a burglar alarm.") So in the end, I think I would cautiously recommend this book, as long as you don't take Stewart's views as the be-all-and-end-all when it comes to what mathematics is.(less)

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Feb 12, 2013 Shayla rated it 2 of 5 stars · review of another edition

"Letters to a Young Mathematician" was not written for me. It was probably not written for you either unless you are a 16 or 17 year old female high school student who is very good at math and planning on becoming a professional mathematician. Keeping in mind the fact that I am not the target audience here is my review...

The book is at times very interesting and inspiring, with fascinating anecdotes and lots of recommendations for other texts, and at other times rather trite and overly specific....more

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Nov 24, 2010 Jeff rated it 3 of 5 stars · review of another edition

Shelves: mathematics

Letters to a Young Mathematician is a short epistolary book with chronological letters addressed to "Meg," what I assume is a fictional mathematician. The letters begin with "Meg" in high school and end with her tenured position at a university. Through the course of the letters, Stewart gives advice and ruminates on the nature of mathematics, learning, teaching, and mathematical research and work.

While the ideas are often enlightening (I was particularly taken with ideas about how mathematicia...more

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Feb 02, 2011 Koen Crolla rated it 2 of 5 stars · review of another edition

A book by Ian Stewart contains, in the second paragraph of the preface, the line ``No longer do mathematicians believe they owe the world an apology''. How many chapters do you expect to contain extended apologies for being a mathematician? If you guessed ``several'', you must have read Stewart's books before.

Letters to a Young Mathematician is written as a series of condescending letters to a girl named Meg, who is considering becoming (and over the course of the book does become) a mathematici...more

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May 03, 2013 Andrew rated it 4 of 5 stars

Shelves: math-fun

I assigned this book to my Trig class, and they responded mostly well to it. The funniest part is that they were surprised to find that Meg wasn't real. This worked well as a launching point into discovering math all around, and the students still mention how math is everywhere, much to their chagrin/surprise! Sometimes the author was a little long-winded or over their head, but the students sometimes considered actually looking into the strange things mentioned. I hope to adapt portions of this...more

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Mar 11, 2013 Holmes rated it 5 of 5 stars

Being no mathematician myself (and certainly lacking in talent), I don't think I have ever been this engrossed in reading a book about math. I basically devoured it. In fact, I believe anyone can devour it: there are no exotic symbols or scary formulas to put one off; the focus is on the humanistic side rather than the technical side; the book reads almost like a story as the imagined "Meg" (to which the book is supposed to be addressed) grows from a curious youngster to an established mathemati...more

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Feb 02, 2011 Andrea AE rated it 3 of 5 stars · review of another edition

Shelves: mathematics

230 de 230. Me hubiera gustado leer Cartas a una Joven Matemática cuando estudiaba la prepa, de seguro me hubiera dedicado a las matemáticas y es que Ian Stewart te presenta todo ese mundo que va desde las mismas matemáticas hasta los matemáticos de una forma tan extraordinaria y fácil de comprender, abriéndote los ojos y borrando estereotipos que se tiene sobre ellas.
Sin embargo hay veces que se muestra más de un lado que le del otro, no es imparcial en algunos aspectos que debería serlo hacie...more

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Nov 04, 2011 Upom rated it 4 of 5 stars

Shelves: mathematics, 2000s, 21st-century, advice, feminism, letters, philosophy, nonfiction

I wish there were more books like this- small works that encourage people to go into science or math while explaining what they can expect for their career. Although primarily geared toward budding academic mathematicians, the book is useful for anyone who has an interest in math or academia. Written as a series of letters to a girl named Meg, the book highlights all the ins and outs of mathematics and an associated career. Though I don't agree with everything Stewart says, and some of the proof...more

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Apr 14, 2012 Alastair rated it 3 of 5 stars

Clever, perceptive, genuine -- and, best of all, my favorite genre of non-fiction, which lies somewhere between memoir and essay but with some expertise behind it. Of course writers write about their own lives. It's also gratifying to get advice, even on a topic in which I'm unlikely to be able to follow it. I wish I'd paid more attention to math, or had more inspiring math teachers -- I would have been able to do interesting things with my developing view of the world if I'd had better math ski...more

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Jan 01, 2013 Leah rated it 1 of 5 stars

The author writes with a level of authority that I am not sure he can evince. Much preferred are:

1. http://terrytao.wordpress.com/career-...
2. A mathematician's Apology by GH Hardy, which this book claims inheritance -- pfffft.
3. Thurston's on proof and progress in mathematics ( what it's like to do math today, from a working mathematician)
4. Uncle Petros and the Goldbach Conjecture (on why one might freak the fuck out and do a lot of math)
5. http://www.math.harvard.edu/hcmr/issu... <- Profe...more

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Jan 26, 2011 Eva Nickelson rated it 4 of 5 stars

Shelves: non-fiction

This review has been hidden because it contains spoilers. To view it, click here.

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Jul 20, 2011 Adam Boudreau rated it 5 of 5 stars · review of another edition

Shelves: mathematics

I've recently decided to go back to school for a degree in Applied Mathematics, so while my girlfriend was looking over the math section at a used book store she came upon this book. It is certainly a quick read as other reviewers have stated and I must say I found it an enjoyable one. I believe the intended audience of this book is for anyone in general. If you are interested in what mathematicians do, how they contribute to the world, or a glimpse into what they think about, then this is a goo...more I've recently decided to go back to school for a degree in Applied Mathematics, so while my girlfriend was looking over the math section at a used book store she came upon this book. It is certainly a quick read as other reviewers have stated and I must say I found it an enjoyable one. I believe the intended audience of this book is for anyone in general. If you are interested in what mathematicians do, how they contribute to the world, or a glimpse into what they think about, then this is a good book to read through. I must emphasize that it is extremely general, which is what maintains its level of readership.

"Letters to a Young Mathematician" is series of letters written to a fictitious niece interested in pursuing a career in mathematics. This book takes you from her childhood when she is first encountering the world of integers all the way up to getting a teaching position at a university. The book covers basic things, such as what mathematicians do and even covers elements of office politics. One of the points I found very interesting was the way Stewart differentiates (no pun intended) between the way mathematicians argue and how other disciplines argue (his example was Art professors). A major difference he points out is that the Art professors will argue till they are blue in the face with little conclusion, but the mathematicians will argue until one eventually figures something out and realizes the error they were making. I may have found this more amusing because my girlfriend is an Art major and she confirmed that those types of arguments between faculty do happen.

This book serves as a bit of an advice for prospective students/workers in the field of math. It also serves as a sneak peak into the world of mathematicians, which I feel is a world not often publicized to the general public very much. From what I can tell a lot of people think we're off manipulating arcane equations in a back room or we're human calculators that solve incredible arithmetical problems. I don't think either is very true, well maybe the first one could have some element of truth... but I digress. I think this is a great book to read through and get a quick glimpse at some of the fields mathematicians actually have the options of working in. Becoming a teacher is not the only option as many seem to assume, as that is the most coming question I get asked when I tell others about my major.

One of my favorite parts in this book is the advice for prospective math teachers/professors. You will get chalk all over the place. It brings me fond memories of my Linear Algebra teacher who really took this to heart, going to such lengths of erasing mistakes with his fist. The sheer volume of chalk this man went through and had on his hands, shirt, and face by the end of lecture was impressive.(less)

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Jan 31, 2011 Deana rated it 5 of 5 stars

Recommended to Deana by: Mom

Shelves: 2009, owned-me, 4-5stars

I have no idea how to explain the genre of this, but it is excellent and highly recommended to EVERYONE, regardless of your interest in math (or lack thereof). The book unfolds as a series of letters from the author to Meg, a fictional (as far as I know) female with an interest in mathematics. The author, in case you are unaware, is a famous mathematician in real life. He's done lots of great research in the field, but in recent years his work has mainly been in writing "popular mathematics" - t...more

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May 24, 2008 David rated it 4 of 5 stars

Shelves: mathematical-me, nonfiction

Ian Stewart is one of the most recognizable math popularizers out there. He has written many popular books, as well as writing a regular math puzzles column for Scientific American for a while. I read some of Stewart's popular math books when I was a kid (a blessing on our local public library!). I also admire his work with Golubitsky on analysis of pattern formation and nonlinear dynamics in terms of symmetry and symmetry breaking (his nontechnical books on symmetry in nature are a treat for an...more

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Mar 25, 2008 Jerzy rated it 3 of 5 stars

Shelves: math

Probably nothing drastically new here for many young mathematicians, but still includes some good stories and useful tips, and it's always interesting to hear how an established professional got into their field in the first place.
Stewart makes an interesting point that, unlike many other fields, you don't just happen to fall into math - it has to be something you're really into (although it may take a lot of lucky coincidences to let you realize that you're good at math and into it as well).
The...more Probably nothing drastically new here for many young mathematicians, but still includes some good stories and useful tips, and it's always interesting to hear how an established professional got into their field in the first place.
Stewart makes an interesting point that, unlike many other fields, you don't just happen to fall into math - it has to be something you're really into (although it may take a lot of lucky coincidences to let you realize that you're good at math and into it as well).
There's also a good illustrative story useful especially for mathematicians, about how committees work. The committee had to choose between 2 options, and the mathematician in the group realized at once that one of the choices was much much better, so immediately he explained why. His reasons were clear and logical and nobody disagreed. But since the other committee members hadn't had a chance to have their say yet, the discussion continued. He stayed out of it, knowing he'd already made the most important point... but when it came to the vote, everybody had forgotten his point in the face of all the other rambling, and they voted for the other (worse) option instead. So... Logic is crucial but timing is important too!
I also liked some of the comments he made about teaching - I don't know if I'd agree with all of it but it'd be worth returning to if I have a teaching position in the future. I especially like where he talks about how important it is to internalize lower-level ideas in math, not just recall their definitions or simplest expressions. For example, multiplying 5x4 is like taking four sets of five items each: 5+5+5+5. But you have to have some practice with the concept and internalize it before you can multiply 555x444, because it's not really sensible to do 555+555+... that many times. And once you've internalized it and reached a higher-level understanding, there's much more you can do with it than when you were still thinking in concrete terms of adding small sets of items.(less)

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Jan 11, 2013 Sofia Lazaridou rated it 3 of 5 stars

Shelves: 2013-reading-challenge

OK,I was out of my element here.My math teacher lend me the book and though it's recommended to high school students but I think if you're a high school student should really like maths and you read books about them then you should read this.I as mostly romance reader couldn't exactly follow the idea of the book because it's plotless.Stewart just talks about maths all by himself.It might had helped if Meg's letters were also inside the book since sometime he answered things to her that I did not...more

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Jul 31, 2009 Mikko Karvonen rated it 4 of 5 stars

Shelves: mathematics, non-fiction

Light-weight, witty and occasionally rather funny overview of the role of mathematics and the work and life of mathematicians in the modern world. It didn't tell me much anything new, except for a bunch of interesting anecdotes, but I enjoyed reading it.

Also worth reading for those not interested in mathematics - you don't need to know anything about the field to understand it, and reading might reveal something of the world that's often somewhat misunderstood, for various reasons.

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May 19, 2010 Andy Perkins rated it 4 of 5 stars

Shelves: science-engineering

Good reading whether you are a mathematician who wants to know you are not alone, or for those who wonder why in the world would one become a mathematician. Math is not the stuff you learn in elementary school.

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Aug 02, 2012 Solange rated it 5 of 5 stars · review of another edition

This review has been hidden because it contains spoilers. To view it, click here.

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Jul 05, 2010 Brett rated it 4 of 5 stars

Shelves: mathematics

Great read for anyone interested in majoring in mathematics. Some worldview issues but he still understands the wonder of math and its beautiful applications in the world.

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Oct 22, 2009 Ned rated it 3 of 5 stars

Worth reading for anybody interested in mathematics to understand the large-scale questions of why and what in mathematics. Doesn't take any special knowledge, either.

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Mar 28, 2009 Bill rated it 4 of 5 stars

Slightly indulgent / ego centric but a useful successor got GH Hardy's apology. Could inspire a young mathematican - at least it would dispell some illusions.

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Mar 10, 2009 Hands rated it 4 of 5 stars

Shelves: green-office

Excellent introduction for the layman to what mathematicians do. I wish I'd read it in high school instead of when I'm 59.

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Sep 25, 2011 Derek rated it 5 of 5 stars

I wish this book had been around when I was a kid.
I definitely would have pursued mathematics.

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Jul 23, 2011 Alicia rated it 3 of 5 stars

Contains good advice, suggests other books to read, and promotes females in the mathematics field.

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Jan 26, 2013 Monique rated it 5 of 5 stars

I bought this book for every kid in my Algebra club years ago. It's awesome.

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Dec 01, 2012 Chad rated it 2 of 5 stars

Was an okay book considering it goals, as you can glean some knowledge from the author; however, the actual good advice was few and far between poorly disguised self-congratulatory writing.

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Jul 31, 2011 Robert rated it 5 of 5 stars

This book charmed my socks off.

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Jul 23, 2012 Peggy Truett rated it 5 of 5 stars

Delightful!

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Feb 21, 2009 Richard rated it 3 of 5 stars

OK, not great. Reminded me that I need to pick up Godel, Escher, Bach; also going to pick up the flick Enigma about the codebreakers in UK during WWII...

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About Ian Stewart

Ian Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors wit...more

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