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Letters to a Young Mathematician [Paperback]

Ian Stewart
3.0 out of 5 stars  See all reviews (1 customer review)
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Book Description

March 27 2007 Art of Mentoring
Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up 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 beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

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From Publishers Weekly

Starred Review. This new entry in the Art of Mentoring series takes the form of letters from a fictitious mathematician to his niece. The letters span a period of 20 years, from the time the niece is thinking about studying mathematics in high school through the early years of her academic career. The format works wonderfully to introduce readers to the basics of the discipline of mathematics while providing a sense of what mathematicians actually do. Throughout, the prolific and talented Stewart (Does God Play Dice?), a British mathematician, entertains while educating. He explains how mathematics is so much more than mere calculations and how it's used in almost every facet of our lives. He also discusses the beauty mathematicians can find in the natural world, demonstrating that a focus on numbers and patterns can enhance rather than detract from an aesthetic appreciation of the environment. Stewart also does a superb job of examining the nature and value of both applied research and pure research, which, he shows, are not nearly as disparate as many think. Although the book must be read by anyone thinking about a career in mathematics, others simply interested in learning about the field and how mathematicians think will find it compelling reading. (Apr. 17)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. --This text refers to the Hardcover edition.


"(This) book's greatest value is its insight into what it is to be a mathematician... His enthusiasm is infectious." The Times "The letter in which Stewart tells Meg how to teach undergraduates should be compulsory reading for all lecturers and tutors". Nature"

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Most helpful customer reviews
This book is a collection of letters presumably addressed to a student by the moniker "Meg" from her years in high school to her postdoc years. It is a nice, quick read and provides a good glimpse of the mathematical world to the dilettante, but many of the things that the book addresses (such as the importance of proofs, how to learn math, et cetera) are either preliminary knowledge that a simple Google search could answer, or is better addressed from other books. For example, its advice on how to learn math is covered in a much more succinct fashion on Professor and Field Medalist Terrence Tao's blog ([...]

The only thing that I found to be genuinely insightful was Ian Stewart's opinions on finding someone to do research under and the hierarchical structure of the mathematical community.

A large portion of the content is filled with anecdotes about the author's own research or experience, which is neat at times but, in general, quite uninformative and at times boastful, such as his mentioning of himself having talent and not needing to study a whole lot during his education at Cambridge University.
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Amazon.com: 4.3 out of 5 stars  23 reviews
29 of 31 people found the following review helpful
4.0 out of 5 stars A fun read March 31 2006
By Polymath-In-Training - Published on Amazon.com
Format:Hardcover|Verified Purchase
If you have any interest in mathematics at all, you will enjoy this book. Like all of Stewart's books on mathematics, this is well-written, understandable, and interesting. The intended audience would be high-school students who are thinking about majoring in mathematics, college students who are majoring in mathematics, and the rest of us who wish we were smart enough to have majored in mathematics.

Stewart talkes broadly about what the fields of math involve, including some philosophy of mathematics, which is a fascinating field in its own right. He provides advice on what its like to study math, teach math, and above all, DO math.

The only downside of this book is the high price (in the bookstore) for such a small book. PolymathInTraining practiced unaccustomed frugality by reading this entire book in the bookstore for the price of a cup of coffee. But I will purchase it when it is released in paperback.
9 of 9 people found the following review helpful
5.0 out of 5 stars Quick Read Aug. 17 2006
By Publius - Published on Amazon.com
After reading many of the books in this series, I was drawn to Mr. Stewart's book immediately. As a lawyer, I find that the study of Math can be useful in such obscure topics as the Property or Mergers & Acquisitions. One of the more enjoyable aspects of this book, was its acknowledgement that Math is not for everyone. I, for one, am glad that Stewart writes that one does not back into a career in mathematics, like say someone who backs into a career as a salesman or lawyer. Overall, a nice easy read that is witty and intellectually stimulating at the same time.
14 of 16 people found the following review helpful
4.0 out of 5 stars Adds Up to a Good Read June 17 2007
By R. Schultz - Published on Amazon.com
Stewart writes a series of letters to a (probably) fictitious young person to inform each step of that student's journey along the path to becoming a mathematician - starting with grade school questions about "What's math good for?"- and going through advice on how to negotiate office politics in post-doctoral academia.

Each of these chronological letters contain practical advice as well as interesting insights into scholarly subjects, not limited to the field of mathematics.

For example, Stewart presents some of the crispest, most comprehensible definitions I've run across. He defines postmodernism as "the belief that everything is social convention." Other people have spent whole windy pages and chapters trying to define that term, and only succeeded in putting me in a greater fog than before I started.

Stewart defines fractals as patterns that "exist in a fractional number of dimensions." And Godel's theorem gets intelligibly summarized as "the theory that there will be statements that can never be proved either true or false, but that can be used as axioms of equations either way - without creating inconsistency."

Along the way, Stewart renders some wise advice on how to live life in general. He points out how often the theory that people struggle for decades to prove or disprove (like Fermat's Last Theorem) is not important in and of itself. But the process of trying to prove it often opens whole new fields of mathematics. That's another take on the old truism - It's the journey not the destination.

Stewart made only one remark that I didn't think was totally reliable in this neat little book of essays. He says that a primary pleasure to be found in the practice of mathematics is that there is only one correct answer. Once that correct answer is found and proved, all squabbling ceases. Everyone unites and moves on. Well, I don't know about that. From what I've heard, mathematicians can squabble indefinitely over an issue and divide into standing camps - precisely because so many equations don't have just one correct answer. What about fuzzy math - equations that allow a smear of different answers over a range? Stewart doesn't mention this field at all, and so omits consideration of what many are beginning to feel might be a paradigm for how the human brain works. Very little is yes or no. Most things are entertained as different strengths of "maybe's."

Aside from that one lapse into unwarranted optimism about the ultimate pacifism of life in the mathematical community, Stewart does a fine job presenting the joys and challenges to be expected pursuing a career as an academic mathematician. And he makes a lot of math's most interesting precepts accessible to even the most math-phobic layman.
7 of 8 people found the following review helpful
5.0 out of 5 stars easy introduction to the life of a mathematician Sept. 5 2006
By Patrick Regan - Published on Amazon.com
Format:Hardcover|Verified Purchase
Letters to a Young Mathematician portrays the life of a mathematician to a hypothetical young woman pursuing a career as a mathematician. The author draws on his own experience as a mathematician to regal his readers with stories from his life but also some useful insights into just what the life of a mathamatician entails. There is information about the use and misuse of computers in mathematics, a chapter on getting over fear of proofs and many others. I found the authors depiction of the career of a mathematician interesting. This book is very easy to read as it does not include much in the way of math. If you are hoping to become a mathematician this book is very useful, but if you are just hoping to learn some math look elsewhere.
3 of 3 people found the following review helpful
4.0 out of 5 stars The Fascination of Math Jan. 9 2007
By Imad Moustapha - Published on Amazon.com
Format:Hardcover|Verified Purchase
The book is a pleasure to read, the narrative is never dull or technical, and the discourse is of a universal appeal. You don't need to have a keen personal interest in mathematics in order to enjoy reading the book and improve your understanding of the essence of mathematics, the importance of its applications, and its lure.

I strongly recommend this book to whoever is interested in exploring realms of beauty outside the strict circles of fine arts and music.
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