Letters to a Young Mathematician Paperback – Mar 27 2007
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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 an out of print or unavailable edition of this title.
"ÝStewart is¨ just as happy discussing whether God is a mathematician or whether alien mathematics will turn out to be the same as ours. As a mentor for a budding mathematician, he is remarkably good company."See all Product Description
Top Customer Reviews
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.
Most Helpful Customer Reviews on Amazon.com (beta)
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.
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.
I am considering graduate school in mathematics and thought this book would help me understand that decision more. Unfortunately, the path of the Author's "young mathematician" is a very specific and very traditional academic path. As such, the author spends more time explaining the specifics of that path and what happens during each stage (lower school, college, phd, professor, and tenured professor) rather than the decisions between each stage.
Before I read the book, I knew I did not want to follow that path. I was hoping for greater insight to mathematical training and thought in other domains, but this book was lacking.
I highly recommend this book for anyone considering a traditional pure mathematical education. However, the book is less useful for someone interested in math but not interested in the same path.