27 of 29 people found the following review helpful:
4.0 out of 5 stars
A fun read, March 31, 2006
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.
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12 of 13 people found the following review helpful:
4.0 out of 5 stars
Adds Up to a Good Read, June 17, 2007
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.
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8 of 8 people found the following review helpful:
5.0 out of 5 stars
Quick Read, August 17, 2006
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.
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