Customer Reviews

Letters to a Young Mathematician (Art of Mentoring)

5 star:		(6)
4 star:		(13)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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.

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.

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.

This is a pleasant little book of just over 200 pages. It deserves more readers than the
title indicates. It might encourage someone to develop their math ability or to choose
math as a profession, overcoming some doubts based on prejudices. It is a useful resource
for someone in a position to advise a young person. It is enjoyable for those with an
abiding interest in math. I believe it would even be entertaining and educational for
those with an open mind but a fear of math.

For the latter, be aware there is some esoteric vocabulary. It is just a way to mention
there are sub, sub, sub specialties in math. There is very little actual math in the
book, and that is mostly about symmetry.

The letters are addressed to Meg, from girl through professor. About 99% applies to males.
Much of it also applies to other scientific fields, and some applies to other fields where
evidence is important. There are even a couple chapters that would be worthwhile to
someone contemplating a career in one of the academic departments where opinions are
paramount.

The weaknesses are few and minor. There is no index. Mathematicians and math in industry
are ignored. The prejudices against female mathematicians are, I believe, somewhat overstated.
The need for writing skills should be emphasized.

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.

I have read and enjoyed books by Prof. Stewart in the past so I was happy to see that he was selected to write this book. This is the second book in "The Art of Mentoring" series that I've read. It's an interesting concept--an experienced expert in a field writes "letters" to a person just starting out, giving them information and advice. It doesn't always seem to come off perfectly but, in my so far limited experience, these brief books certainly seem to be worth the effort.

In this volume, Prof. Stewart gives us insight into the world of mathematics. As a long-time teacher of math and physics, I am always looking for things that will open my students' eyes to the wonders of the subject and help them understand the "mathematical perspective." Fortunately, there are a number of excellent passages here that do just that. I am particularly pleased by his descriptions of the thrill mathematicians have when they solve a challenging problem--something I've tried to share with my students from my own experience. I also find his discussions of proof interesting and something I will find useful for my students.

Of course, the assumption of this book is that the reader is already interested in math, so some of it is really beyond what would likely interest a casual reader. Still, I found many of these even more rarified letters hitting close to home. For example, his discussion of the difference between pure and applied math, something I came across a lot in my physics studies. I also have to give Prof. Stewart credit for a writing style that is much more accessible than that of many mathematicians. He hooked me right away by addressing his letters to Meg (pulled from one of my favorite novels as a kid, A Wrinkle in Time).

But it must also be said that there is much here, particularly as the book goes on, that is going to be less interesting for those not familiar with or considering a career in mathematics. The details and experiences he describes, while well-done, are simply not going to be close to the experience of the average reader. That doesn't mean it's not valuable stuff, but a potential reader should consider himself or herself forewarned.

This is a good book of advice to young mathematicians, it covers every aspect of a mathematician's study, career path and aspirations. As a father of 3 teenage children, as well as a former french mathematics student (who makes a living in IT using some pathetic applied math occasionally), I am grateful for the wisdom given in this book which I can impart to my own children - should one day they tell me they want to pursue a career in mathematics. Math deserves the most gifted young students to pursue, contrary to the common 'wisdom' (or 'Herd Mentality') that Engineering, Accountancy, Law, Medicine, or Life Science which is à-la-mode in my country now, are most promising careers.

Math's beauty is in par with the Nature's beauty. And only those who are keen to explore would be revealed the secret of the Creator. I quoted 2006-Fields Medalist Prof Terence Tao's personal favourite algebra equation: "Sum of Cubes will always be a Square" (1^3+2^3+3^3+... + N^3) = (1+2+3...+N)^2. The secret behind this beautiful equation is "3-dimension can be reduced to 2-dimension". Can N-dimension be reduced to (N-1) dimension in some similar way ? this is a fascinating congesture for promising mathematicians to explore and derive useful applications from it.

I met Ian Stewart quite a long time ago, as he lectured at my college back in the 70s, long before he was the well-known writer that he is today. He lectured on "The Insoluble Quintic", and our resident college artist illustrated the poster with a smoking gun, reflecting the duel that ended the brilliant young mathematician Galois' life at a very early age (Galois being the one who demonstrated that the quintic was unsolvable.)

This is a tamer effort, though no less interesting. Stewart writes a series of letters to an imagined young woman, "Meg", who has decided on mathematics as a career. This allows him to pursue subjects as basic as the pervasiveness of mathematics and why it's important, where mathematics stands in respect to the sciences, and as specific as the best way of studying mathematics and how to deal with the politics of the math department. Stewart's enthusiasm for the subject shines through. I'm not one of those who detests math, but I have to admit my enthusiasm has gotten rather jaded over the years. But Stewart certainly pushed me toward a greater enthusiasm.

I'd recommend this for anyone with any interest in mathematics and its significance in human society.