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"Letters to a Young Mathematician" by Ian Stewart is a delightful small book written in the form of a collection of letters from a fictitious mathematician to his equally fictitious mentee Meg, as she charts her career in mathematics. It is a fascinating look into what mathematics is, what it takes and means to be a mathematician and what (and how) they think. As stated by the author in the 'Preface':

Letters to a Young Mathematician is my attempt to bring some parts of "A Mathematician's Apology" up to date, namely, those parts that might influence the decisions of a young person contemplating a degree in mathematics and a possible career in the subject.

Though the book might be of best use to someone who is at the crossroads, deciding on his/her area of further studies, it does not prevent others, like me, from having a new found (or rekindled) insight into the world of mathematics. Starting with the first letter titled "Why Do Math", in which the writer explains how mathematics can be found all around us, he goes on to explain how high school students are disillusioned by the arithmetic in mathematics' clothing they encounter at high school, how that is just a phase where one learns how to use tools that can be used later to tackle bigger and more creative problems. A later letter takes the subject heads on and discusses what exactly is mathematics.

As one glides through the letters, not only is one impressed by the clarity of thought expressed by the writer, but we are at the same time impressed by the pointed and inquisitive questions "asked" by Meg, which is then responded to in the next letter. It is impressive that not only do the letters discuss philosophical questions like "What is Mathematics", it also remains down to earth.

For the first six months you'll wonder why the school ever let you in. (After that you'll wonder how some of the others were let in.)

The letters traces the career path of Meg, as she does her PhD, postdoc and reaches a tenured position at an academic institution. The letters become at once more practical ("Never believe your host when they tell you that all the equipments will work perfectly"), jovial ("For recreation and affection, restrict yourself to fellow students, or people from off campus, please.") and philosophical ("Are mathematical patterns really present in nature, or do we invent them? Or, if real, are they merely a superficial aspect of nature that we fixate on because it's what we can comprehend?").

All in all, "Letters to a Young Mathematician" is an nice enjoyable book that anyone with a slight inclination in sciences can and should read.

If you liked this book, you may also like "Secret Life of Numbers: 50 Easy Pieces on How Mathematicians Work And Think" by George G. Szpiro, "God Created the Integers: The Mathematical Breakthroughs That Changed History" by Stephen W. Hawking and "Chances Are . . . : Adventures in Probability" by Michael Kaplan.