John Stillwell (1) (1942–)

The synopsis of this book printed on the dust jacket suggests that the book's audience ranges "from high school students to professional mathematicians". Assessing the high end of that range, I think that it is true that most professional mathematicians will find something new and interesting in this book. But you don't purchase and read a book because it has *something* new and interesting, do you? Wouldn't you want a large portion of the book to be new and interesting? It's that ratio for show more this book that I think professional mathematicians will tend to find dissatisfactory.

How many professional mathematicians are, for example, going to patiently read Chapter 6 on Calculus? If, as seems to still be the case, Georgia Tech basketball players are required to take 2 semesters of Calculus, shouldn't it now be considered something understood by the educated layman?

I still view Stillwell as one of mathematics' most talented expositors, but trying to make a book like this be a worthwhile purchase for both high school students and professional mathematicians may be an impossible task for even him. show less

John Stillwell is quite possibly the world's most successful expositor of mathematics. He seems not to write "pop math" books but rather books that get their hands dirty with some of the deep mathematical concepts involved. Nevertheless, they are not as detailed and rigorous as a scholarly monograph would be.

This book, in particular, leaves me with some sense of dissatisfaction. I'm not much of a "big picture" mathematician; I've often said and felt that the truth is in the details.

I've got show more a couple of Stillwell's other books with me at home to help keep me occupied during the time of social distancing, but I think I'll be balancing those with some non-expository reading to keep me grounded. show less

With Reverse Mathematics John Stillwell demonstrates the ideas and properties of Reverse Mathematics. I know it is a bit of a tautology to speak of it in this manner, so I will try to explain. Stillwell shows that mathematics had always been establishing axioms and then finding the results of those axioms. Reverse Mathematics goes in the other direction by taking a theorem and finding the axioms needed to prove it.

It is an interesting approach to Analysis, but I don’t really know all that show more much about Mathematical Analysis. I never took it in school, since I only got up to Calculus II in college. Therefore, there are several things that I find annoying, but that is only because I wasn’t paying attention the first time through. For instance, there is a portion where ZF is mentioned and I didn’t know what that was. The book might use a lot of acronyms but it usually explains what they mean before the author dives into the gist. This is important for when Stillwell decides to drop stuff like ACA and WKL and other such ideas.

In writing this book, it is clear from the text that the author wanted to establish a solid foundation for analysis given some advances in Logic. This is mentioned in the text itself. It doesn’t have any problems to solve or questions to answer.

The book is quite interesting as I mentioned before. It is rather short, but it is densely packed with ideas. It doesn’t have a glossary, choosing instead to jump straight to the Bibliography and Index. In that sense, I could say that the author dropped the ball, but it is possible that the editor thought it unnecessary for the target audience. Then again, you could always search for what he means by using the Internet. show less

A nifty and accessible (for people who like math) little book on set theory, mathematical logic, computability theory, incompleteness, unsolvability, and _large_ transfinite cardinals. One thing I knew little or nothing about before: induction over transfinite ordinals -- used, for example, in proving the consistency of arithmetic. "A better understanding of finite objects depends on a better understanding of infinity." (p 165)