George F. Simmons

Browsing a back issue of the BSHM bulletin, I found a review of the book Calculus Gems by George F. Simmons, from which I learned that he died in 2019 at the age of 94.

I never met Simmons, and his field, functional analysis, was far removed from mine; yet I felt a connection to him. In 1963, just before I started my mathematics degree at the University of Queensland, he published a book called Introduction to Topology and Modern Analysis with McGraw-Hill. I had a copy of this book while I was a student. I think it is possibly the best text-book I ever had.

It was comprehensive and clear, both in explaining things and in giving rigorous proofs, but that is not the main reason I liked it: rather, because it told a story.

The book is divided into three roughly equal parts. The first is a first course on topology, covering all the things you would expect: connectedness, compactness, separation axioms, and so on. The second part is a course on linear algebra. Probably not a first course, since almost everyone who would use the first has already studied some linear algebra; but it is a very nice account, starting from basics and getting up to a thorough treatment of the spectral theorem. The final part, taking the view that functional analysis is just linear algebra with some topology thrown in, went up to some of the basic theorems, and included applications to, if I remember correctly, existence of solutions of differential equations.

I suppose it was only because I had a strong leaning towards discrete mathematics that I wasn’t seduced into becoming a functional analyst by that book.

Of course, my copy disappeared many years ago, possibly in the big shake-out when I had to leave my office in Queen Mary at two weeks’ notice (I had a “book sale” and invited my colleagues and students along, the price of any item being zero, and I only kept a few books for my own use).