Of the books mentioned in this thread so far I think I'd have been most excited about the Princeton Companion to Mathematics as a birthday present. Here's why:

Of the books mentioned in this thread so far I think I'd have been most excited about the Princeton Companion to Mathematics as a birthday present. Here's why: - Your goal of the gift is something more than a plain textbook. The Princeton Companion is something your child will return to throughout their math career. It will be an anchor book that will remind them of your support for them when they were still a budding mathematician. - Relatedly, the book is far too broad to be consumed as a textbook. Hence it will be more like a friend (or companion :) ) on their journey. Even a really amazing textbook (like Baby Rudin) in contrast is just a snapshot of where they are now.