[Someone]

“A Concise History of Mathematics” by D.J. Struik apparently (I have read only a tiny part of it) is good, but being 70+ years old, it is getting more and more dated.

It also doesn’t discuss the mathematics itself in much depth; it more connects topics and has references (plenty of them) for those who want to learn about those topics.

“The World of Mathematics” by J.R. Newman isn’t a history, but more a sample of pure and, mostly, applied (“How to hunt a submarine” is the title of a chapter on operations research) mathematics.

I think it is worth mentioning, though, certainly for “tourists” who aren’t aiming for full coverage of the subject, but just want to visit nice viewpoints.

Also, I think it’s quite readable for non-mathematicians, as it doesn’t do much ‘real’ math (Stillwell's _Mathematics and its History_, mentioned elsewhere, has more of that in its first 25 pages than this 1000+ page work), and its chapters can be read in isolation.