I recommend this a lot "A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)" by Michael Crowe. It's a page turner.

I have two recommendations that I don't see mentioned by anyone else yet:

1. An Introduction to Mathematics by Alfred North Whitehead, 1911 available at http://www.gutenberg.org/ebooks/41568

It not specifically about history, but I found it nice how it builds up concepts from first principles, e.g. "We had problem X, so we invented math concept Y to help with problem X, and then extended the idea concept Z that handles more general class of problems."

2. Mathematics 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations Hardcover by Richard Elwes, 2010. (non free)

This one doesn't go into any details on any topics, but it gives you a bird's eye overview of many topics and based on the "sampling" I did for the few concepts that I know, I found the bite-size explanations to be fairly good (i.e. mathematician explains things in plain language, and not science journalist simplistic analogy).

The Mathematical Experience is not a history of mathematics per se, but there is a lot of history and context in it. Highly recommended.

https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav... is a link to Amazon.

“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.

For a very informal tour, The Three Body Problem by Cixin Liu is a science fiction novel where the history of mathematics, physics, and computation play a large role. So much so that I think it puts many people off the book and its entire trilogy.

NJ Wildberger's lectures are online https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL55C7C8378...

I don't know how helpful it is to the common reader, L.E Dickson's 3-volume 'History of the Theory of Numbers' is mentioned frequently as a definitive history of that branch of Mathematics.

"A Cultural History of Physics" by Karoli Simonyi is a brilliant book on the history of Science and math from antiquity to recent past. Even though the title reads as history of physics, the book touches upon everything from Math to Philosophy as they were all under one umbrella until recent past.

https://www.amazon.com/Cultural-History-Physics-K%C3%A1roly-...

Nature and Growth of Modern Mathematics by Edna Kramer. If you love history and mathematics, this is a good combination from what I remember, sort of alternating between historical placements and biographies with actual mathematical content explained.

I read this decades ago before I learned advanced mathematics and I found it enlightening and inspiring at the time though I have not revisited it since though it is a cherished memory. The book's age prevents it from covering the many modern innovations since.

Stillwell's _Mathematics and its History_ is, imo, excellent.

From the Birth of Numbers. ISBN 9780393040029

The Princeton Companion to Mathematics. More an Encyclopedia of mathematics with history in it.