If you want a cursory view of various parts of mathematics, you might prefer Courant's book "What is Mathematics?". Depending on your background and interest, there is a volume of books (available as a consolidated cheap Dover paperback) called Mathematics: Its Content, Meaning, and Methods.
I recently came across A Programmer's Book of Mathematics[0] -- I haven't read it, but the author is a developer and the content might be more appropriate if you're just starting out -- both of the other books I mentioned are older, and are really wonderful texts, but might possibly be overwhelming depending on your appetite and background.
Finally, if you're more interested in math that's relevant to software engineers, there's Knuth's book "Concrete Mathematics".
Additionally:
- "Princeton Companion to Mathematics" is really fun to have around for exploration
- if you're really really rusty with math, take a week or two with "Mathematical Handbook - Elementary Mathematics" by Vygodsky
I literally have all these on my desk at this very moment, what a fun coincidence.
And, it's not even particularly good in instilling some appreciation of the beauty of mathematics.
Save your time.
If you do read the Apology, be sure to get an edition with C.P. Snow's forward, which gives the back story that puts Hardy's memoir in context. It also includes the wonderful story of Hardy and Ramanujan.
[1] https://en.wikipedia.org/wiki/A_Course_of_Pure_Mathematics
[0] https://www.maths.cam.ac.uk/sites/www.maths.cam.ac.uk/files/...
I found that studying specific topics (currently probability theory and statistics) helped me comprehend the field better and in ways that make it practical for my planned career.