I am looking for a book that describes the historical development of mathematics from the ancient times to our advanced developed concept. Along with the derivation and mathematical concepts as introduced in the respective time. For example if it was on history of number theory of gauss , then the proofs as given by him would also be stated. It doesn't has to be a single book. Any help would be appreciated.
There are many histories of mathematics. These two might be what you're looking for:
- Carl B. Boyer, A History of Mathematics
- W. W. Rouse Ball, A Short Account Of The History Of Mathematics
Your question is too broad, I think.
One nice scholarly book (which covers only the changes around 1850 to 1910, as mathematics went from a mishmash of physics and psychology, and became an abstract deductive science):
Jeremy Gray, Plato's Ghost: The Modernist Transformation of Mathematics, Princeton University Press, 2008