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Best math book which consists of the best and most important work of the greatest mathematicians till date? (With explanations)

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Closest one I can think of is the God created the integers by Stephen Hawking..he adds commentary about his favourite theorems from their work and explains why those are his favourite and their importance.
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I can think of two books which are pretty close to what you are looking for:

- proofs from the book - a collection of some of the most elegant proofs in mathematics
- Princeton companion to mathematics - it's pretty much an encyclopedia of mathematics, but it has some really nice expository entries
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A great book that I recommend that is in line with what you ask is Journey through Genius by William Dunham.

Goes through the history of mathematics by selecting some of the most famous and/or important proofs and mathematicians and places them in historic context as well as explains the proofs in an accessible manner.
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It's a while since I read it but Simon Singh Fermat's last theorem is a good read and IIRC it covers some important work on the way to telling the story of FLT.  
Not a book, but the BBC had an excellent series on the history of mathematics called 'The story of maths' with Marcus du Sautoy.
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Men of Mathematics by ET Bell. It covers exactly what you’re asking for but was written in 1937 so stops there. It’s a big book as you can imagine
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it's a little outdated, but you may like the relatively exhaustive series "The World of Mathematics" by Newman. It consists of 4 volumes.

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