Is there a book that will explain famous historical formulas?

I know of no deeper and more complete explanation of Gödel’s theorem than Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter. Although it’s Pulitzer Prize-winning clarity and wit are incomparable, it’s a bit long for just a casual perusal—but worth the time invested. The same author’s more recent I Am a Strange Loop also gives a good account of Gödel’s work in a shorter space.

Five Equations that Changed the World by Michael Guillen is a nicely written volume that includes Einstein’s famous formula among its title subject. In fact just about any popularization of relativity (there are many) gives a suitable explanation.

What you are suggesting sounds like a good idea, but nobody has put it all in one book. @gasman‘s suggestions are good for the particular subjects covered and that is probably as good as you are going to be able to find. Part of the problem is that even simple formulas require a fair amount of explanation and it would be difficult to put all in one book. I am still looking for books that give a good intuitive explanation of special relativity (much simpler than general relativity) and entropy.

You may find the book God Created the Integers by Stephen Hawking to be what you are looking for. I saw it in the bookstore and there is a lot there, I haven’t read it though.

From Amazon:
“God created the integers,” wrote mathematician Leopold Kronecker, “All the rest is the work of Man.” In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains. Each of the 17 sections opens with a historical introduction of the featured author, and proceeds to a faithful translation of their most famous work. While most mathematicians will already have complete editions of Isaac Newton’s Principia or Georg Cantor’s Contributions to the Founding of the Theory of Transfinite Numbers, this book is unique in presenting just the best bits of these and other theoretical works. The collection spans 2,500 years and covers a vast range of theories: the parallel postulate, Boolean logic, differential calculus, and the philosophy of the unknowable among them. Dense with numbers, formulae, and ideas, God Created the Integers is quite challenging, but Hawking rewards curious readers with a look at how mathematics has been built. In contrast to the towering physical edifices of great civilizations of the past, Hawking writes, “The greatest wonder of the modern world is our understanding.”

I came across this book while browsing Amazon.com:
Godel’s Proof

I haven’t read it, but reviews are positive. Apparently it was originally published in 1958 by Ernest Nagel & James Newman, now available in a new edition. According to the promotional blurb: ”This reissuance of Nagel and Newman’s classic has been vastly improved by the deft editing of Douglas Hofstadter”