I remember in Harry Potter and the Prisoner of Azkaban, a wizard was reading A Brief History of Time by the author Stephen Hawking.
Why should a wizard read something like this? And was there any specific reason as to why this book only was chosen?
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There's no reason a wizard wouldn't read such a book. I'm sure there are some minority of wizards who want to understand the 'Muggle World' and Stephen Hawking's books that are aimed at the layperson (such as A Brief History of Time) are actually fairly good. They explain things simply, so that an average person can understand, and give a nice entry to the concepts. It would be a nice way for a wizard to begin to get the gist of where Muggle knowledge is.
Such a book might be recommended to someone who entered a bookstore in search of 'science books' or to someone who read a Muggle newspaper and discovered the names of some top scientists.
Alternatively, it could be somewhat popular in the Wizard world at large:
A wizard would likely find Hawking to be amusing - 'physics' and 'material limits' just don't apply to them. To a wizard who knows about time turners, Hawking's assertations about the impossibility of time travel would be laughable. Even to those without, many concepts of modern physics (such as conservation of momentum and the concept that matter can't be created or destroyed) would seem silly.
Since such things are presented with all seriousness by Muggle physics, the end result for a wizard might be taken as extremely deadpan humor.
Most people read for the following reasons:
Finally, Stephen Hawking's A Brief History of Time just might be a bit of a more fascinating read than the following wizarding books: