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I think you can do no better than Proofs from THE BOOK, a collection of mathematical beauties:

Aigner, Martin, and Günter M. Ziegler. Proofs from THE BOOK. Springer, 2014. (Springer link.)

There is a nice recent interview of Günter in Quanta Magazine, where he says:

"We’ve always shied away from trying to define what is a perfect proof. And I think that’s not only shyness, but actually, there is no definition and no uniform criterion. Of course, there are all these components of a beautiful proof. It can’t be too long; it has to be clear; there has to be a special idea; it might connect things that usually one wouldn’t think of as having any connection.

 

For some theorems, there are different perfect proofs for different types of readers. I mean, what is a proof? A proof, in the end, is something that convinces the reader of things being true. And whether the proof is understandable and beautiful depends not only on the proof but also on the reader: What do you know? What do you like? What do you find obvious?"

I think you can do no better than Proofs from THE BOOK, a collection of mathematical beauties:

Aigner, Martin, and Günter M. Ziegler. Proofs from THE BOOK. Springer, 2014. (Springer link.)

There is a nice recent interview of Günter in Quanta Magazine, where he says:

"We’ve always shied away from trying to define what is a perfect proof. And I think that’s not only shyness, but actually, there is no definition and no uniform criterion. Of course, there are all these components of a beautiful proof. It can’t be too long; it has to be clear; there has to be a special idea; it might connect things that usually one wouldn’t think of as having any connection.

 

For some theorems, there are different perfect proofs for different types of readers. I mean, what is a proof? A proof, in the end, is something that convinces the reader of things being true. And whether the proof is understandable and beautiful depends not only on the proof but also on the reader: What do you know? What do you like? What do you find obvious?"

I think you can do no better than Proofs from THE BOOK, a collection of mathematical beauties:

Aigner, Martin, and Günter M. Ziegler. Proofs from THE BOOK. Springer, 2014. (Springer link.)

There is a nice recent interview of Günter in Quanta Magazine, where he says:

"We’ve always shied away from trying to define what is a perfect proof. And I think that’s not only shyness, but actually, there is no definition and no uniform criterion. Of course, there are all these components of a beautiful proof. It can’t be too long; it has to be clear; there has to be a special idea; it might connect things that usually one wouldn’t think of as having any connection.

For some theorems, there are different perfect proofs for different types of readers. I mean, what is a proof? A proof, in the end, is something that convinces the reader of things being true. And whether the proof is understandable and beautiful depends not only on the proof but also on the reader: What do you know? What do you like? What do you find obvious?"

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I think you can do no better than Proofs from THE BOOK, a collection of mathematical beauties:

Aigner, Martin, and Günter M. Ziegler. Proofs from THE BOOK. Springer, 2014. (Springer link.)

There is a nice recent interview of Günter in Quanta Magazine, where he says:

"We’ve always shied away from trying to define what is a perfect proof. And I think that’s not only shyness, but actually, there is no definition and no uniform criterion. Of course, there are all these components of a beautiful proof. It can’t be too long; it has to be clear; there has to be a special idea; it might connect things that usually one wouldn’t think of as having any connection.

For some theorems, there are different perfect proofs for different types of readers. I mean, what is a proof? A proof, in the end, is something that convinces the reader of things being true. And whether the proof is understandable and beautiful depends not only on the proof but also on the reader: What do you know? What do you like? What do you find obvious?"