"...includes landmark discoveries spanning 2500 years and representing the work of mathematicians such as Euclid, Georg Cantor, Kurt Godel, Augustin Cauchy, Bernard Riemann and Alan Turing. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication, many in new translations."
My absolute favorite is Descartes Geometrie. Reading the original humanizes him. He is at once humble and yet confident that he'd discovered something important. Today, we take Descartes ideas completely for granted, and even find them trivial, and yet to realize the immense shift in thinking it represented in his time, makes it all the more impressive. I would even argue that Descartes' ideas were more important than any save Euclid in forming the foundation of modern math and physics - he was the one that divorced the notion of "quantity" from "length of a line segment"! It's just so great to read the original.
Interestingly, Riemann got almost all of his papers included in this book, the most pages by far of any author. Clearly Hawking loved Riemann - and no wonder. Riemann was the one who truly generalized geometry, and its interesting that his work in that area was mostly ignored until 50 years after it was published, when Einstein used it for General Relativity. He made enormous contributions to lots of other fields, too.
Oh, and it was really cool reading Boole's words, and recognizing that he was explicitly talking in terms of creating a calculus of thought!
So, yeah, I love this book because we often talk about "the shoulders of giants" but we rarely actually read them directly. And it's amazing, inspiring, and wonderful to relate to them!
From the blurb:
"...includes landmark discoveries spanning 2500 years and representing the work of mathematicians such as Euclid, Georg Cantor, Kurt Godel, Augustin Cauchy, Bernard Riemann and Alan Turing. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication, many in new translations."
My absolute favorite is Descartes Geometrie. Reading the original humanizes him. He is at once humble and yet confident that he'd discovered something important. Today, we take Descartes ideas completely for granted, and even find them trivial, and yet to realize the immense shift in thinking it represented in his time, makes it all the more impressive. I would even argue that Descartes' ideas were more important than any save Euclid in forming the foundation of modern math and physics - he was the one that divorced the notion of "quantity" from "length of a line segment"! It's just so great to read the original.
Interestingly, Riemann got almost all of his papers included in this book, the most pages by far of any author. Clearly Hawking loved Riemann - and no wonder. Riemann was the one who truly generalized geometry, and its interesting that his work in that area was mostly ignored until 50 years after it was published, when Einstein used it for General Relativity. He made enormous contributions to lots of other fields, too.
Oh, and it was really cool reading Boole's words, and recognizing that he was explicitly talking in terms of creating a calculus of thought!
So, yeah, I love this book because we often talk about "the shoulders of giants" but we rarely actually read them directly. And it's amazing, inspiring, and wonderful to relate to them!