Books from the Masters: Learn from Gauss, Newton & Euclid

[damabo]

Hi,

I'm doing my first year in mathematics and physics. I heard (I think it was Mathwonk), that it ofter helps to read 'the masters' instead of the pupils, meaning it benefits to read Gauss, Newton, Euclid.
Can I start with this, or is it too early? I was thinking of buying three monumental works 'disquistiones arithmeticae', 'principia mathematica' and 'elements'. Does anybody know which version I should buy? Are there perhaps even more interesting books to look out for?

Thanks

 

[kakarotyjn]

I think there is no need to read books of masters like Gauss or Newton, their masterpieces are too old to learn. You can learn Newton's work by taking the course Calculus, learn Gauss's work buy learning differential geometry or complex analysis or number theory. There is no need to read their original papers or books, because they are too old, the explanation is much more complex than standard textbook, so reading them costs much more time. And most of the notion and symbol they use in their books are also unused now. But maybe you could get some ideas by reading their masterpieces.

But I suggest you read masters' book or papers not that old. Maybe since 1960' or 1970', I don't know. But it's not easy because you need to learn materials before that :)

 

[zoobyshoe]

I was thinking of buying three monumental works 'disquistiones arithmeticae', 'principia mathematica' and 'elements'. Does anybody know which version I should buy?

I haven't tried to read Gauss but both "Principia" and "Elements" are online completely for free.

I think all anyone needs to read of "Principia"," if they're interested, is the first 19 pages. These are the two chapters called "Defintitions" and "Axioms or Laws of Motion".

The trouble with the rest of it is that Newton doesn't actually use or explain calculus in his arguments. He reasons things out with a very strange hybrid of geometry and calculus-like concepts. You won't ever encounter this math anywhere else.

I'm not sure what to say about "Elements." I gave up on it after a few pages because it seemed much too laborious compared to more compact modern digests. A person who sticks with it might be rewarded with a deeper understanding down the line, I don't know.

(The book I actually ended up enjoying a lot is not on your list: Galileo's "Dialog Concerning Two New Sciences." It's written in the form of a discussion between three people, so it's like reading a PF thread from 400 years ago.)