Do "older" books provide unique insights?

[martinbn]

I know this thread is about QM books and interpretations, so I am off topic, but anyway...

One thing that old books in maths can give is the original proofs of theorems. After time and generations of exposition proofs can change considerably from the original idea, which may be not the shortest and slickest way but sometimes is more natural and can give insight that cannot be found in a modern book. That's just a hypothetical possibility I cannot give an example.

 

[atyy]

I know this thread is about QM books and interpretations, so I am off topic, but anyway...

One thing that old books in maths can give is the original proofs of theorems. After time and generations of exposition proofs can change considerably from the original idea, which may be not the shortest and slickest way but sometimes is more natural and can give insight that cannot be found in a modern book. That's just a hypothetical possibility I cannot give an example.

Newton's original proofs are (somewhat) of this nature, as vanhees71 said in an earlier post.

However, I think most of us would find the modern proofs more natural.

I think Goedel's and Rosser's original proofs of the incompleteness theorems are also perhaps not as natural as modern expositions which stress the relationship to Cantor's diagonalization. What's nice about Goedel's and Rosser's original proofs that is not so obvious with diagonalization is their relationship to the liar paradox.

 

[martinbn]

However, I think most of us would find the modern proofs more natural.

Of course, I didn't mean that all proofs are more natural in the old books. I meant that they can be (sometimes, perhaps rarely).

 

[vanhees71]

Well, it's not so easy. On the one hand, I'm of the strong opinion that math and the natural science should not be taught using the historical approach to begin with. It's the very nature of these subjects that there is progress with time, and problems get solved which have been obscure before. It's not necessary to learn old-fashioned misconceptions to start with a subject. E.g., you don't need Bohr's model of the atom (which in fact cements very wrong ideas about what's "going on" in the microscopic realm, even on a qualitative level) to learn up-to-date quantum mechanics. It may be even hindering a clear understanding of the subject.

On the other hand, one should know a bit about the historical development of ideas of all these subjects to fully understand the implications of the up-to-date state of the art. It's, e.g., very illuminating to understand the trouble of classical electron theory a la Lorentz et al, partially still unsolved today (e.g., self-consistent dynamics of classical charged point particles including radiation reaction; motion of classical charged particles with spin/magnetic moment in a general em. field) to appreciate the modern view fully.

Coming back to the topic of this section of the forum, it thus can be very illuminating to study "old textbooks". Then there are exceptional good ones, which exceed the quality of modern textbooks, particularly about subjects which have not considerably changed in the meantime. Examples in theoretical physics are, "The Feynman Lectures", Sommerfeld's "Lectures on Theoretical Physics" (which in my opinion is still the most concise treatment of classical physics including the mathematical methodology ever written, particularly vol. VI on partial differential equations in physics), Pauli's "Lectures on Theoretical Physics" (particularly quantum mechanics), Dirac's "Quantum Mechanics", Weinberg's "Gravitation and Cosmology" (although maybe that doesn't qualify as an "old textbook").

 

[bolbteppa]

(10) Bourbaki https://en.wikipedia.org/wiki/Éléments_de_mathématique
(09) Dieudonne https://en.wikipedia.org/wiki/Treatise_on_analysis
(10) Landau https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics
(06) Sommerfeld https://en.wikipedia.org/wiki/Arnold_Sommerfeld#Munich
(05) Goursat https://en.wikipedia.org/wiki/Édouard_Goursat#Books_by_Edouard_Goursat
(02) Van Der Waerden https://en.wikipedia.org/wiki/Moderne_Algebra
(01) Whittaker https://en.wikipedia.org/wiki/A_Course_of_Modern_Analysis
(03) Cartan http://www.maa.org/press/maa-reviews/differential-forms
https://www.amazon.com/dp/0395120330/?tag=pfamazon01-20

= ?

Notice most have their own separate wiki page, as in the books, not just the authors, have their own pages...

 

[fedor slam]

(10) Bourbaki https://en.wikipedia.org/wiki/Éléments_de_mathématique
(09) Dieudonne https://en.wikipedia.org/wiki/Treatise_on_analysis
(10) Landau https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics
(06) Sommerfeld https://en.wikipedia.org/wiki/Arnold_Sommerfeld#Munich
(05) Goursat https://en.wikipedia.org/wiki/Édouard_Goursat#Books_by_Edouard_Goursat
(02) Van Der Waerden https://en.wikipedia.org/wiki/Moderne_Algebra
(01) Whittaker https://en.wikipedia.org/wiki/A_Course_of_Modern_Analysis
(03) Cartan http://www.maa.org/press/maa-reviews/differential-forms
https://www.amazon.com/dp/0395120330/?tag=pfamazon01-20

= ?

Notice most have their own separate wiki page, as in the books, not just the authors, have their own pages...

Thank you, and on a sidenote what is your opinion on Edmund Landua's book on calculus and the one on analysis.

 

[vanhees71]

Finding Bourbaki and Dieudonne in your list surprises me a bit. It's more like an encyclopedia, but they make horrible textbooks in my opinion, i.e., they don't provide too much "insight". They are related to math as a creative process like the description of music in terms of pressure fluctuations of the air making up sound waves .