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Just last week I relieved myself of a mathematical burden, freeing up some time for myself.

Coincidentally I came across the following passage by Arnol'd around the same time:

So, having a bit of free time & the ability to understand old textbooks on mathematics,

both of which I'd previously not been fortunate enough to be in possession of, I got

Goursat's books on calculus & differential equations on archive.org. Wow! Phenomenal

stuff so far! This pushed me to look for a historical algebra text to go over some of the

more elementary stuff. I found a book by G. Chrystal on Algebra that gives a proof of

the partial fraction expansion & derives the lagrange interpolation formula from scratch!

I haven't been able to find much on either of these topics tbh, especially not in the way

that is done in that book. They have been very non-intuitive explanations that I have

gotten from more modern books.

So, with this in mind, could people recommend other similar books from the late 19th,

early 20th century era that contain similar gold? I'm speaking particularly of the geometric

aspect that Arnol'd is describing, further elaborated by this passage:

Now I don't think Hardy's book is a good example of this, I have it & I don't like it that

much. I'm just hoping people would be aware of a lot of other books that one could check

out, contrast & compare etc... to find something akin to what Arnol'd is talking about,

especially other books that people know about & have a good reputation that are not

the Elements, or the Principia, or Archimedes or something I'm not interested

in newer books as I'm aware of what they contain, we're talking about the seedy

undercurrent of old mathematics textbooks

Coincidentally I came across the following passage by Arnol'd around the same time:

To the question "what is 2 + 3" a French primary school pupil replied: "3 + 2, since

addition is commutative". He did not know what the sum was equal to and could not

even understand what he was asked about! Another French pupil (quite rational, in my

opinion) defined mathematics as follows: "There is a square, but that still has to be

proved". Judging by my teaching experience in France, the university students' idea

of mathematics (even of those taught mathematics at the École Normale Supérieure -

I feel sorry most of all for these obviously intelligent but deformed kids) is as poor as

that of this pupil. Mentally challenged zealots of "abstract mathematics" threw all the

geometry (through which connection with physics and reality most often takes place

in mathematics) out of teaching. Calculus textbooks by Goursat, Hermite, Picard were

recently dumped by the student library of the Universitiés Paris 6 and 7 (Jussieu) as

obsolete and, therefore, harmful (they were only rescued by my intervention).

link

So, having a bit of free time & the ability to understand old textbooks on mathematics,

both of which I'd previously not been fortunate enough to be in possession of, I got

Goursat's books on calculus & differential equations on archive.org. Wow! Phenomenal

stuff so far! This pushed me to look for a historical algebra text to go over some of the

more elementary stuff. I found a book by G. Chrystal on Algebra that gives a proof of

the partial fraction expansion & derives the lagrange interpolation formula from scratch!

I haven't been able to find much on either of these topics tbh, especially not in the way

that is done in that book. They have been very non-intuitive explanations that I have

gotten from more modern books.

So, with this in mind, could people recommend other similar books from the late 19th,

early 20th century era that contain similar gold? I'm speaking particularly of the geometric

aspect that Arnol'd is describing, further elaborated by this passage:

...these students have never seen a paraboloid and a question on the form of the

surface given by the equation xy = z^2 puts the mathematicians studying at ENS into a

stupor. Drawing a curve given by parametric equations (like x = t^3 - 3t, y = t^4 - 2t^2)

on a plane is a totally impossible problem for students (and, probably, even for most

French professors of mathematics).

Beginning with l'Hospital's first textbook on calculus ("calculus for understanding of

curved lines") and roughly until Goursat's textbook, the ability to solve such problems

was considered to be (along with the knowledge of the times table) a necessary part of

the craft of every mathematician.

http://www.geniebusters.org/Riemann_intro.html

Now I don't think Hardy's book is a good example of this, I have it & I don't like it that

much. I'm just hoping people would be aware of a lot of other books that one could check

out, contrast & compare etc... to find something akin to what Arnol'd is talking about,

especially other books that people know about & have a good reputation that are not

the Elements, or the Principia, or Archimedes or something I'm not interested

in newer books as I'm aware of what they contain, we're talking about the seedy

undercurrent of old mathematics textbooks

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