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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 :tongue2: 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 [Broken]
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 :tongue2: 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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