> The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.
> ..The fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.
This paper is what got me interested in mathematics. I happened to read it when I was 14 in geometry class, and it fundamentally reshaped math from something that I happened to be good at to something I was deeply fascinated by and motivated to do more of
The bit at the end with his description of the various math classes was pretty funny:
PRE-CALCULUS. A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of ‘limits’ and ‘continuity’ are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.
CALCULUS. This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises which do not really apply in this setting, and which will of course not be mentioned. To be taken again in college, verbatim
I'm a huge fan of Paul's, and his book Measurement is easily the most beautiful introduction to geometry out there.
I appreciate his focus on how to maintain engagement with students who are predisposed to math, but I think it's equally important to consider how to teach students who are deeply uninterested in math but still need a working knowledge to live life. Granted, the current system seems to be failing both kinds of students.
> ..The fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.
PRE-CALCULUS. A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of ‘limits’ and ‘continuity’ are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.
CALCULUS. This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises which do not really apply in this setting, and which will of course not be mentioned. To be taken again in college, verbatim
I appreciate his focus on how to maintain engagement with students who are predisposed to math, but I think it's equally important to consider how to teach students who are deeply uninterested in math but still need a working knowledge to live life. Granted, the current system seems to be failing both kinds of students.