A Mathematician's Lament

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Only recently I stumbled over A Mathematician's Lament by Paul Lockhart. More specifically over the freely available PDF linked from the Wikipedia entry.

Area of a triangle

As I studied mathematics myself, I am glad that someone could put my own experiences into such eloquent words. Actually I studied "Technomathematik" (technical mathematics) as it was a combination of computer science, electrical engineering and mathematics but I certainly chose it for the former two subjects and only discovered the discussed aspects of mathematics being at university. Even though mathematics in Germany is certainly taught differently than in the United States, here one can also be excellent in the subject only by reproducing things learnt by heart.

It certainly took me a while to see the artistic components but it is no accident that I have a few quotes in this spirit in my (hand collected) signature database:

The  mathematician's patterns,  like the  painter's or  the poet's,  must be
beautiful;  the ideas, like the colours or the words, must fit together in a
harmonious way. Beauty is the first test: there is no permanent place in the
world for ugly mathematics.                       -- G. H. Hardy

And another one from Douglas Hofstadter:

Progress in  mathematics comes from  repeated acts of  generalization.
If mathematics is anything, it is the art of choosing the most elegant
generalization for some abstract pattern.  Thus aesthetics is central.
                                   -- Douglas Hofstadter

My memory is still vivid of how very different my first "Linear Algebra" courses at university were to whatever I thought to be mathematics before that. The class was taught in a round robin fashion by three different professors back then and I happened to start in Prof. Wolfgang Trinks turn. The script was very "proof heavy" and contained bits of history that totally fascinated me. I remember though that most students completely disliked those pieces "not relevant for the tests", found the script "way too dry" and completely freaked out in the final test that included only a few calculation exercises but mostly wanted proofs for answers. Mr. Lockhart likely would have loved that course.

Thinking back, Mr. Trinks unfortunately did not have the charisma to show the beauty of mathematics to many, but for myself it certainly was a stroke of luck. To this day I remember literal pieces of the script connected with the circumstances under which I learned them. It certainly influenced my further studies to a degree where I liked the mathematical parts a lot more than the parts I originally started the course for. I was lucky to realize how much of a difference the person of a teacher can make before Professor Heuser retired. My last chance to take one of his course was "Funktionalanalysis" which I thoroughly enjoyed.

But enough of that - go read the PDF, it is worth the time. I especially laughed loud at this section:

All metaphor aside,  geometry class is by far the  most mentally and
emotionally  destructive component  of the  entire K-12  mathematics
curriculum. Other math  courses may hide the beautiful  bird, or put
it  in a  cage,  but in  geometry  class it  is  openly and  cruelly
tortured.
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