.. title: A Mathematician's Lament
.. slug: a-mathematicians-lament
.. date: 2017-05-20 11:39:13 UTC+02:00
.. tags: mathematics
.. category:
.. link:
.. description:
.. type: text
Only recently I stumbled over `A Mathematician's Lament
`_ by Paul
Lockhart. More specifically over the freely available `PDF linked
from the Wikipedia entry
`_.
.. image:: /images/triangle-area.png
:width: 200
:align: center
:alt: Area of a triangle
.. TEASER_END
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.