Math, Science and Beauty
I recently read an article about the mathematics of beauty. Researchers found
out that beauty is not in the eye of the beholder, and that beauty can indeed be
quantified.
Now, if it is possible to describe what beauty is using mathematical formulas,
maybe it is also possible to look at the issue the other way around. Can math
itself be considered beautiful or ugly? I did find an answer to this question by the
English mathematician G. H. Hardy (1877-1947):
“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 this world for ugly
mathematics.’’ G. H. Hardy
Imagine that you are working on a math problem. You do your calculations
and you calculate an answer to the problem. Let’s say that the solution turns
out to be 23.119231. Someone else works on the same math problem and also
comes up with an answer. In this case turns out to be exactly 1. Evidently one of
you two made a calculation mistake. Which answer do you tend to trust more,
the 23.119231 or the 1? Which one of the two is more likely to be correct?
Many people would distrust the 23.119231 much more because it is an “ugly”
answer. The 1 is simply the more “beautiful” answer. But from a mathematical
standpoint, there is no real reason why the 1 should be given a preference. Seen
from a purely statistical viewpoint, both numbers are equally likely to occur. Still,
many of us prefer the 1. Let’s think back a bit and be honest, have we not all once
said the words “this is not a beautiful solution”, “this answer doesn’t look nice”
or “what a nice result” when solving math problems? Could it be that we are
using beauty as a “truth test”? Do we consider a beautiful answer more likely to
be correct?
Pythagoras (c. 570-c. 495 BC), for example, was very unhappy about the
discovery of irrational...