The beauty that Pythagoras saw in mathematics is an interesting example of the way that an obsession with what we perceive as beauty can take us further from truth. So it perhaps suggests that beauty is not always truth.Is there beauty in mathematics? One of the qualities is elegance, is that a face of beauty? Is truth a form of beauty? Abstract truths that is, which Pythagoras dedicated his life to find.
When Pythagoras discovered the mathematical proof that the square-root of two is an irrational number (a number than cannot be expressed as a ratio of two whole numbers) the instinct was to suppress this knowledge because irrational numbers were thought to fall short of the criteria for true mathematical beauty.
This ancient Greek obsession with the beauty of perceived mathematical perfection had long tentacles that stretched down the centuries, perhaps most famously to Johannes Kepler. He took another beautiful ancient Greek mathematical proof - the 5 platonic solids - and tried to fit them to the orbits of the then-known extraterrestrial planets, insisting also that they must move in perfectly circular orbits. When Kepler used Tycho Brahe's observational data to come to the important realisation that the planets actually travel in elliptical orbits, and when he came up with his set of laws to describe that elliptical motion, it took him a long time to accept his own findings. He was still infected by the idea that a circle is somehow more "perfect" than an ellipse.
It's interesting to see cases like this as exemplars of the double-edged sword that is the pursuit of beauty in mathematics and physics. It can both drive us forward and blind us. If Kepler had known that his work would then go on to be used by Newton to create the beautifully simple Theory of Universal Gravitation, perhaps he would have regarded those "ugly" ellipses as a temporary stage that had to be passed through in order to reach order and simplicity again?