Methematical Beauty and Hidden Beauty

Mathematicians find beauty in the following formula (Euler formula). Or they say that this is a very elegant formula.

e^ix=cosx+i sinx

Where is beauty and elegance in it? It is not easy for many people to see beauty and elegance in it.
Why not? This is because ordinary people - those who have have little interest in math - do not have enough background math knowledge. Without accumulation of the related math knowledge it is impossible to find profound meanings which this simple formula contains. The degree of beauty people find in it depends on their background math knowledge. If you know more about the related math you find more beauty in this simple formula. And it usually takes a long time to accumulate the necessary knowledge.

It is similar to Enlightenment in Zen（禅）. It takes time to attain a higher level Enlightenment or Understanding (悟） and usually you must have a lot of experiences, observations and thinking by yourself.

Paintings represent beauty. It is easy to see some beauty in beautiful things. But to find beauty existing but hidden in seemingly ordinary and not so beautiful things is difficult, takes time and requires some knowledge, experiences, observations and thinking. Paintings made by the really great artists reveal this hidden beauty made in their own creative ways. These great paintings are sometimes very simple and somewhat abstract but people could find profound beauty and meanings in them.

Finding this kind of hidden beauty is a pleasure, perhaps a similar pleasure for math people when they find beauty in a simple but having deep meaning formula and for Zen people when they find Enlightenment (悟）.

AAG