Mathematical Beauty

Mathematical Beauty
Beauty in results

[pic]Starting at e0 = 1, travelling at the velocity i relative to one's position for the length of time π, and adding 1, one arrives at 0. (The diagram is an Argand diagram)
Some mathematicians (Rota (1977), p. 173) see beauty in mathematical results that establish connections between two areas of mathematics that at first sight appear to be totally unrelated. These results are often described as deep.
Beauty in experience

[pic]There is a certain "cold and austere" beauty in this compound of five cubes

Some degree of delight in the manipulation of numbers and symbols is probably required to engage in any mathematics. Given the utility of mathematics inscience and engineering, it is likely that any technological society will actively cultivate these aesthetics, certainly in its philosophy of science if nowhere else.

Beauty and philosophy
These mathematicians believe that the detailed and precise results of mathematics may be reasonably taken to be true without any dependence on the universe in which we live. For example, they would argue that the theory of the natural numbers is fundamentally valid, in a way that does not require any specific context. Some mathematicians have extrapolated this viewpoint that mathematical beauty is truth further, in some cases becoming mysticism.
Beauty and mathematical information theory

In the 1970s, Abraham Moles and Frieder Nake analyzed links between beauty, information processing, and information theory.[9][10] In the 1990s, Jürgen Schmidhuber formulated a mathematical theory of observer-dependent subjective beauty based on algorithmic information theory: the most beautiful objects among subjectively comparable objects have short algorithmic descriptions (i.e., Kolmogorov complexity) relative to what the observer already knows.

Mathematics and art

Main articles: Mathematics and art and Mathematics and music

The psychology of the aesthetics of mathematics is...