Cellular Automata, the Game of Life, are one of the subjects in math that are suspect and gauche because they are too interesting. Interesting math, it is generally believed, attracts all the wrong people. Subjects with a similar reputation including the Banach-Tarski theorem (cut up a sphere into a finite number of "pieces" via the axiom of choice -> rearrange them without stretching into two equally large spheres!), Gödel's incompleteness theorem (there exist unprovable but true statements in models of second-order logic!), and chaos theory (for certain continuous, arbitrarily small changes in x may result in arbitrarily large changes in y: potentially making it tricky to predict the weather or stock market).
Cellular Automata, the Game of Life, are one of the subjects in math that are suspect and gauche because they are too interesting. Interesting math, it is generally believed, attracts all the wrong people. Subjects with a similar reputation including the Banach-Tarski theorem (cut up a sphere into a finite number of "pieces" via the axiom of choice -> rearrange them without stretching into two equally large spheres!), Gödel's incompleteness theorem (there exist unprovable but true statements in models of second-order logic!), and chaos theory (for certain continuous, arbitrarily small changes in x may result in arbitrarily large changes in y: potentially making it tricky to predict the weather or stock market).