In case you can’t fall asleep, don’t indulge in caffeine. These problems by Arnold(PDF) will do the job.

Trembling is the very opening of Arnold’s trivium: “The standard of mathematical culture is failing…”

Download PDF here, courtesy of Montana Uni.

Read Turbulence, the oldest unsolved problem in physics by Lee PhillipsLee Phillips

An interesting read on the phenomenon of turbulence from Physicist Lee Phillips:

An example of why turbulence is said to be an unsolved problem is that we can’t generally predict the speed at which an orderly, non-turbulent (“laminar”) flow will make the transition to a turbulent flow. We can do pretty well in some special cases—this was one of the problems that Heisenberg had some success with — but, in general, our rules of thumb for predicting the transition speeds are summaries of experiments and engineering experience.

Due to the difficulty in mathematically describing turbulence as accurately as we have modeled non-chaotic phenomena, computational fluid dynamics (CFD) could assist physicists in approximating a description. However,

[T]he search for a better theoretical understanding of turbulence continues, for computers can only calculate flow solutions in particular situations, one case at a time. Only through the use of mathematics do physicists feel that they’ve achieved a general understanding of a group of related phenomena.

Which, as Phillips alludes to, will continue to excite the curiosity of physicists, thus perpetuating the need for the discipline.