  A physical system is determined by a finite set of initial conditions and
"laws" represented by equations. The system is computable if we can solve the
equations in all instances using a "finite body of mathematical knowledge". In
this case, if the laws of the system can be coded into a computer program, then
given the initial conditions of the system, one can compute the system's
evolution. Are there incomputable physical systems? This question has been
theoretically studied in the last 30-40 years. In this paper, we experimentally
show for the first time the strong incomputability of a quantum experiment,
namely the outputs of a quantum random number generator. Moreover, the
experimental results are robust and statistically significant.
