E. Mach revealed a major mathematical problem in 1878 in
his famous experiment in which a shock wave is sent to hit
a wedge, known as ``Mach reflection experiment'' or
a ``plane shock hitting a wedge.'' The problem became very
prominent during the atomic bomb age or supersonic flight
age, when von Neumann devoted a tremendous amount of time
and energy to the problem -- only to reveal that the problem
was harder than thought, and several von Neumann paradoxes
were since known. The problem remains open until today,
I mean today Nov 15, 2004. And tomorrow I will show you
a theorem that will shake the openness.