Not very long ago I had an argue about whether there is a solution to the equation a!b!=a!+b!+c!. It was an argue between a mathematician and engineer, so while my math friend was trying to find the solution to the problem the scientific (analytical mathematic) way I decided to give it a try and brute-force it using some nested loops in Matlab. Initially I somehow made a simple uncatchable syntax mistake and my program seemed to be looping forever. The very same evening my math soul continued with the analytical solution and finally came with a statement that the equation does not have a solution. We both agreed and assumed that we are all right.
Well, the day after we found out that there indeed is at least one solution. This is a=3, b=3, c=4. The conclusion I want to bring here is that no matter how good one is in his profession, his self-confidence should stay at maximum 0.999999999999999999.