The probability of discovery

In 2009 the Large Hadron Collider (LHC) turned on and became the most complex scientific instrument ever put into operation by mankind. The LHC is what is called a “discovery machine”, meant to explore new limits at the high-energy frontier. Any cost–benefit analysis for such an instrument for fundamental research has to gauge the opportunities and risks of such a facility, and in particular major discoveries have a significant role in that balance. In this paper we discuss the challenges and uncertainties of discoveries in fundamental science, using the recent history and expected near future of the LHC as an example.