The World Wide Web was born with the previous collider, LEP, which was using the same tunnel as the LHC. It was born because for the first time there were many countries and tens of institutes and hundreds of physicists in each of the four experiments and there was great need to communicate clearly and easily and fast,bypassing group e-mails.
The LHC physics groups are an order of magnitude larger than the LEP ones. The data gathering and the computer needs both during the ten years of development and during the runs are enormous. A new computer system was developed for handling large data samples and Monte Carlo samples, in a distributed manner, called the GRID. This is at the frontier of large data handling and the methods developed will certainly find applications world wide.
There will also be knowledge gathered on radiation hardness, on superconducting technologies and magnetic fields.
In my opinion no new mathematics is coming out of the LHC per se. The data analysis from the experiments at LHC may show confirmation of existing theoretical predictions/models, but the mathematics of these are already developed.
An unexpected discovery might force new theories to form, that might need new mathematical tools, but I would consider it rather improbable.
