This is the first part of the video of a lecture given by Prof Timothy Gowers at the millennium meeting of the Clay Mathematics Institute at College de France, Paris on May 24, 2000. Prof Gowers mentions on his webpage,

As its title suggests, it is an attempt to justify pure mathematics. The lecture was aimed at the general public and assumes very little mathematical background.

There are eight parts in all. The rest of the seven may be found on YouTube.

A transcript of the lecture (without the illustrations) can be found here.