We were lucky enough to interview Stas Smirnov at the ICM in Hyderabad, India. As well as being very pleased at winning the Fields Medal and being recognised by his colleagues, Stas reminded us that mathematicians don't do research to win medals. They do it because of curiosity and he personally can't wait to get back to his theorems.
What would you think if the nice café latte in your cup suddenly separated itself out into one half containing just milk and the other containing just coffee? Probably that you, or the world, have just gone crazy. There is, perhaps, a theoretical chance that after stirring the coffee all the swirling atoms in your cup just happen to find themselves in the right place for this to occur, but this chance is astronomically small.
Results in mathematics come in several flavours — theorems are the big important results, conjectures will be important results one day when they are proved, and lemmas are small results that are just stepping stones on the way to the big stuff. Right? Then why has the Fields medal just been awarded to Ngô Bào Châu for his proof of a lemma?