Mathematics is a set of many rules one applies in given situations a bit like moves in chess...The Sicilian, Albin Counter, King's Indian defense (can you tell I'm just watching Queen's Gambit ?). What makes a good mathematician (or chess player) is applying the most fitting rules in a given situation (or devising new rules). John said he wasn't as good at that as his colleague at Cambridge at doing this who he said 'completely thought in maths" whereas he, a brilliant mathematician 'translated' ideas into maths and back again into thoughts. This is why he changed fields from Cosmology to computational neuroscience and how I got to meet him!