Hermann Weyl stated "In these days the angel of toplogy and the devil of abstract algebra fight for the soul of every individual discipline of mathematics." 1) Why does he refer to topology as angel and abstract algebra as the devil? 2) How do they get into every field of maths? I can see how algebra is in many fields and so abstract algebra is a generalisation of intuitive algebra. But how does topology get into it? 3) What about analysis? That is another major field of pure maths and is in many other disciplines of maths?