The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.
John von NeumannThe most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.
John von NeumannIf you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
John von NeumannThe emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.
John von Neumann