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If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.
If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.
The 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.