Approach your problems from the right end It isn't that they can't see
the solution. It is and begin with the answers. Then one day, that they
can't see the problem. perhaps you will find the final question. G. K.
Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in
R Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders.
Growing specialization and diversification have brought a host of
monographs and textbooks on increasingly specialized topics. However,
the "tree" of knowledge of mathematics and related fields does not grow
only by putting forth new branches. It also happens, quite often in
fact, that branches which were thought to be completely disparate are
suddenly seen to be related. Further, the kind and level of
sophistication of mathematics applied in various sciences has changed
drastically in recent years: measure theory is used (non- trivially) in
regional and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory and the structure of water
meet one another in packing and covering theory; quantum fields, crystal
defects and mathematical programming profit from homotopy theory; Lie
algebras are relevant to filtering; and prediction and electrical
engineering can use Stein spaces. And in addition to this there are such
new emerging subdisciplines as "experimental mathematics", "CFD",
"completely integrable systems", "chaos, synergetics and large-scale
order", which are almost impossible to fit into the existing
classification schemes. They draw upon widely different sections of
mathematics.
