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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.
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.
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