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A mathematician working in ideal conditions would be able to look at a
fresh problem and easily to access any related material, find all the
work on simpler but similar problems, and quickly carry out any
sub-computations needed for the solution of the fresh problem. Such a
person also would be able to consult freely not only with colleagues,
but with experts not previously known to the mathematician.
Naturally, a successful mathematician also needs the ability to
generate fresh, workable, and appropriate ideas for each new problem,
and this spark is to us the essence of good mathematics. Such a
mathematician would surely thrive within the conditions outlined above.
That said, there are formidable difficulties to providing and maintaining
such an ideal environment.