Vladimir Voevodsky is one of the most acclaimed contemporary pure mathematicians. It is very interesting therefore to read his opinion about pure and applied mathematics. Here is a recent interview, made by another very good pure mathematician Roman Mikhailov (the interview is by no means about science, however, some parts are):
Here is an extract (translation is mine):
Concerning the pure and applied mathematics, I have the following picture. Pure mathematics is working with the models of high abstraction and low complexity (mathematicians like to call this low complexity elegance). Applied mathematics is working with more concrete models but on the higher complexity level (many equations, unknowns, etc). Interesting application of the modern pure mathematics are most likely in the area of high abstraction and high complexity. This area is practically inaccessible today, mostly due to the limitations of the human brain to work with such models…
Mathematical Biology 
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