Older days scientists were universalists and philosophy, physics and mathematics were a part the same question - understanding the world. Nowadays one may get feeling that the role of applications in development of modern mathematics is negligible - of course it depends on the field. And aim of the question is to get different opinions from different points of view.

Question 1 What is the role of applications in modern mathematics ?

Question 2 Different countries have different mechanisms to stimulate interaction between mathematics and applications - what are these mechanisms and what are their advantages and disadvantages ?

Question 3 (for pure mathematicians) What is your personal stance on applications ? Is it out of your scope of interests or you are have (trying to have) some contact with applications ?