It is probable that the future will be more limited by the slow evolution of the human animal and the corresponding human laws, social institutions, … - Richard Hamming

In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval." ...most importantly, you should be able to generate the result you need even if no one has ever done it before you—you will not be dependent on the past to have done everything you will ever need in mathematics.

Perhaps the best way to approach the question of what mathematics is, is to start at the beginning. In the far distant prehistoric past, where we must look for the beginnings of mathematics, there were already four major faces of mathematics. First, there was the ability to carry on the long chains of close reasoning that to this day characterize much of mathematics. Second, there was geometry, leading through the concept of continuity to topology and beyond. Third, there was number, leading to arithmetic, algebra, and beyond. Finally there was artistic taste, which plays so large a role in modern mathematics. There are, of course, many different kinds of beauty in mathematics. In number theory it seems to be mainly the beauty of the almost infinite detail; in abstract algebra the beauty is mainly in the generality. Various areas of mathematics thus have various standards of aesthetics.

The purpose of computation is insight, not numbers.