I am curious if the "Bourbaki's approach" to mathematics is still a viable point of view in modern mathematics, despite the fact that Bourbaki is vilified by many.

Even more specifically, does anyone actively approach mathematics from the more "yielding" point of view famously practiced by Grothendieck? Which, or what type of, research areas are welcoming to (or practicing) Grothendieck's approach to mathematics?

**Motivation:**

To me, there is a deep question regarding motivation of mathematicians over time which is addressed by this viewpoint. An emphasis on resolving hard technical problems is quite depressing, generally, whereas the idea of finding a general framework which presents a natural and explanatory solution through the development of a vast theory seems very motivating. In such a view, the open problem only serves to motivate a better development of the general theory surrounding the core difficulty, bringing into focus a clearer picture of the essential issue at hand.

It seems to me that carefully developing a general (sometimes axiomatic) theory is analogous to performing scientific experiment. One is not looking to be clever, but instead is filling in data which may, when examined later, reveal clear and natural answers to mathematical questions. Obviously such an approach can be exhausting, in that one must spend much more time to fill in an entire picture than to, at some point, jump to a resolution of a particular question. On the other hand, It may be possible to persevere longer at such a task, as one is not so sensitive to one's loss of quickness or cleverness and can simply engage the task at hand.

Is this viewpoint valid?

[**Edited (Dec. 17, 2012) by A. Caicedo**, following suggestions here. Question originally asked by user
curious1.]

verypowerful mathematician. I think it is more useful to think of his style as a manifestation of his power, rather than the converse. Among other qualities, his power included enormous, penetrating, mathematical insight. When you write that you "would like to begin to try to do mathematics in this way", this is tantamount to asking "how can I too become a more penetrating mathematician"? This is a hard question to answer, either in the abstract or in the particular, but I think that usingthisas a criterion for a field is likely to be a mistake. ... – Emerton Dec 17 '12 at 2:17