[Karthik]

Having a peered into the world of theoretical mathematics, let me try and shed some light on this situation.

The life of a pure mathematician is one of solitude. Most work alone and are completely engrossed in their research. I wish I had my source on this, but the majority of mathematicians score as introvert on the Meyers-Briggs personality sorter. The solitude that their research requires is exactly what these people are seeking. Many use their work as an excuse to remain isolated from the rest of the world. Most likely, their introverted personality led to difficulties interacting with others when they were younger, as a result they isolate themselves. Attention is definitely not something they are looking for.

The Poincare Conjecture has been worked on for years, with very little success. This result is a huge breakthrough in the field of topology. Is this why Perelman worked on the conjecture? Probably not. To a pure mathematician, the challenge can greatly outweigh the potential breakthrough. As Richard so aptly described, mathematics at this level is closer to an art than a science. (Actually, high level mathematics is highly abstract and a right-brained skill)

My take on the situation is that Perelman naturally avoids the spotlight, and wishes to continue to do so. He's probably far more comfortable working on his art out of the view of others. Sure he published his result, but most likely not for any recognition, rather to share his "masterpiece" with those who appreciate this sort of thing.

The irony is, Perelman is turning down the Fields Medal to shun the spotlight, yet as a result is generating far more attention than he would have if he had accepted the prize.