Preliminary Idea for Exposition Paper

Many Mathematicians and people in the academia agree on a few important unsolved problems in Mathematics, and most of these have been around for centuries. Seven of these problems have been listed as the Clay Millennium Prize Problems by the Clay Mathematics Institute --- anyone who can solve the problem will be awarded a million US dollars by the institute on top of all the glory and honour. The seven problems include (from Wikipedia - Millennium Prize Problems)

1. P versus NP problem
2. Hodge conjecture
3. Poincaré conjecture
4. Riemann hypothesis
5. Yang–Mills existence and mass gap
6. Navier–Stokes existence and smoothness
7. Birch and Swinnerton-Dyer conjecture

Grigori Perelman proved the Poincaré Conjecture in 2003. Subsequently, he declined the million dollar prize from the institute, and the Field's Medal, which is considered the Nobel Prize equivalent for Mathematics.

In my paper, I intend to investigate what a prize really mean by looking at the case of Grigori Perelman. I intend to discuss prizes serving as the following:

• The recognition of the receiver
• The recognition of the receiver's work
• The receiver's recognition of the prize body
• Randerson from The Guardian wrote

  "He has also refused a major European maths prize, supposedly on the grounds that he did not believe the committee awarding the prize was sufficiently qualified to judge his work."

• Whether a prize even serves as a recognition of one's work, or if it is actually redundant
• Grigori famously said, "Everybody understood that if the proof is correct, then no other recognition is needed."

I intend to read Masha Gessen's book on Grigori (Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century), as well as various commentaries or papers on the Millennium Prize, Field's Medal, and to search for any other rejections of prestigious prizes and the reasons behind them.


Cast in the form of the template:
I want to study Grigori Perelman's rejection of the Millennium Prize to learn about what the acceptance of a prize means, because this will shed light on the dynamics of the prize body and receiving party to give new insights on the existence of prizes.