From the limited amount I've read about this, he seems to believe that academic mathematics is corrupt and unethical. Basically, he objects to the whole machinery that would award him this prize.
Edit: If you're interested about Yau, here's a NYT article (http://www.nytimes.com/2006/10/17/science/17yau.html?_r=1)
"But even his admirers say he has a political side. “As Shiing-Shen Chern’s successor as emperor of Chinese mathematics,” Deane Yang, a professor of mathematics at Polytechnic University in Brooklyn and an old family friend, wrote in a letter to The New Yorker, “Yau has an outsized ego and great ambition, and has done things that dismay his peers.” But, Dr. Yang said, Dr. Yau has been a major force for good in mathematics and in China, a prodigious teacher who has trained 39 Ph.D.’s."
I know, my PhD is in pure mathematics - I've seen up-close that mathematicians can be an odd bunch ;)
Using the money to fund some kind of an alternative to the organisation he believes is corrupt, surely wouldn't make him corrupt though, just to take one example?
Had he just accepted the prize, there would probably be little mention of it in the main stream media.
I couldn't resist thinking about this a bit more. Something comparable would be firefox's double-page New York Times ad, which apparently cost about $200k (http://weblogs.mozillazine.org/asa/archives/007103.html) and certainly reached a lot of non-mathematicians.
Even though Perelman's action has generated quite a bit of press attention, my gut feeling is he could have paid for even more attention if he chose to use the prize money to raise awareness directly.
That said, if he really wanted to get maximum exposure, he could continue to ignore the prize for almost a year, but accept it at the last minute and then spend it all on ads telling the world how corrupt academic mathematics is ;)
I'd think generating interest from something minute would be harder than from something a lot of people have at least heard of.
Or maybe he just has other things he wants to be doing that don't require that money.
For me that's called being consistent as a man and it's the type of choice that separates men from peons.
So, let's not put a man on trial for refusing a gift. What's wrong with that? It didn't harm anybody I think...
Go Grigory Perelman!
What you're saying makes perfect sense in the context of our (modern Western) attitude to money, but Perelman has always struck me as a throwback to an older conception of these things. He might well regard money -- or at least money obtained in this way -- as intrinsically incompatible with pure intellectual life. If accepting the money would entail losing something that he values more, his refusal is not so strange.
It's also the case that Russian intellectuals are -- or at least used to be -- biased more in this direction than Western ones. Which reminds me of one of the greatest and funniest things ever said on the subject, Saltykov-Shchedrin on the difference between Russia and the West: "A Westerner sells his soul to the devil; a Russian just gives his soul to the devil."
Not sure whether he likes the attention or if it fits his political agenda.