Does exercise -- physical exercise -- improve your brain?

The NYT asks, and a chorus of people who exercise all say... what do you think? Here's the first response:

Yes. Definately

The second:

The exercise can help to think more clearly. Because when you are doing the excise, your brain becomes simple not too many things to consider, so you think about one thing, it’s more clear to get the results.

And the third one... well, let's be merciful and stop...

ADDED: Here's the background article in the NYT Magazine (about research about the regeneration of neurons). And here's something Pogo writes in the comments:

Of course exercise improves your brain. That's why all the jocks in high school were also the dweebs with pocket protectors.

And Stephen Hawking is a fool.

Quite aside from the number of neurons you have at any given time is what you do with your brain. You can't read and play a sport (though you can walk and listen to an audiobook). If you can't do much other than read, on the other hand, you will probably read a lot. But what do you really want for yourself? The article seems to be mainly about staving off the mental deterioration associated with old age. Exercise might help, but so might reading or doing puzzles or thinking deeply about complicated things.

ADDED: Dan from Madison tells his story of exercise, the brain, and Muay Thai.