Ok, we’ve all heard this, but I want specifics. How can I find the straightdope on what fish can do for brain development, and which fish? Does shellfish count?
I believe the claims are made regarding Omega 3 fatty acid, which is concentrated in oily fish.
I guess it derives from the fact of fish possessing relatively high concentrations of polyunsaturated fatty acids. Studies show they seem to help:
The phrase has been tied in with promoting the Omega 3 of fish oil for a few decades already.
People have been calling fish ‘brain food’ for decades though - certainly since a long time before the current Omega fatty acids thing - perhaps because it’s a good protein source that is easy to eat and digest, or maybe - if the phrase goes back far enough - because of some quite weird ideas about foods and their effect on the body.
Fish will probably happily eat brain in return.
Ahh, the cycle of life.
Here is ancient evidence to back up Mangetout’s first point:
Customer to Fishmonger: Hey! You told me fish heads are brain food, and I’ve been eating fish head stew for a week. Now, I realize you’re charging me twice as much for the fish heads as I’d pay for the rest of the fish!
Fishmonger: You see? You’re getting smarter already!
You’ll want to be careful with those assumptions about fish being brain food. My mother firmly believed that, and she got me! 
Of course, my brother is a genius.
If a salmon eats nine hazelnuts that fell from the nine trees into the fountain of wisdom, the first person to eat of that salmon will gain all the knowledge in the world, or something.
Only in Soviet Russia.
“What’s that?”
“That’s my costume. The Salmon of Knowledge.”
I can testify that they’ve been saying it for at least 40 years. When I first heard it, it wasn’t tied to anything in particular except, maybe, to the old joke.
Q Why do they say that fish is good brain food?
A 'Cause they travel in schools.
When I was a kid way back in the 60s I had a book called Superstitious? Here’s Why. This was a children’s book, paperback, a few nice illustrations. It would explain the reasons behind many well-known superstitions, very few I had ever heard about myself, including the food is brain food thing.
It explained that there had been a scientific study that had shown that fish was high is a particular chemical, and that another study had shown that the brain was also high in the same chemical. I cannot remember what the chemical was (not enough fish, obviously). I’m thinking potassium, but who knows. Anyway, less informed people heard about these two studies and decided there was a connection. It also said that while eating some fish was good for you, it wouldn’t make you any smarter.
Phosphorus. People used to think eating fish made you smarter because of the phosphorus.
Well, phosphorus will make you … brighter.
A matchless comment.
Wodehouse’s Bertie Wooster usually says something in every book about Jeeves’ intake of fish and his brain power. I’m posting from work, and so have no books at hand for a better cite/quote.