Working memory, which isn't really memory in our common parlance, can be trained by using dual-n-back software. See the study by Jaeggi et al. There's some free dual-n-back software out there called Brain Workshop which tries to replicate the study.

For long term memory I recommend using a spaced repetition system. First, read the Wired article on Peter Wozniak, then look up the Wikipedia entry on spaced repetition. Then search for the program called "Anki." Download it, it's free. Watch their introductory video for an explanation. This single tip could give you returns in your life that are currently unimaginable to you.

Concentration is also trained. The first step is to stop multi-tasking, especially on the computer. Don't chat online, browse 5 windows, and have the TV or radio going in the background. Single task, and work up to longer and longer periods of single tasking. If I were to offer one product or program related to this it would be "Wake Up Productive" by Eben Pagan, but it may be expensive to you.

Again for long term memory, there are plenty of mnemonic techniques to use that go back all the way to the ancient Greeks. Look up memory contests on Google. Those people that memorize the order of a deck of cards in under a minute have trained themselves to be that way. There's a program called PMemory which might be useful. They offer the book for free, but marking and help by the teachers has to be paid for.

Of course, all of this is outside what "Grok" would do. Then again Grok didn't speak 10 languages, yet you can accomplish that with an SRS system.

performance of the brain is best when chronic stress is low and blood sugar is stable and in normal range (chronic elevated cortisol and blood sugar levels are probably #1 reason for mental decline with age). furthermore, make sure to not be deficient in any important nutrient for the brain like B12, B6, DHA, cholines, etc. for example, just by taking, say, 100mg of activated B6 and 100mg phosphatidylserine, most people will experience a strong brain and mood boost. there are many other natural supplements that do similar things like ginseng or gingko. but keeping stress low and blood sugar stable/low is by far then most important factor long term.

Try intermittent fasting!

A recent study at Yale University Medical School proposes that hunger aides in helping us learn and remember things!

The study found that increased ghrelin levels increased learning in mice. Ghrelin is released by the stomach when the body is experiencing hunger.

They found that ghrelin was binding to cells not just in the primitive part of the brain that registers hunger (the hypothalamus) but also in the region that plays a role in learning, memory and spatial analysis (the hippocampus). The researchers then put mice injected with ghrelin and control mice through a maze and other intelligence tests. In each case, the biochemically “hungry” mice — mice infused with ghrelin — performed notably better than those with normal levels of the hormone. The finding was startling, but “it makes sense,” Horvath says. “When you are hungry, you need to focus your entire system on finding food in the environment.” In fact, some biologists believe that human intelligence itself evolved because it made early hominids more effective hunters, gathers and foragers.

The theory goes if you want to learn and retain something maybe do a little IF before and during the lesson and your brain will be more receptive.

Article link...

The brain is a use it or lose it tool.

I treat it like a muscle and train it.

If I want better memory, I practice memorizing things.

If I want better math skills, I do math in my head.

Eating paleo, sufficient EFA etc takes care of my brain fuel. DHA is brain food

I feel it's kinda preaching to the choir but since you asked, Seth Roberts has data to suggest that eating more butter and animal fats in general increase his arithmetic ability. Here's a good summary: http://quantifiedself.com/2010/08/arithmetic-and-butter.php

He's a good read in general, for example he often blogs about ways on how to measure if you are really making the progress you want too.

Caveat: he seems to love his flax seed oil. WTF!!

UPDATE 26/11/10

It's somewhat tangential to the original discussion but Seth seems to address the flax seed preference in a recent post "Flaxseed Oil vs. Fish Oil":

http://www.blog.sethroberts.net/2010/11/21/flaxseed-oil-vs-fish-oil/

To expand on Bryan's comment on memnomics I want to suggest "The memory house of matto ricci" which is about. A monk teaching memory techniques in asia. The memory house technique works pretty well for long term storage and is one of the oldest tricks I know of. There are other sources but this is available and quite readable.

ah, btw, forgot to add these two awesome presentations about brain health from two of my favorite "gurus" in the realm of health, disease prevention and nutrition:

• first a talk held by mark hyman at "authors@google" : http://t.co/eQDzgFy

• secondly, a podcast by byron richards about brain health: http://www.wellnessresources.com/audio/podcast_111710.mp3

both are light years ahead of mainstream medicine and also fit into our paleo approach very well. you should definitively subscribe to both of them.

Here in Spain (and all over Mediterranean Basin I suppose...) it's said that eating raisins enhances memory. I really don't know what might be true behind this claim, but I suppose it would be because its high sugars content, or maybe boron...