Describing good play as "making few mistakes" seems like the wrong terminology to me. A mistake is not a thing, in and of itself, it's just the entire space of possible games outside the very narrow subset that lead to victory. If you give me a list of 100 chess mistakes, you've actually told me a lot less about the game than if you've given me a list of 50 good strategies -- identifying a point in the larger space of losing strategies encodes far less information than picking one in the smaller space of winning.

And the real reason I'm nitpicking here is because my advisor has always proceeded mostly by pointing out mistakes, but rarely by identifying helpful, effective strategies, and so I feel like I've failed to learn much from him for very solid information-theoretic reasons.

The mistakes are there, waiting to be made.

Savielly Tartakower, on the starting position in chess. Source.

Good work guys!

This might be the excuse I need to finally go through the complete sequences as opposed to relying on cherry-picking posts whenever I encounter a reference I don't already know.

What are you trying to buy yourself by getting better at Raven's matrices?

So, along that same thread, I noticed inefficiencies in my IQ test taking skills (as I outlined in my original question), which prompted me to query you guys for any tips for improvement.

... but a key point of my post is that context-free abstract pattern recognition ability is innate and can't be learned :-). You can learn how to answer standard Raven's matrices type questions, by learning patterns used to construct the items, but the skills built aren't transferable – if given a different kind of test of context-free abstract pattern recognition ability, you would do no better than you would now. It is possible to improve a great deal as a mathematical thinker, but trying to build this sort of skill is not the way to do it.

Seconding this, weird notation makes many folks lose morale easily. I guess one watershed moment comes when, having conquered enough notation in specific cases, one realizes it's just a formal symbol pushing game in general, and then new weird looking notation doesn't cause a morale crisis.

Novel math papers often just invent new notation as they go.

I suspect that all that shows is that you aren't used to the relevant bits of mathematics, and being confronted with unfamiliar and weird-looking notation intimidates you. There's no shame in that, and it says basically nothing about your intelligence or your natural aptitude for mathematics.

(Remember that the Raven matrices are designed to have as little dependence on prior knowledge as possible; mathematical questions, almost by definition, are not.)

Echoing Ilya here. IQ tests are a rough guide of what's possible to achieve, not a predictor of success and satisfaction in life. Like height is a rough guide of what's possible to achieve in basketball. If you are 5'10", NBA is probably not for you. If your IQ tests keep returning under 120, you will probably not be an MIT prof. Unless you have some exceptional abilities not captured by these simple tests. Find something at you enjoy doing AND are very good at, and work on it. It'll pay.

What are your goals?

One thing that kept nagging at me while reading this post is my own experience with taking the SAT's back in grade 11.

I don't remember my score exactly on the verbal section, but it was something like 590. Now, I've always had a noticeably above average command of language and verbal reasoning in my native tongue (based on academic feedback + my own observations), but this is obviously not reflected in the above score.

However, this is explained in my case by the fact that I only really began learning English in grade 10 (I only knew basic words from being raised in a foreign schooling system, but suddenly switched to an all English schooling system in grade 10).

I distinctly remember, during the SAT test, thinking that questions where I actually knew the vocabulary involved (whether in the question itself, the choice answers, or both) were quite enjoyable and "easy", for lack of a better word. However, I also distinctly remember staring at many questions where the vocabulary was completely unknown to me (after only 2 years of studying full-time in English); those questions I left blank or took a random guess (when I had any inkling, no matter how weak).

So, having said that, I believe it's quite reasonable to assume that TT's outstanding performance on the SAT math section at such a young age is largely attributable to the fact that math is logical and can be derived from first principles given enough intelligence. However, the ability to perform equally well on the verbal section is highly dependent on the amount of vocabulary you have accumulated up to that point (which is significantly limited when you're a mere 10-year old and haven't had to go through another 7+ years of formal education and self-learning).

To put it more concisely, I believe the SAT's verbal section depends significantly on the crystallized intelligence aspect (in the form of accumulated vocabulary), whereas the math section can be conquered with sufficiently high fluid intelligence alone.