How can someone with AS be good at math/spatial issues?

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Big gulp.

I've skipped over most of this thread. Will read later. Have to try to write this now. Feel a little faint, this is such a huge subject for me.

I don't think I'm quite AS/HFA/...[whatever]. It had crossed my mind a few times, during the last decade or so, that I might be, but the descriptions I saw in print never really seemed to fit.

I had even worked temporarily in a school for autistic children in the 1980s (a kind of rehab job for the unemployed, not a success, another story, although thinking about it has brought up some other connections), without ever having an inkling that there could be any connection whatever between my condition and theirs.

The first thing that really hit me like a physical blow was a television documentary about AS/HFA secondary school students in the UK preparing for the 2006 International Mathematical Olympiad. I felt a kind of shock of recognition. Back in the early 1970s, I was on the UK team, and one of the other team members said (in a nice way - and I really liked him, I would have liked to be friends, but I had no idea how to make friends) that I was "mad". No-one else on the team seemed "mad" to me (or to him, I suppose). I also still have a clear and painful visual memory, from 40 years ago, of the team coach looking at me in a stern and disapproving way - for what reason, I had no idea, and indeed I still have no idea. Nor had I ever had any idea of myself as "mad", in any sense; I thought I was "boringly sane", as I put it in (slightly stunned) reply. Anyway, watching this documentary, it was as if I could see, for the first time, what he had meant by describing me as "mad". And these boys in the documentary, all of them diagnosed with AS/HFA (some or all by Prof. Baron-Cohen) were, with possibly only one exception, all more socially competent than me! Not that this proves I'm AS/HFA, because there is more than one way of being "out of it", socially. (I expect to be writing a lot more on that general topic, in other threads to come.)

Anyway, I did OK in the IMO - not brilliantly, just so-so - and I was surprised to find myself on a level intellectually with other people for the first time, not superior, not inferior, not hung up about being an "idiot" or a "genius" (I tended to see myself as being one or the other), just one of the crowd. That was nice, relaxing; and indeed almost the whole experience was relaxing - even though the very thought of doing anything like that scares me beyond words now! I went on to Cambridge (as indeed the whole team did, I think), where I was again pleasantly surprised to find that I was regarded as exceptionally good even by their standards, and expected to compete for a top place in the Mathematical Tripos, and bring honour to the college, etc. I had always kept expecting my bluff to be called: but not yet, it seemed.

The OP expresses puzzlement about some AS/HFA people being exceptionally good at mathematics, etc., in spite of being supposed to have poor non-verbal communication skills.

Here comes the one thing in my life, among all my many and various problems, which (after decades of reflection) I think caused me to "break down" almost at the very instant when I went up to university, with the result that the remaining 40 years of my life have been a story of failure in almost every imaginable respect. I'm oversimplifying slightly, because I don't want to go into a discussion of mathematics itself! (A full explanation of what happened would have to do so.)

I couldn't talk to anybody about mathematics. I had never been able to, but it had never mattered. I had tended to work things out in my head and just write down the answers without explanation: I had been criticised for this, but again it never mattered, because my answers were almost always right, and no-one could argue with that. Later, when I really got the mathematics bug, I was so far ahead of the class that I was allowed to sit at the back and read university level textbooks on my own. Fine by me. Still didn't have to talk. It didn't matter in the Olympiad, either, because again it was just an exam, coupled with what was in effect a kind of school trip abroad. No need to actually talk about mathematics.

But at university, when if I was to get anywhere I would really have to stretch myself and learn from people who were leagues above me in actual ability (Conway, the inventor of the Game of Life, was one of the teachers at my college!), I would have not only to listen ... I found lectures a real strain, but that was not a fatal block to progress, and I even showed my usual acuteness, once winning a book prize for being the only one of 200 students to spot the deliberate mistake a lecturer had introduced, to check that we were paying careful attention (I have sometimes amazed myself as well as others with my capacity for detecting mistakes) ... but I would also have to talk, expressing both what I could and what I could not understand. But I could express neither my understanding nor my lack of understanding. (One very fundamental thing I did not understand, and I do not understand to this day: but I said I would not go into that!)

Mathematics for me had always been an alternative to language. How on Earth was I expected to use language to talk about mathematics?

Again I'm oversimplifying. I had an abusive upbringing. That's another thing I don't want to go into right now. But I do have to mention that my abhorrence of natural language, and my retreat into mathematics as an alternative to language, came about in a very complex way, involving the personae of all four of the other members of the family in which I grew up. In particular, in involved my younger brother, who was severely brain-damaged at birth, and it involved my father, who seemed tongue-tied himself, sometimes even seeming unable to use language above the level of his younger son (who embarrassed him). Weird, and very painful ... beyond words, ironically enough. Just to add to the weirdness, my abhorrence of, and retreat from, masculinity (yet another story) was related to the same things.

Here I must also mention that I have always been very reluctant to think that I was born with any kind of neurological abnormality. It seemed (not only to me, but to others) to make infinitely more sense to relate any sense of "idiocy" or mental or linguistic incapacity on my part to the physical fact of what happened to my brother at birth, and to the psychological fact of how my dysfunctional family affected me. (That's just my thought; no-one else has ever shown any interest in how my upbringing affected me.) When (well into my adult life) my mother casually mentioned that I had not been cuddly as a baby, I simply didn't believe her: I took it as a rationalisation for her lack of any wish to cuddle me. Also, I simply couldn't imagine any baby not being cuddly! (I like babies, and find them fascinating to look at.) Moreover, the one other significant thing my mother told me, at about the same time, was that she had suffered a life-threatening illness when (I think) I was less than a year old, so I lost my mother, and wouldn't have known it wasn't for ever, because I would have had almost no use of language. All in all, there seemed plenty of trauma to explain what a f**ked-up mess I am, and no need to invoke any idea of my nervous system being any different from normal. So I have strongly resisted any suggestion that I am autistic in any way, or at least, any autistic-like traits I might have seemed far more likely to me to be explicable in terms of life events than in terms of innate neurological difference.

Sorry, in spite of my efforts to simplify, this has become (typically) complicated!

Anyway, not actually knowing the extent to which (if at all) I am AS/HFA, I'm not in a position to answer the OP's exact question: "How can someone with Aspergers be good at math and/or technical things? [...] wouldn't the difficulty that virtually all Aspies have with non-verbal communication also make it difficult for them to learn math and science?"

What I can say is this:

(1) There is some overlap between my (unnamed) condition and AS/HFA. (By the way, at least two experienced consultant psychiatrists - both of them nice people, who spent a fair amount of time interviewing me - have shocked me by candidly admitting that neither of them had ever come across any other case resembling mine. This was pretty devastating!)

(2) The exception proves the rule, in the following sense. Yes, I have (or had! - but I'm still not a complete slouch) exceptional mathematical skills, which were described as "phenomenal" by the Director of Studies at my Cambridge college. (Praise which I must admit went to my head!) But I also couldn't talk about the subject, and couldn't learn about it from another human being (only books). I did quite literally (not just as a euphemism) have a "learning difficulty". (One which went completely unrecognised - this was at the start of the 1970s.) And I soon enough came to believe, right to the roots of my being, that I was an "idiot", even at mathematics - which, even though it was not the only thing I could do well at school, was the only thing (almost the only thing in the world) I cared about.

So, even if my high level of ability was connected with my condition (whatever that condition is, and however it is or is not related to AS/HFA), so was my "learning difficulty", and the latter destroyed the former.

Even at the age of 59, I am still struggling to learn mathematics which I should have learned 40 years ago, because of a profound difficulty with communication, even though I was, at the same time as being thus "handicapped" (like my brother) - and perhaps as part of the same condition (whether or not it is a basically neurological condition) - also "profoundly gifted".

Long, sorry! (That's typical of me, when I get onto subjects of strong personal concern to me; and several people have told me, rather convincingly I must admit, that I "write like an Aspie".)

I signed up for this site just to post a reply to this thread because it's so fascinating. "Math" is a broad term. You could be talking about arithmetic, i.e. doing algorithms on numbers like the multiplication algorithm (although they didn't explain it that way in the 3rd grade), or abstract math (math isn't that interesting until you get rid of numbers).

So someone could be good at "math" meaning they can perform arithmetic algorithms in their head very quickly. The rest of us use calculators! (Or know how to fudge. For example, I can usually calculate the percent off for a discounted item in my head almost immediately because I know the technique. I am not a "savant", I just know the trick.) For me personally, I can understand mathematical concepts very well, I am just helpless at actually grinding through the steps to get a correct answer. (Actually writing this down coherently and legibly was another issue.)

More advanced math, such as calculus and differential equations, is much harder, but is largely still algorithmic. Anyone who does this kind of math seriously (makes a living with it) uses a computer. The same is true of statistics. No one would seriously grind through some sort of statistical thing by hand with a large dataset, they'd use an R program. So you could be good at this without being good at doing all the steps, as long as you understood the theory well enough to know if your computer gave you a plausible answer.

Pure abstract math, such as set theory and so on, doesn't involve numbers or calculations, but mainly involves step-by-step proofs. Most people probably don't even know this field within math exists. You rarely encounter it in college unless you are a math major.

It's very possible someone could be bad at "math" (arithmetic) while being an advanced PhD in "math" (abstract math) - I'm only pointing this out because this is one area where a precise definition makes a world of difference because very, very different skills and mental abilities are needed for different areas of math. (Einstein, as far as I know, wasn't good with arithmetic. But he was good with abstract math, applying non-Euclidian geometry to physics. I don't know anything about physics, so I don't know exactly what he did.)

The idea of being good at a technical field is what interested me about this thread. I am very good with computers. I do not think I have any "savant" ability at all. I just work very hard to be good at computers. When I was in college, I probably got more experience with computers in a month than most computer science majors got in four years. I didn't know anything about autism while I was in college. I was just preparing for my career. My autistic traits were a stumbling block during that time.

I signed up for this site just to post a reply to this thread because it's so fascinating. "Math" is a broad term. You could be talking about arithmetic, i.e. doing algorithms on numbers like the multiplication algorithm (although they didn't explain it that way in the 3rd grade), or abstract math (math isn't that interesting until you get rid of numbers).

So someone could be good at "math" meaning they can perform arithmetic algorithms in their head very quickly. The rest of us use calculators! (Or know how to fudge. For example, I can usually calculate the percent off for a discounted item in my head almost immediately because I know the technique. I am not a "savant", I just know the trick.) For me personally, I can understand mathematical concepts very well, I am just helpless at actually grinding through the steps to get a correct answer. (Actually writing this down coherently and legibly was another issue.)

More advanced math, such as calculus and differential equations, is much harder, but is largely still algorithmic. Anyone who does this kind of math seriously (makes a living with it) uses a computer. The same is true of statistics. No one would seriously grind through some sort of statistical thing by hand with a large dataset, they'd use an R program. So you could be good at this without being good at doing all the steps, as long as you understood the theory well enough to know if your computer gave you a plausible answer.

Pure abstract math, such as set theory and so on, doesn't involve numbers or calculations, but mainly involves step-by-step proofs. Most people probably don't even know this field within math exists. You rarely encounter it in college unless you are a math major.

It's very possible someone could be bad at "math" (arithmetic) while being an advanced PhD in "math" (abstract math) - I'm only pointing this out because this is one area where a precise definition makes a world of difference because very, very different skills and mental abilities are needed for different areas of math. (Einstein, as far as I know, wasn't good with arithmetic. But he was good with abstract math, applying non-Euclidian geometry to physics. I don't know anything about physics, so I don't know exactly what he did.)

The idea of being good at a technical field is what interested me about this thread. I am very good with computers. I do not think I have any "savant" ability at all. I just work very hard to be good at computers. When I was in college, I probably got more experience with computers in a month than most computer science majors got in four years. I didn't know anything about autism while I was in college. I was just preparing for my career. My autistic traits were a stumbling block during that time.