Who has aspergers/autism here, who are good/bad at maths?

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I'm good at advanced math but average at basic math.

I'm the same way. I tend to work out proofs visually/conceptually before translating them into a formal argument. I enjoy mathematical rigor but my thinking style is more intuitive than strictly logical. I think my autism makes me more persistent than NTs. I've spent a whole week attempting to understand something or fill in a missing detail in a proof, to the detriment of finishing the normal homework assignment on time.

I'm kinda both.

The 'cookbook', step-by-step procedures. I can't use information without understanding it, and I suck at memorization. I basically need a proof for each equation before I can use it effectively. I also need to know exactly in what context this would be useful - I don't go into pure math.



Sometimes silly mistakes, because I hate math and tend to rush through it. But more often it's using the wrong formula.



I guess that roughly fits. But it's more complicated than that.



Yes.



I don't understand the question.



Not knowing the right equation.



Partly it's this, but a big part is emotional as well. I had some very bad experiences in school with teachers trying to make me into a 'cookie cutter person' and it especially came out in math because of my unusual learning style in math. As a result, I basically have a phobia of math. I keep expecting that I'll have to slog through a whole page of boring math problems, and show my work even though that means doing steps I don't actually do to calculate the answer.



I reason it out visually. For example in physics, when I'm told the forces on an object, I see a picture of the object and how it's going to move. It's not exact, but it gives me a ballpark so I can spot an obvious wrong answer.



There's a mix of reasons.

Firstly, some people have NVLD as well as being autistic. And part of NVLD is poor math skills. I think it's the difficulty visualizing?

Secondly, it seems that some people with AS and/or ADHD have my learning style - good at conceptual math but bad at rote calculation. A person with this learning style could, with only slightly different handling, end up either seeming very good or very bad at math. In my case, I always thought I sucked at math, until I took a statistics class in university and found it was easier than I thought. (Still hard, but nowhere near as much for me as it was for my friends - all fellow psych majors.) And I actually found some aspects of statistics fun (especially using SPSS).

Incidentally, my mother is OK at math, my father is a math major, and my brother has the same learning style as me but with less glaring weaknesses.

A lot of really good mathematicians are very visual thinkers. Anyone interested in this should read Jacques Hadamard's book "The Mathematician's Mind" published by Princeton University Press. It can be a real eye-opener for some aspies.

Not too long ago mathematics lost the late and much missed Academician Vladimir Igorevich Arnold of the Steklov Mathematical Institute in Moscow. Google for "Arnold" and "teaching" and "mathematics" to find a delightfully acerbic piece he wrote on how mathematics is (badly) taught in some universities.

Arnold was a visual thinker ... and at the time of his death by common consent the greatest living Russian mathematician.

Have aspergers, and I'd say i was above average on numeracy. That'll get better as I'm studying accountancy soon :p

I understand math extremely well. For the most part, I am a visual thinker and visualizing a problem often helps me understand it. However, I also make lots of stupid mistakes such as writing the wrong number down or reading the problem wrong. That or I make an assumption that isn't true. For example, in Calculus, I might read a question that says, "find all relative maximums" as "find all relative extrema" instead, or I might make a stupid mistake such as forgetting to apply the distributive property to one term.

I guess that I can understand concepts fairly well, but I am not exactly good at memorizing equations (although when I finally memorize them, I seem to withhold that knowledge for a long time).

I have had problems with x/0 = undefined and here is why. By the very act of declaring something undefined aren't you defining it?

I think the resolution to this is the law of identity. http://www.importanceofphilosophy.com/M ... ntity.html

Why didn't the schools teach this and college barely even touches this concept? It would've saved me a lot of problems with the math concepts teachers were teaching.

1.) Pretty much all of it. From basic arithmetic to trigonometry. In fact, i barely remember what I did in school.
2.) I don't know. I guess I get the wrong answer because I don't know how to conceptualize numbers. So I usually have to work a lot harder to work out the problem.
3.) I understand the need for critical thinking and problem solving, but do not understand maths.
4.) If the question is only pertaining to maths, then yes I suppose I do.
5.) I don't.
6.) Pretty much everything.
7.) The more a accurate question is what problems don't I have in maths?

I'm sorry if i can't be more helpful.

The expression "x/0 = undefined" does not define what the expression "x/0" refers to. The standard definition of the expression "x/b" defines a meaning for the expression if and only if "b" does not refer to zero. The expression "x/0 = undefined" is itself meaningless (i.e. there is nothing that it refers to) because it contains a sub-expression, "x/0", that is meaningless.

Not metaphysics but metamathematics (See: S. C. Kleene, "Introduction to Metamathematics") but be warned, it's very tough going.

As regards schools, *nothing* these days surprises me about how badly they teach mathematics. The standard of school maths teaching here in the UK is now truly abysmal.

I heard a really funny rant about dividing by zero and the way math is taught a few months ago (in a starcraft video of all things).

Pardon my delayed echolalia

I think I understand what you're saying. I would obtain an infinite progression of itself? I worked this out myself before and that is what occurred. What you are saying as well is it does not produce a finite and concrete answer. Is this what you mean by defining a meaning? I am still trying to wrap my head around this. I think I may be close to doing so.

In my mind when one says there is no answer to something isn't that an answer in itself? I just see a logical paradox to this. Am I correct that the law of identity resolve these types of paradoxes?

The concept of "undefined" is very misleading when it is taught in school. Mathematics does not really have a concept called "undefined". When people say that something is "undefined", what they really mean is literally that we didn't define it.

The problem is that in school, you never actually define what division is. And so it is "cheating" to call division by zero "undefined" in the context of school, because you are not really working with an explicit definition of division!

Here is an outline of how we might define division, given that we already have the concept of multiplication:


Now we can see what it means to say that "7 / 0" is undefined. It means that we didn't define it!

Of course, this leaves us with the more hand-wavey question of why we didn't define it. Well, let's be optimistic and imagine that we can define "x / y" for all real numbers x and y, even when y is zero, and we can do it in a similar way to how we did it above. Well, then we would have to do something that looks like this:



It wouldn't work, because we can't prove (2*), since it isn't true. For example, there are at least two real numbers z such that z*0 = 0. And there are no real numbers z such that z*0 = 7.

I get it now. By doing what I did before by saying undefined is a form of defined I do not produce a unique real number. What you are saying is if I do d/c=y I have to be able to multiply c*y to obtain d back. If I did this y/0=undefined I would have multiply undefined by 0 to obtain y back. If I substituted 1/0 for undefined I would obtain the indeterminent(0/0) back as the quotient and not actually d. Because of this it doesn't work.

undefined means we do can't obtain a real numerical quotient by dividing by 0 am I correct? It really means we do not define any real numerical quotient multiplied by the divisor in order to obtain the dividend back am I correct or am I at least on the right track of understanding.



Got it. Why do they say 0*anything equals 0 when they are talking about real numbers only?

From this, I thought they literally meant anything. By their logic if 0 times anything equals 0 then why couldn't 0 times non-anything = a nonzero digit? Do you see where I become confused?

You're definitely on the right track, but I think that you still have the idea that "undefined" is something to do with division by zero. It isn't really. "Undefined" just means "we didn't define it", and it could appear in any context, not just division by zero.

For example, suppose that I define addition to be an operation which takes in a pair of real numbers and produces a real number. Well, then "3 + elephant" is undefined. I didn't define what it is! I only defined addition for pairs of real numbers, and "elephant" isn't a real number.

Division is defined as an operation which takes in a real number and a nonzero real number and produces a real number. That's just how it is defined. Asking for "5 / 0" is like asking for "5 / elephant".

If you want to know why division has to be defined in this restricted way, I edited my earlier post to try to make it clear.

EDIT: Yeah, you've got it now. I understand why you were confused. School maths is not very explicit about what exactly you are doing. In a way, you were confused because you are too mathematical. You spotted the vagueness in school maths sentences like "zero times anything is zero", and it confused you. But in school maths, people don't usually like to be careful about what they are doing, because it would raise foundational questions, and then you would have to spend a year carefully constructing mathematics from simple foundations instead of learning calculus.

Thank you my friend! I owe you one. I did have foundational questions and you helped to clear them up. By the way they taught it it made no sense. When I asked my questions did they become mean or ignore me. Why did they become mean or ignore me when all I wanted to do was understand? Your definition makes a lot more sense because it tells me what the constraints are. Why don't they spend the year carefully constructing mathematics from the simple foundations? What do you mean I am too mathematical?

The philosophy of primary and secondary education is that it is supposed to teach you practical skills that might come in handy someday. So they have to rush the maths so that you can quickly get to the stuff which is used in economics and physics. Also, a lot of primary and secondary maths teachers have either forgotten about the technical side of maths, or maybe they never really understood it in the first place. If you want the real stuff, then either wait until university or start working through an introductory textbook on a topic in higher-level maths. Maybe set theory, or group theory.



If I understood you correctly, you tried to construct your own mathematical ontology in order to make sense of the vague statements you were hearing, like "zero times anything is zero" and "5 / 0 is undefined". You took these statements seriously enough that you became worried about what exactly it means to multiply zero by "anything", or what exactly this object called "undefined" is. That's mathematical thinking - you were trying to make rigorous sense of the strange mathematical world that you have been presented with.